7KH+ 0RGHRI$6'(;

SPECIAL TOPIC

The H-Mode of ASDEXTo cite this article ASDEX Team 1989 Nucl Fusion 29 1959

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SPECIAL TOPIC

THE H-MODE OF ASDEX

ASDEX TeamMax-Planck-Institut fur PlasmaphysikEuratom-IPP AssociationGarching bei MiinchenFederal Republic of Germany

ABSTRACT The paper is a review of investigations of the H-mode on ASDEX performed since its discoveryin 1982 The topics discussed are (1) the development of the plasma profiles with steep gradients in the edge regionand flat profiles in the bulk plasma (2) the MHD properties resulting from the profile changes including an extensivestability analysis (3) the impurity development with special emphasis on the MHD aspects and on neoclassical impuritytransport effects in quiescent H-phases and (4) the properties of the edge plasma including the evidence of three-dimensional distortions at the edge The part on confinement includes scaling studies and the results of transport analysisThe power threshold of the H-mode is found to depend weakly on the density but there is probably no dependenceon the toroidal field or the current For the operational range of the H-mode new results for the limiter H-mode onASDEX and the development of the H-mode under beam current drive conditions are included A number of experi-ments are described which demonstrate the crucial role of the edge electron temperature in the L-H transition Newresults of magnetic and density fluctuation studies at the plasma edge within the edge transport barrier are presentedFinally the findings on ASDEX are compared with results obtained on other machines and are used to test variousH-mode theories

CONTENTS GENERAL INTRODUCTION 1 INTRODUCTION AND OVERVIEW OF THE H-MODE2 CHARACTERISTICS OF H-MODE PLASMAS 21 Equilibrium parameters 22 Main plasma parameters

221 Profile development 222 Bootstrap currents and beam driven currents in the H-mode 23 MHD charac-teristics of the H-mode 231 Behaviour of the m = 1 mode and the sawteeth 232 Localized m pound 2 modes233 Edge localized modes 24 Impurity development in the H-mode 25 Scrape-off layer and divertor plasmaparameters 3 CONFINEMENT IN THE H-MODE 31 Power fluxes in the H-mode 32 Global confinement33 Transport analysis 34 Scaling of the energy confinement time in the H-mode 341 Density dependence

342 Current dependence 343 Power dependence 3431 Power scaling of TE in the quiescent H-mode3432 Effect of ELMs on global confinement 344 Plasma species dependence 345 Toroidal field dependence346 Summary of the TE scaling results 347 Scaling of transport coefficients 4 OPERATIONAL RANGE OFTHE H-MODE 41 Parameter dependence of the H-mode power threshold 42 Study of the H-mode under variousdivertor topologies 43 Limiter H-mode of ASDEX 5 USE OF OTHER HEATING AND REFUELLINGTECHNIQUES FOR H-MODE PLASMAS 51 ICRF heating 511 Hydrogen minority heating 512 Second-harmonic hydrogen heating 52 Lower hybrid heating and beam current drive in the H-mode 53 Pellet refuellingin the H-mode 6 PHYSICS ASPECTS OF THE L-H TRANSITION 61 Role of the edge electron temperature

611 Addition of impurities 612 Development of the electron temperature in limiter discharges 613 Post-beampulse H-phase 614 Comparison of L-H and H-L transitions 615 Sawteeth as H-mode trigger 62 Formationof a transport barrier at the plasma edge 63 Microscopic turbulence in H-phases 631 Density fluctuations

632 Fluctuations of the Ha light emission 633 Magnetic field fluctuations 634 Confinement of runawayelectrons 7 MHD STABILITY ANALYSIS OF H-MODE DISCHARGES 71 Medium m-mode stability72 Resistive MHD simulations of ELMs 73 Ballooning stability calculations 731 Ideal ballooning modes732 Resistive ballooning modes 8 COMPARISON OF H-MODE PROPERTDZS ON ASDEX WITH THOSEFOR OTHER EXPERIMENTS 81 Agreement between the observations on ASDEX and DITJ-D 82 Disagree-ment between the observations on ASDEX and DIII-D 9 DIFFERENT THEORETICAL MODELS FOR THEH-MODE 91 H-regime theories involving SOL physics 92 Models of high shear zone effects 93 Effects of thediscontinuity between open and closed flux surfaces on plasma transport 94 H-mode transport in the plasma interior10 SUMMARY References

NUCLEAR FUSION Vol29 No 11 (1989) 1959

ASDEX TEAM

GENERAL INTRODUCTION

The aim of fusion-oriented plasma research is thestudy and understanding of the behaviour of hot plasmawith the ultimate goal of providing the conditions for aburning plasma The parameter values which have tobe achieved are well known the product of densityand energy confinement time has to be 3 x 1014 cm3 bull sand the average plasma temperature has to be 10 keVThe target values of these two parameters have beenobtained separately however in experiments wherethe temperature was adequate the confinement productwas inadequate and vice versa Simultaneous achieve-ment of the two values was found to be difficult Theuse of auxiliary heating to increase the plasma temper-ature in a tokamak gave rise to severe degradation ofthe confinement with the net result of no effectiveapproach to break-even conditions The operationalregime of tokamak plasmas characterized by a confine-ment time that decreases strongly with increasingauxiliary heating power is termed the L-regime

The energy confinement time in the present genera-tion of large tokamaks with auxiliary heating is deter-mined by conductive heat transport In the edge regionand in low density discharges convective losses mayprevail Both the ion and the electron heat transport

40

FIG 2 (a) Electron density ne 3 p i and Ha radiation in the divertorchamber the L-H transition is indicated by the dashed vertical line(b) Development of the electron temperature and density profiles

from the Ohmic phase to the L- and H-phases

t ( s )

FIG I Variation of the line averaged density ne the atom flux ltpound0

from the outer neutralizer plate at the intersection of the separatrixand the neutralizer plate 0p + it2 from the plasma equilibriumand 3p i from the diamagnetic signal during a neutral injection(NI) pulse (hatched area) Compared are an H-discharge (solidlines) and an L-discharge (dotted lines) The L-H transition isindicated by the dashed vertical line The two discharges differonly in the current which is 300 kA in the L-discharge and 275 kAin the H-discharge

coefficients are considerably larger than those calculatedon the basis of classical scattering processes The actualheat conductivity in a tokamak plasma is dominated bythe increased transport due to fluctuating electric andmagnetic fields that are caused by plasma instabilitiesThe exploration of the mechanisms which give rise tothe anomalously enhanced transport is one of the maintopics of tokamak research The lack of understandingthese mechanisms makes it impossible to reach well-founded predictions of the performance of futureexperimental devices and is the main reason for thestill existing uncertainty about the feasibility of aburning plasma

This report deals with the investigation of a plasmaconfinement regime in which the severe deteriorationof the confinement quality at high heating power isavoided This regime is called the H-mode becauseof its high confinement characteristics and the regimeof low confinement is called the L-mode There isevidence that the L-mode characteristics will not leadto sufficient confinement for successful plasma burningThe H-mode was observed for the first time on ASDEXAt present it is considered to be the confinement regimewith the best prospects for future tokamak operation

1960 NUCLEAR FUSION Vol29 No 11 (1989)

THE H-MODE OF ASDEX

However the study of both H-mode and L-modeconfinement physics has increased our understandingof energy transport in tokamaks

1 INTRODUCTION ANDOVERVIEW OF THE H-MODE

The difference in energy confinement is the mostimportant aspect of an H-mode plasma compared withan L-mode plasma [1 2] The improvement of theglobal energy confinement time is due to a reductionof the electron heat diffusivity and the particle diffusioncoefficient The different energy and particle confine-ment properties of L- and H-discharges are evidentfrom the differences in the plasma beta 3P and in theline averaged density lie during neutral injection (NI)Figure 1 compares L- and H-discharges that have thesame density in the OH phase and the same heatingpower Plotted are the line averaged density he 3p + f-2from the plasma equilibrium 3pX measured diamagnet-ically and the atom flux ltjgta from the outer upper targetplate located inside the divertor chamber The atomflux is due to the impinging ions which are neutralizedand reflected Since ltgta is measured for particle energiesof gt 100 eV it only represents ions from the mainplasma periphery and therefore its intensity is relatedto the particle confinement properties of the plasmabound by the separatrix

Figure 2(a) shows the variation of the Ha radiationin the divertor chamber Both ltpa and Ha increaseduring the L-phase and drop sharply at the L-Htransition The particle content of the plasma is keptconstant in the Ohmic phase by a density feedbacksystem in an L-discharge the density decreases despiteadditional particle fuelling by the beams and intensifiedgas puffing from the outside In an H-discharge theparticle content of the plasma rises sharply withoutexternal gas feed The improved energy confinementcauses the energy content of the discharge to rise asis obvious from both the equilibrium signal and thediamagnetic signal The energy content of an H-modeplasma is nearly twice that of an L-mode plasma andmdash since the heating power is the same in the two casesmdash the energy confinement time in the H-mode is nearlytwice as long as in the L-mode In the divertor chamberthe Ha radiation is determined by local recycling due tothe ionization of the neutral gas by the divertor plasmaand due to the neutralization of the divertor plasma atthe target plates The intensity of this circular processmdash neutralization and re-ionization mdash depends on thepower flux into the divertor chamber The Ha intensity

FIG 3 Variation of the line averaged electron density ne theatom flux ltfgta from the outer neutralizer plate at the intersectionof the separatrix and the neutralizer plate and j3pl from thediamagnetic loop during the NI phase (hatched area) and duringthe H- and L-phases

in the divertor chamber is to a large extent a measureof the energy confinement capability of the main plasmaIn particular a change in the Ha intensity or in theatom flux indicates a variation in the energy or particleconfinement properties For example the transition tothe H-phase (dashed vertical line in Figs 1 and 2(a)) isindicated by a sudden drop in a and in the Ha intensity

A characteristic feature of the H-mode in ASDEX isthat it develops from a preceding L-phase whose durationvaries between 30 and 150 ms A case where an Ohmicplasma directly develops to an H-mode as soon as thebeams are switched on has never been observed inASDEX The transition from the L-phase to the H-phasecan be seen in Fig 1 and is shown in more detail inFig 3 where the time development of He 3p and ltpa

is shown At the L-H transition ltgta drops to a valuecomparable to the Ohmic level The simultaneous dropof the divertor signals (ltgta or Ha) and the correlatedrise of the main plasma density and of 3p mark thetransition to the H-phase The transition is sharp andcan happen within 2 ms indicating the existence of


ASDEX TEAM

distinct transition conditions The transition occursspontaneously without any operational interventionfrom the outside The development of an H-dischargeduring the beam heating phase is determined by thesetting of the plasma parameters for the precedingOhmic phase and by the level of heating power TheH-mode requires a high heating power above a certainpower threshold (see Section 4) When the beam pulseis terminated the plasma remains in the H-phase forabout 35 ms (two to three times the beam ion slowing-down time) after which time ltjgta suddenly increasesonce more In the same way as in the initial beamphase but now during a phase with hardly any powerinput a transition to a second L-mode occurs andgives rise to a discontinuity of the slopes of Hg andj8p which thereafter decrease even faster Apparentlyin ASDEX the plasma cannot develop an H-phase fromthe Ohmic phase nor can it directly return to Ohmictransport properties The plasma evolution with anH-mode during beam heating always occurs in thesequence OH-L-H-L-OH

The plasma conditions developing in the H-phasegive rise to a new type of MHD instability whichrepetitively modulates the Ha radiation in the divertorchamber and the atom flux ltpounda (see Figs 1 and 3) andcauses additional particle and energy losses therebydegrading the good confinement properties of theH-phase These fluctuations have been dubbed edgelocalized modes (ELMs) because they affect primarilythe plasma boundary [3] By extending the plasmamajor radius Ro in ASDEX from 165 cm to 170 cmELMs can be avoided for 100-200 ms These dischargesare termed quiescent H-discharges (H) They displaythe transport properties intrinsic to the H-mode withoutadditional MHD losses caused by ELMs [4-6] (seeSection 343)

There are several regimes with auxiliary heatingwhich demonstrate improved confinement An H-modeis characterized by the properties mentioned above[5-8] The improvement of the energy confinementtime in the H-mode is substantial mdash a factor of twobeing typical In ASDEX H-discharges are onlypossible in the divertor configuration except for afew belt limiter plasmas which show L-H transitionswith minor improvements in confinement (seeSection 43)

The H-mode was discovered on ASDEX in 1982[1] Since then the inside of the ASDEX vessel waschanged several times A toroidal belt limiter wasremoved in 1982 after the H-mode had been discoveredlow field side ICRH antennas were added in 1984 thedivertor configuration was changed in 198687 from

DV-I (large divertor volume titanium target platesradiation cooled) to DV-II (small divertor volumecopper target plates water cooled) in the course ofthe years more graphite was added The configura-tional aspects of the divertor in the H-mode arediscussed in Section 42

2 CHARACTERISTICS OFH-MODE PLASMAS

21 Equilibrium parameters

The initiation of beam heating and the changes inconfinement transiently affect the horizontal positionof the centre of the flux surface which defines theseparatrix as shown in Fig 4(b) When the beamsare switched on the sudden contribution of the beamions to the plasma pressure causes the plasma toexpand radially until the vertical magnetic fieldrestores the pre-set radial position Because of theimprovement of 3p the horizontal plasma position AH0R

increases once more after the L-H transition ELMshave a strong effect on the plasma equilibrium andlead to modulations in the horizontal plasma positionwith a typical amplitude of a few millimetres [9] Tomaintain the horizontal plasma equilibrium the verticalfield of an H-discharge is higher than that of anL-discharge Fig 4(a) compares the current IVF in thevertical field coils of an L-discharge and of a similarH-discharge The rise of IVF with beam heating in anH-discharge is nearly twice that in an L-discharge withsimilar plasma and beam setting because of the two-foldincrease in plasma beta

The higher vertical field in the H-phase also affectsthe separatrix position in the divertor chamber andcauses a shift of the location where the target platesintersect the separatrix in the direction of the mainplasma by about 1 cm which is about half the widthof the energy and particle deposition profiles at thetarget plate

22 Main plasma parameters

The dominant plasma characteristic of the H-modeseems to be the development of a transport barrierclose to but inside the separatrix with a radial extentwhich is not well determined but which is in the rangeof several centimetres The particle and energy transportcoefficients are decreased within this layer This decreasealso seems to reduce the cross-field transport coefficientsin the scrape-off layer (SOL) whose radial extent


THE H-MODE OF ASDEX

30

lt 20

ugt

~ 10

0

2

bulla i

0

(a) ~^

t 4804bull 4803

(b) A

1

Nl

j

i

13 U 15 16

t ts) t Isl

FIG 4 Comparison of several plasma parameters of an L-discharge (No 4803 dotted lines) and anH-discharge (No 4804 solid lines)(a) Vertical field curent lVF (b) shift of the plasma position R-Ro (Ro = 165 cm) (c) loop voltage UL(d) neutron count rate 0n The transition to the H-phase is indicated by dashed lines

decreases As a consequence the wall recycling andthe Ha intensity in the main plasma also decreaseFigure 5 summarizes the Ha variation measured at thetypical locations as indicated in the insert Variousaspects of the transport barrier will be discussed inSection 62 The changes in plasma properties causedby the transport barrier are described here it gives riseto rather broad bulk plasma profiles with high peripheralvalues and steep gradients at the edge

The profile changes affect the MHD behaviour ofthe discharge the high electrical conductivity at theedge which is a consequence of the good confinementproperties of the plasma even at the periphery causesthe current channel to expand Evidently as a conse-quence of the steep edge gradients a new MHD featuremdash the edge localized mode mdash appears

The impurity development is determined by a rathercomplicated chain of events the reduced transport inthe SOL leads to better particle exhaust and thereforeless recycling at and reduced impurity erosion fromthe divertor throats The improved particle confinementreduces the charge exchange fluxes to the walls Onthe other hand the increased edge ion temperature willgive rise to higher sputtering The confinement ofimpurities and of the main plasma species will beimproved in particular without sawteeth the effectiveimpurity confinement in the plasma centre is high

whereas in the boundary region it will be reduced byELMs The combination of these different erosion andconfinement effects determines the evolution of theimpurity concentration in the plasma and the develop-ment of steady state conditions The broadening of theconductivity profile after the L-H transition willintroduce a further time constant in the developmentof the plasma properties in the H-phase

Finally the transport barrier affects the powerfluxes out of the discharge and ELMs mdash being aviolent MHD feature mdash open up a new power losschannel with different transport and power depositioncharacteristics which may require a specific design ofthe target plates for future experiments

221 Profile development

The tendency of all plasma profiles is to broaden inthe H-mode Figure 6 shows the time dependence ofthe electron temperature at three spatial locations andthe line averaged density along three chords In case (a)the density is regulated by a feedback system in theH-phase the external gas flux becomes zero In case (b)a strong and constant gas flux is maintained during thebeam phase This additional gas flux is initiated shortlybefore the beam is switched on and causes the Ohmicdensity to rise The L-H transition leads to a sharp


ASDEX TEAM

3

11 12 t ( s )

FIG 5 Variation of the Ha intensity at different viewing angles

(as shown separately) with neutral injection and at the L-H

transition

rise of both the electron temperature and density Incase (a) the rise in Te is more pronounced while incase (b) the rise in 1 is stronger In both cases therelative rise in Te and 1 increases towards the plasmaedge

Figure 2(b) shows the development of the Te andne profiles from the Ohmic phase via the L-phase tothe H-phase measured with the multi-pulse Thomsonscattering system which gives a profile every 17 msIn the H-phase high Te and 1 values at the peripheryquickly develop from one laser time-point to the otherIn some cases both profiles develop shoulders at theedge Without ELMs the density continuously increasesafter the L-H transition causing the central Te and Tjvalues to decrease after an initial rise

The Te gradient at the edge increases from 45 eV-cm1

by a factor of four to 185 eV-cm1 This increasereflects a change of the plasma heat diffusivity at theedge (discussed in more detail in Section 62) Theelectron pressure gradient at the edge which is1 x 105 Pa-m1 increases by a factor of six Thesteep gradient at the edge of the H-mode plasma mayprovide the instability conditions for ELMs (discussedin Section 233)

In Fig 7 the profiles of the ion temperature Tjmeasured by passive charge exchange in the pre-transitionphase are compared with those in the H-mode with ELMsThe tendency of the T profile is to broaden reachinghigh values at the periphery As mentioned above the

2-

FIG 6 Time evolution of the electron temperature Te and the line averaged density ne at three posi-tions during the beam heating phase with L-H transitions (dashed vertical line)

In case (a) the density is regulated by a feedback system in case (b) the internal gas flux is increasedjust before the beam is switched on and is then maintained at a constant level The breaks in the elec-tron cyclotron emission traces are caused by a chopper which is used to monitor possible drifts in thebackground signal


THE H-MODE OF ASDEX

FIG 7 Ion temperature profiles in the H-phase and at the end ofthe preceding L-phase as measured by passive charge exchange(Hdeg - D+) Ip = 038 MA B = 22 T Pm = 33 MW

high edge ion temperatures will give rise to increasedcharge exchange wall sputtering in the H-modeThe heating efficiencies for electrons and ions Tei

(rje j = jAPabs = rise of electron or ion tem-perature with heating power normalized to the lineaveraged density) are found to be higher in the H-modethan in the L-mode in particular Te(0) does not seemto saturate in the H-mode as it does in the L-modeFor a plasma current of 300 (380) kA 77 increasesfrom 16 (28) x 1013 keV-MW--cm3 in the L-modeto 25 (42) x 103 keV-MW--cm3 in the H-mode

The thermal neutron flux ltjgtn increases after the L-Htransition with Hdeg injection into a D + plasma as shownin Fig 4(d) in comparison with an L-dischargeltgtn increases typically by a factor of two to fourthe difference in 0n between an H-discharge and anL-discharge of the same density however is a factorof about six The increase in ltfgtn is caused by thebroadening of the Tj profile and the rise in densityin a confinement situation where however the iontemperature does not decrease when H increases Theanalysis of the neutron flux points towards an improve-ment of the deuterium to hydrogen ratio after the L-Htransition During deuterium injection into deuteriumplasmas the neutron production is dominated by beam-target reactions and is larger than in the case of hydrogeninjection by about two orders of magnitude The fusionrate of beam-target reactions is determined by the dis-tribution function finj of the injected deuterons and bythe target ion temperature This distribution function isestablished during the slowing down of the ions and

thus the product of target electron density and finj is afunction of the target electron temperature onlyTherefore the time development of the neutron countrate follows that of the central electron temperatureindependent of changes in the target density Since theelectron temperature is not drastically changed after theL-H transition in spite of the rising density the neutroncount rate for Ddeg mdash D + is similar in the L-regime andin the H-regime

222 Bootstrap currents and beam driven currentsin the H-mode

The increase of the electron temperature in theH-mode causes a further decrease of the loop voltagemdash in some cases to nearly zero Figure 8 shows thedevelopment of the loop voltage from the OH-phasethrough the L-phase to the H-phase Computer simula-tions have been used to investigate the effect of boot-strap currents and beam driven currents on the loopvoltage and the toroidal current profile in H-plasmas[10] It is found that loop voltages computed withneoclassival resistivity agree with measured valuesonly if Ohmic bootstrap and beam driven currents areincluded

In a 320 kA discharge bootstrap currents of up to100 kA with broad profiles and beam driven currentsof 50 kA with peaked profiles are generated (see Fig 9)The sum of these currents can be 47 of the total plasmacurrent The resulting current density j(r) is found toadjust to the broader electron temperature and electricalconductivity profiles in the H-phase on a time-scalecomparable to the resistive time-scale for the redistribu-tion of current density rres = 400 ms The broadeningof j (r) due to bootstrap and beam driven currents hasbeen shown to be a smaller effect which also occurson the resistive time-scale

experimentOhmic onlyOhmic bootstrap beam-driven

110

FIG 8 Time evolution of the measured loop voltage UL comparedwith predictions from models for current drive


ASDEX TEAM

lt200-

~ 100-

H phase1262 s

lp= 320 kA

100kA

50 kA

40

FIG 9 Current density profiles of the bootstrap current j b s the

beam driven current yM and the total current j in the ELM-free

H-phase A denotes the width of the steep gradient zone

23 MHD characteristics of the H-mode

In this section the MHD properties of the H-modeare discussed Also the preceding L-phase has to beconsidered for several reasons In particular thebehaviour of the m = 1n = 1 mode and the sawteethplays a dominant role and is therefore treated inSection 231 together with the m gt 1n = 1 modescoupled to the central mode Apart from these modesm gt 2 instabilities are observed which are clearlylocalized at the corresponding rational magnetic surfacesq = mn gt 2 As shown in Section 232 there arecharacteristic differences between L-type and H-typeplasmas as far as Mirnov oscillations are concernedA still more characteristic and more important featureof the H-mode is the occurrence of a new type ofinstability the ELM Section 233 is dedicated tothis topic A comparison of the experimental findingsand the theoretical models is presented in Section 7

231 Behaviour of the m = 1 mode and the sawteeth

Ohmic discharges are generally subject to sawtoothfluctuations The m = 1 precursors are small andgrow within a few cycles their rotation is in theelectron diamagnetic drift direction with a frequencyof a few kilohertz No coupled signal on the Mirnovloops is detectable

In DIH-D [11] it has been observed that no H-modedevelops when neutral injection is applied to an Ohmicdischarge without sawteeth In ASDEX we have studiedthe importance of sawteeth in the Ohmic phase regardingthe development of the H-mode and compared discharges

which differed only in this MHD aspect Figure 10(a)shows the central electron temperature of two dischargesillustrating the lack of sawteeth in one of them Figure 10(b)plots the time variation of He j3pl and Ha in the divertorchamber The comparison shows that in the H-phasethe two discharges do not differ in any important aspectContrary to what was found in DIII-D in ASDEX it isirrelevant for the development of the H-mode whetherthere are sawteeth or not in the OH plasma before theL-phase preceding the L-H transition

When neutral injection is applied the m = 1 modeis still the leading mode in the bulk plasma The waveform of this oscillation depends on external parameterswhich influence the profiles ie the plasma configura-tion (limiter versus divertor) the NI power level andthe local electron transport properties which are differentin L- and H-discharges and in hydrogen and deuteriumplasmas

Te (keV)

M-5

bull10

-05

-0

Te(keV)e

15-

10-

05-

o-

5982mdash bull^M -~~ bulllaquo

6046

(a )

j

y(

VNl

A

A

A09 10 11 12 13

Ms)

HCL

d

Eob

vIC

dd

2-

1-

o-4-

2-

-

0-

raquo 5982

^_

i 111 1

1 ML mi l

10 12 14 10 12 14

t(s) Ms)

FIG 10 (a) Central electron temperature of two discharges onewith sawteeth (No 6046) and one without sawteeth (No 5982)in the Ohmic phase The arrows denote the L-H transition(b) Comparison ofhe 3p i and Ha radiation in the divertorchamber for the two cases


THE H-MODE OF ASDEX

PN| = 75MW

K 86C

PNI=15 MW

laquo 8603

(a

(b )

FIG 11 Central soft X-ray signals showing the evolution ofm = 1 modes and sawteeth during neutral injection at differentbeam powers PNI

Neutral injection into limiter discharges gives rise toperiodically growing m = 1 modes which cause sawtoothdisruptions and then vanish The sawtooth repetitiontime increases somewhat with the beam power but itquickly saturates at about 35 ms

A different behaviour is observed in divertor dischargesFigure 11 shows the m = 1 and sawtooth behaviour atthree different power levels At low NI power (Fig 1 l(a))the m = 1 amplitude is small and its occurrence isrepetitive being terminated by a sawtooth Contrary towhat is observed in limiter discharges the sawtoothrepetition time increases with the beam power At aninjection power of gt2 MW (Fig ll(c)) the divertordischarges are free of sawteeth except for a singlesawtooth at the beginning of the NI pulse this sawtoothis caused by a slowly growing m = 1 mode whichleads to internal disruption after about 50 cyclesAfter the sawtooth when q0 has sufficiently droppedbelow 1 an m = 1 mode appears which saturatesat a large amplitude without giving rise to any furthersawteeth Irrespective of the MHD oscillation levelall three examples represent L-type discharges withdeteriorated confinement

It is possible to achieve H-mode plasmas well belowan injection power of 2 MW ie below the power thres-hold for sawteeth to disappear in L-mode dischargesIn these cases the L-H transition is frequently triggeredby a sawtooth crash as is shown in Fig 12 After the

sawtooth at t = 118 s the electron temperature atthe edge does not decrease as it did in the previouscases rather it continues to grow Observations ofsuch transitions have provided the first evidence ofthe role of a critical temperature (or a related quantity)in the near-boundary region this subject is furtherdiscussed in Section 6

Typically deuterium H-mode plasmas are free ofsawteeth sawteeth occur only at low injection powertogether with a high plasma current In contrasthydrogen H-mode discharges exhibit sawteeth withinthe available power range (PNI lt 35 MW)

If a saturated continuous m = 1n = 1 modehas been established it usually persists during neutralinjection provided the plasma remains in the L-regimeSometimes however the plasma develops fishbone-likebursts More often an L-H transition occurs in thepresence of such continuous modes the amplitudes ofwhich then decrease on time-scales of between severalmilliseconds and several tens of milliseconds Anexample of a rather fast decrease is shown in Fig 13

After the transition the m = 1 mode occurs repetitivelyas fishbone-like bursts The occurrence of these burstsindicates that q(0) the central value of the safety factoris mdash at least temporarily mdash below 1 during the H-phase

04

5 03 H0)

I 02-

^ 01 -

Eu

m

raquo St

i V

tf bull 88U L I ^

FIG 12 Edge electron temperature Te (measured by ECE) andline averaged electron density ~ht of an L-discharge (No 8814) andan H-discharge (No 8813) Sawteeth (st) are indicated by anarrow The L-H transition is triggered by a sawtooth


ASDEX TEAM

112

FIG 13 Temporal evolution of soft X-ray emission (central chord

m = 1) Be (m = 2) and HJDa emission from the divertor The

L-H transition occurs at t = 119 s

Since the time between two bursts is typically of the orderof 10 ms it is inconceivable that q(0) exceeds 1 substan-tially if at all during such periods The m = 1 modethus provides very important information on the currentdensity profile which would otherwise have to beobtained in a much more indirect way when the Zeff

profiles are sufficiently flat the broad electron temper-ature profiles lead to accordingly broad conductivityprofiles The current density profile is expected tofollow this development on the skin time-scale whichis comparable to the NI pulse duration of 200-400 msThus it is obvious that the current density distributioncannot vary drastically On the other hand the possi-ble development of peaked or hollow Zeff profiles andthe contribution of bootstrap and beam driven currents(see Section 222) might change this simple picture

Because of the unidirectional neutral injection intothe ASDEX device the plasma rotates toroidally withcentral velocities of the order of 105 m-s1 per MWwhich leads to a frequency of the m = 1n = 1 signalof 10 kHz per MW If this rotation is fully developedthe contribution of the electron diamagnetic drift tothis frequency is considerably smaller The centralm = 1 mode is always observed to be coupled to anm gt 2n = 1 mode which manifests itself as Mirnovoscillation having the same direction of propagationthe same frequency and a similar temporal evolution ofthe amplitude (see Fig 13) (Note that the amplitudeof a soft X-ray (SX) diode signal is proportional to theperturbation level only in the case where the electrontemperature the electron density and the spectralcomposition of the recorded light do not vary appre-ciably) The occurrence of these coupled modes isobserved for all wave forms of the m = 1 instability

ie sawtooth precursor continuous oscillation andfishbone-like burst It is noteworthy that the poloidalmode number of the m gt 2n = 1 satellite modealways exceeds the q value at the boundary calculatedfrom Bt Ip and 3P -I- 42 taking into account the toroidaleffect but neglecting the contribution of the divertorcoils The q value is singular at the separatrix of anideal poloidal configuration In practice the q valueattains a finite maximum (owing to for example slightdeviations from toroidal symmetry) which neverthelessexceeds the value of a non-divertor configuration Thecoupled mode is not detectable by the SX camera andtherefore it is not possible to decide whether it isexcited inside or outside the separatrix

The amplitude of this coupled mode is rather smalland hence it does not lead to islands of considerablesize particularly since the mode resides in a region ofincreased shear close to the separatrix Nevertheless itis mostly sufficient to exceed the amplitude of anotherMirnov oscillation which apparently is a characteristicsignature of L-type discharges as is discussed in thenext section

232 Localized m ^ 2 modes

It has already been mentioned that the propagationof the near-centre m = 1 mode is dominated by thetoroidal rotation of the plasma while the diamagneticelectron drift causes only a minor modification In thecase of co-injection (the most frequent heating scenario)the phase velocity and hence the signal frequency isreduced by the contribution from this mode The resultingdirection of mode propagation depends therefore on theprofiles of both the toroidal rotation and the diamagneticdrift velocities In Ref [12] this behaviour is treatedin detail For the purpose of this paper a qualitativediscussion should be sufficient It can be concludedfrom measured pressure profiles that the poloidalangular frequency wp = vdr of the diamagnetic driftvelocity vd does not vary appreciably over the minorradius In contrast at the plasma boundary the velocityof the toroidal rotation and hence the toroidal angularfrequency wt = vtR are nearly zero and thus thediamagnetic drift velocity may overcome the effect ofthe toroidal rotation for modes localized near the plasmaboundary This trend is of course supported by theweighting factors m and n the ratio of which increasestowards the plasma edge

Obviously the m = 1n = 1 mode discussed in thepreceding section is a localized mode since it propagatesaccording to the resulting local velocity while them gt 2n = 1 satellite is a driven mode In many L-type


THE H-MODE OF ASDEX

1292 1294

FIG 14 Onset of the m = 2 oscillation in discharge No 18033Trace (a) HJDa signal (diode saturates)Trace (b) Mirnov signal midplane outsideTrace (c) Mirnov signal midplane inside

discharges and in many L-phases before the L-H tran-sition besides these two modes a third mode with adistinctly lower frequency is observed in the Mirnovoscillations Sometimes the amplitudes are such thatboth frequencies are clearly seen in the raw signalsMore frequently however the fast oscillation dominatesthe slower one appearing only as an additional line inthe Fourier spectrum Using an ideal filter method thetwo modes can be separated and in this way it is shownthat the slower mode propagates in the electrondiamagnetic drift direction [13] The toroidal modenumber n is always 1 and the poloidal mode number mis 3 or 4 the latter is always close to but smaller than qa

To some extent this mode is typical of L-typeplasmas It can be observed over phases of 100 ms ormore but it quickly disappears after the L-H transitionthe amplitude becomes undetectable within a few milli-seconds After the L-H transition it reappears rapidlyDuring the H-phase it reappears only transientlytogether with ELMs From the temporal sequence ofevents it is concluded that this mode is not a precursorof ELMs rather it seems to be triggered by themThis aspect will be discussed in the following sectionConcerning the behaviour of this mode in the L-H-Lsequence one might speculate whether or not thesetransitions are due to changes in the current densityprofile

In several H-mode discharges two other localizedmodes are observed namely m = 2n = 1 and m= 3n = 2 The latter is the only Mirnov oscillation with atoroidal mode number n gt 1 it may exist over severalhundreds of periods but with small amplitudes whichdo not impair confinement

In contrast if an m = 2n = 1 mode comes up itquickly attains amplitudes corresponding to island sizesof up to 10 cm The resulting degradation of confine-ment is clearly seen by comparison with dischargesthat do not exhibit this mode but have otherwise equalconditions [14]

If the m = 2n = 1 mode occurs its onset isalways characterized by the sequence of events shownin Fig 14 A fishbone-like burst is followed by anELM which apparently triggers the m = 2 modewhich also propagates in the direction of the toroidalrotation but with a distinctly lower frequency owing tothe features discussed above Thereafter the frequencyof this mode tends to decrease which may be attributedto mode locking Frequently a disruption occurs afterseveral tens of milliseconds there are howeverdischarges in which the mode persists up to the end ofthe injection pulse

If qa is sufficiently large (eg gt 27) L-modeplasmas are not susceptible to m = 2 modes or disrup-tions the same applies to H-mode plasmas as long asbeta is well below the Troyon limit [15] The occurrenceof disruption is restricted to discharges that aim atreaching or exceeding this limit Most frequently them = 2 mode is excited in the phase of rising betaOn the other hand non-disruptive decay of beta occursmore often in beta limit discharges in ASDEX

233 Edge localized modes

Edge-localized modes are a new type of MHD insta-bility which is observed in ASDEX [3] and in otherdevices in the H-phase only They appear as ratherirregular events which cause energy and particle lossesfrom the main plasma on a time-scale of the order of10 4 s In this respect the ELM has an effect similarto that of the disruptive instability In contrast to dis-ruptions during ELMs the losses are restricted to theouter regions of the plasma and lead to changes in j3p

of at most 01 The repetitive occurrence of ELMshowever appreciably reduces the effective confinementtime as can be seen from the study of quiescent ELM-free phases (see Section 3431) The effect of ELMson energy confinement is discussed in Section 3432

These modes are localized at the plasma edge Thelocation of ELMs is indicated in Fig 15 which isa plot of the ECE measured electron temperature atthe plasma centre (r = 1 cm) and halfway to theedge (r = 24 cm) during the NI phase precededand succeeded by Ohmic phases During the Ohmicphases the central electron temperature is periodicallymodulated by sawteeth During neutral injection the


ASDEX TEAM

FIG 15 ECE measured electron temperature Te at the plasmacentre (r - 1 cm) and half-way to the edge (r = 24 cm) showingthat ELMs are localized in the outer part of the plasma In theOH-phases the central electron temperature is modulated bysawteeth

centre is unaffected but mdash in the H-phase mdash rathersimilar relaxation phenomena appear as modulations onthe outer Te channel The spatial variation of ATeTe

and Angng as shown in Fig 16 demonstrates that thismode affects the plasma in the range from about a3to a The ATeTe variation of sawteeth is also plottedfor comparison

It is well known that the disruptive instability isusually preceded by a growth of the m = 2n = 1mode which is often readily observable over at leasta few cycles No corresponding precursor to an ELMhas been found Sometimes ELMs are preceded bysawteeth and appear to be triggered by them Thesame holds for fishbone-like bursts More frequentlyhowever the occurrence of ELMs is clearly separatedfrom m = 1 activity both types of events can beobserved in the same discharge Thus it must beconcluded that the m = 1 mode and its satellite modeare not precursors of ELMs

Particular attention has been paid to discharges inwhich neither a sawtooth nor a fishbone-like burstnor any other competing MHD activity (such as the21 and 31 modes described in the previous section)occurred before an ELM This situation is quitecommon but it is only in very rare cases that weakprecursor-like Mirnov oscillations with a duration ofroughly half a cycle and with toroidal mode numbersn lt 3 have been detected [16]

The fast decrease of the poloidal beta caused byan ELM leads to a fast inward motion of the plasmacolumn by typically a few millimetres which obviouslygives a signal on the Mirnov probes that is usually largecompared with oscillating mode amplitudes By summa-tion of the signals of the outside and inside coils the

effect of the fast inward motion could be removedNevertheless with this technique it was possible todetect a helical instability which occurs during theELM and lasts for typically ten cycles or less [17]By comparison with other signals corresponding toELMs it is found that this instability is not aprecursor rather it appears to be triggered by theELM The mode structure and propagation are verysimilar to those of the uncoupled mode existing inthe L-phase as described in the preceding sectionIn particular in the course of a discharge the modenumber remains the same

Regardless of the existence of this instability therelaxation process itself does not appear to be correlatedwith a certain rational surface This is concluded fromthe measurement of SX emission profiles shown inFig 17 The minimum at r = 36 cm does not shiftwhen qa (cylindrical definition) is varied between 24and 56 It is therefore assumed that ELMs are notlocated at a fixed resonant surface but are always veryclose to the plasma boundary Since ELMs are onlyobserved in the H-mode it is tempting to conclude thatthe crucial element leading to the H-mode (which seemsto be the transport barrier at the edge) also gives riseto a new instability condition

Since ELMs are localized close the the plasma edgeit is obvious that the steep edge gradients of the H-modeare responsible for ELMs (see Fig 28)

h 20

V

ne

o

X

A

qa = 365qQ = 29qa = 26qa=275

--10

FIG 16 Relative variation of the electron temperature and densitydue to ELMs versus plasma radius The variation of Te due toELMs is compared with that due to sawteeth


THE H-MODE OF ASDEX

AA

sawtooth

r fcmJ

FIG 17 Radial distributions of soft X-ray fluctuations connectedwith an ELM and a sawtooth The measurements indicate that theELMs are localized at the plasma edge

The increase in SX intensity as observed duringELMs is ascribed to the release of particles and energyfrom the main plasma This release is most clearlyrecorded by the lithium beam probing the local densityaround the separatrix Figure 18 is a three-dimensionalplot of the Li[2p-2s] light intensity which is approxi-mately proportional to the electron density

Since the energy and particle flows into the divertorchamber are transiently increased during ELMs thereis a burst-like modulation of all divertor diagnosticsignals in particular those of the HaDa light emissionfrom the divertor chamber Thus the same signalmonitors the L-H and the H-L transitions as well asthe occurrence of ELMs as is shown in many figures(for example Figs 1 2 and 6) This signal is routinelyrecorded with a sampling rate of 1 kHz and in manycases with a sampling rate of 250 kHz From thesedata the rise time is taken to be typically 50-100 uswhich is longer than the response time of the photo-diode The half-width of the signal ranges from 100to 400 (is The rise time of the HaDa emission in thedivertor chamber with respect to data from the mainchamber is delayed by typically 100 us From all theseobservations it follows that ELMs occur on the MHDtime-scale Simply expressed an ELM could be regardedas a transient return to the L-regime This view issupported by the reappearance of the non-coupledmode which as shown in Section 232 is a charac-teristic feature of L-type plasmas On the other hand

the energy and particle flows during ELMs can farexceed those of the L-phase

In the H-phase ELMs have various amplitudes andfrequencies They can be singular events producing alarge and distinct spike in the divertor Ha radiationOn the other hand ELMs can occur as groups ofsmall events these ELMs have been dubbed grassyELMs because the appearance of divertor Ha radiationleads to this association It has been speculated thatsingular ELMs are caused by an MHD phenomenonbut that grassy ELMs are caused by an unstabledevelopment of the H-phase during which the plasmaoscillates between the L-phase and the H-phase

The same wave form of the SX radiation is causedby a singular ELM and by one of the grassy ELMsAt the plasma edge both singular ELMs and grassyELMs cause a transient signal rise more inside thesignal decreases The relative decrease of the SXradiation 5 cm inside the separatrix is mdash50 in thecase of a singular ELM but only - 1 0 in the case ofa grassy ELM A singular ELM modulates the SXradiation measured along a chord through the centrein the case of a grassy ELM the signal modulationpeters out between 10 and 20 cm from the centreFrom this comparison we conclude that a grassy ELMalso constitutes an MHD feature but that it has a smalleramplitude than a singular ELM

The spatial structure of the energy release due toELMs is difficult to assess since there are no sufficientlyfast and detailed measurements especially regardingtoroidal variations Because of the expected axisymmetry

9630

ELMin

ltMio

CM

FIG 18 Three-dimensional plot of the Li [2s-2p] light intensityalong the beam over the period 1209-122 s encompassing twoELMs


ASDEX TEAM

90 180 270 360

Toroidal angle (deg)

FIG 19 Temperature rise of the cooling water in the eight toroi-

dal segments of the upper outer target plate The three curves

represent averages over four Ohmic discharges seven L-mode

dominated discharges and six H-mode ELM-dominated discharges

The beam heated shots have about the same total energy input

of the equilibrium most diagnostics are restricted toone poloidal plane and toroidal asymmetries are there-fore not detected Recently however new and impor-tant information was obtained on ASDEX when theoriginal radiation cooled titanium target plates (DV-I)were replaced by a water cooled structure (DV-II)with these new divertor plates it is possible to performtime integrated but toroidally resolved measurementsof the target power load by calorimetry In Ohmicdischarges as well as in discharges dominated by along L-phase the toroidal variation was less than 20However in discharges with a long H-phase and manylarge ELMs with only short L-phases at the beginningand at the end of beam heating a nearly sinusoidalmodulation of the deposited energy with n = 1 wasobserved (see Fig 19) A difference between the maxi-mum and the minimum power loads of up to a factorof three was found depending on the actual evolutionof the discharge

Part of the power load obviously comes from themore homogeneous Ohmic phase and the L-phase as wellas from the quiescent period between ELMs Since inaddition the signal represents a time average overmany ELM events it is concluded that the asymmetryfor an individual ELM is significantly larger and thatsuccessive virtually independent ELMs occur withapproximately the same toroidal phase angle indicatingphase locking with respect to some fixed externalperturbation Since the only significant plasma-wallcontact occurs at the target plates the ELMs appear tobe locked at non-axisymmetric external magnetic fieldperturbations These may be caused by for example

a slight misalignment of the divertor coil triplets inASDEX In fact it has been shown by field linetracing that a random sideward shift or tilting of themultipole coils within mechanical tolerances of a fewmillimetres causes magnetic field ergodization aroundthe separatrix and spatially fixed islands of a fewcentimetres in radial width on low rational surfacesinside the separatrix [18] Since the magnetic fieldcoils were not changed during the reconstruction ofthe divertor we believe that the same perturbation andhence similar mode locking were also present in theprevious arrangement (DV-I)

Previously experimental evidence of such fielderrors was obtained from the destruction pattern on theoriginal titanium target plates [19] these errors couldbe traced back to local thermal overload by a highenergy electron minority produced by lower hybridcurrent drive and partially lost along perturbed fieldlines intersecting the target plates

Figure 19 shows that the total power load in theELM dominated case is somewhat lower than in normalL-shots at the same total energy input This indicatesthat some energy is deposited elsewhere for exampleat the divertor throat because of the wider radial profileof ELMs

11 12 13 t (s)

FIG 20 (a) Variation of nt j3pX from the diamagnetic signaland Ha at a sudden termination of ELMs(b) Variation ofne j3p + 12 from equilibrium and Ha withsingular large ELMs


THE H-MODE OF ASDEX

a

2 4 6

dnedr (1012cm-4)

FIG 21 Variation of the electron temperature and density gradientwith the pressure gradient at the plasma periphery at the end ofquiescent H-phases shortly before the H-L transition The edgepressure gradient is varied by changing the distance between theseparatrix and the outer vessel wall and by the plasma current

The energy loss due to an ELM can be up to 4 Uon one target plate summed over all target plates thiscorresponds to the energy content of an annulus at theplasma surface of several centimetres Steady stateconditions for the plasma energy content are providedonly for ELMs with a period of about 6 ms The effectof ELMs on the confinement of an H-discharge cannoteasily be assessed in all cases because ELMs can be ofhigh frequency with low amplitude or of low frequencywith high amplitude (see Section 343) (Here and inthe following the amplitude of the HaDa signal isconsidered as a measure of the violence of an ELM)Generally ELMs are more frequent at lower heatingpower at higher heating power they are less frequentbut have a more distinct pattern Figure 20 shows thedevelopment of the density the poloidal beta and theHa radiation in the divertor chamber for two cases Onecase is characterized by frequent ELMs which suddenlystop for short quiescent periods in the other case thebasically quiescent H-phase is interrupted by largeELMs The poloidal beta in Fig 20(b) is taken fromthe flux and from Be loops positioned inside the vacuumvessel the diamagnetic loop is positioned outside thevacuum vessel and hence the signal is integrated withthe vessel time constant of 16 ms Both cases documentthe impact of ELMs on the particle and energy contentsand show that ELMs can indeed lead to saturation ofthese parameters The case of Fig 20(b) with singularELMs shows that the gain in particle and energy contentsin the quiescent periods between ELMs is lost againduring the ELM events This is similar to the effect of

a sawtooth While a sawtooth however is an internalmode which redistributes the energy in the plasmacore an ELM is an external mode with a deterioratingeffect on global confinement

Since the occurrence of ELMs is erratic it is difficultto study the cause of their appearance The frequencyof ELMs tends to increase at lower current and constanttoroidal field whereas their amplitude decreaseswhich indicates that ELMs may be correlated with thecurrent density profile in the range of the steep electrontemperature gradient at the edge However ELMs havea stronger impact on the edge density than on thetemperature (see Fig 64) No correlation between ELMfrequencies is observed for the cases of ramp-up andramp-down of the plasma current (especially when thecurrent is increased or decreased at the plasma edgeduring the H-phase) It is also possible that ELMs aredriven by the steep pressure gradient at the edge Thepressure gradient may be steep enough (within theaccuracy of the edge measurements) to violate the idealballooning limit (on the assumption of a shear of S = 2at the edge) At present it is not possible to make a cleardistinction between the two potential driving mechanismsmdash the current or the pressure gradient The edge stabilityconditions are discussed in Section 7

ELMs can be stabilized by moving the plasma columncloser to the outer wall This has been applied success-fully at various stages of the experiment QuiescentH-phases can be achieved with this method WhetherELMs can be wall stabilized has not been proven yetHowever the maximum edge electron pressure seemsto be correlated with the separation from the wall(correlation coefficient == 06) During the quiescentphase the edge pressure gradient continuously increasesuntil the plasma transits back to the L-phase A largerpressure gradient is possible at higher current Thepressure gradient at the end of a quiescent phase islarger than the average pressure gradient during a sub-sequent phase with ELMs The variation of the edgepressure gradient in quiescent phases (either by changingthe current or the distance to the wall) is mostly dueto changes in density and not so much to changes intemperature gradient Results are shown in Fig 21

24 Impurity development in the H-mode

As summarized in Section 22 the development ofthe impurity concentration in an H-discharge dependson many factors such as the reduced wall erosion inthe H-phase and the changed confinement and MHDcharacteristics [20 21] Figure 22 plots spectroscopictraces representing the influx of oxygen and iron


ASDEX TEAM

10

10

2 poundbull

4

1 4804

4745

Lj( b )

13 15 16

t Is]

FIG 22 (a) Plasma radiation from L- and H-type discharges as measured by a bolometerThe signal is divided by the plasma density The line averaged density is also plotted for reference(b) Radiation of O VI and Fe XVI normalized for the plasma density from the two discharge typesThe dashed lines indicate the L-H transition

with ELMs wo ELMs

rRAO

(MW)

(au)

FIG 23 Time evolution of various plasma parameters of H-mode discharges with andwithout ELMs (Ip = 032 MA B = 217 T PN = 33 MW Hdeg - D+) line averagedplasma density ne Da light intensity in the divertor chamber poloidal beta |3p globalenergy confinement time TE Fe XVIII and Fe XXII line intensities (representative of ironradiation from ra = 23 and from the plasma centre respectively) and total andcentral radiation losses P^D and HO)


THE H-MODE OF ASDEX

08

04

- - 5

with ELMs 11338

time 11) 1095 s12) 1155 s13) 1215 s14) 1230 s15) 1245 s6I 1260 s

10 20r (cm)

30

s

6

gt

- bull 2

wo ELMs 11447

( b )s

i bull i i f

time- (1)(2)13114)IS]161

1095 s1155 s1215 s1230 s1245 s1260 S

10 20 30rcm)

FIG 24 Radiation power density profiles of (a) an ELMdominated H-discharge and (b) an ELM free H-discharge

together with the line averaged density and the totalradiation power The radiation and spectroscopic dataare normalized to the line density in order to demon-strate the effect of the impurity influx The normalizedintensities decrease after the L-H transition for bothoxygen and iron the decreased impurity influx after theL-H transition is also shown by the total impurity radia-tion which however increases in the course of theH-phase to levels higher than those in the L-phase (evenwhen normalized to the density) The increase in radiationis stopped when beam heating is termined The rise inimpurity radiation during the H-phase is caused by theimproved confinement which also affects the impurityions In particular the absence of sawteeth in the plasmacentre makes this zone susceptible to impurity accumu-lation The outer zone is affected by ELMs and theimpurity development of the discharge depends verymuch on their presence and intensity In Fig 23 adischarge without ELMs is compared with a longdischarge (beam stacking) with ELMs In this sectionwe are interested only in the development of the impu-rity radiation and the energy content Without ELMsimpurities quickly accumulate in the plasma centrecausing the total radiation and in particular the centralradiation to increase In the plasma centre since thereare no sawteeth the inward flux of impurities is notstopped The increased impurity radiation causes asaturation of the energy content of the discharge and aroll-over in j8p finally a forced transition back to theL-mode occurs

In contrast to a quiescent discharge in a dischargewith ELMs the central radiation losses do not exceeda level of 08 W-cm3 and the discharge becomesstationary for more than 13 s The development of theradiation profiles in cases with and without ELMs isshown in Fig 24 The two profiles evolve in a similarmanner until they have centrally peaked shapes theabsolute values however differ by a factor of aboutthree This difference in the absolute radiation is alsofound during the preceding L-phase and in the caseleading to a quiescent H-phase it is essentially caused bylarger contamination These discharges were producedby shifting the plasma 4 cm towards the outer stainless-steel protection limiters thereby reducing the scrape-off region to a width of about 3 cm [21] Furthermoreby means of laser blow-off injection of metals into theH-phase the suppression of ELMs could also bedemonstrated [22] The increased radiation can lead toa reduction of the pressure gradient in the edge regionthus eliminating the driving force of the ELM instabilityRelatively high-Z elements (Cr Ti) however areneeded to quench the ELM activity Puffing of neonand methane for instance which radiate preferentiallyclose to the separatrix has the opposite effect the ELMfrequency is increased and it is even possible to fullyrestore the L-phase in this way (see Section 611) Asimilar response is observed in the case of hydrogenpuffing or in cases where high recycling conditions inthe main plasma chamber are established

The development of the central iron concentrationnFe(0)ne(0) in H-discharges with and without ELMs

nFel0)nel0) =

io-2-

bullo

5 io3J

10110 120 130

t(s)

FIG 25 Temporal evolution of the iron concentrations at theplasma centre calculated from the central radiation density and thetemperature dependent radiative power loss function of iron (seeinserted formula)


ASDEX TEAM

FIG 26 Various signals as a Junction of time for a discharge

in the new divertor configuration DV-II exhibiting a quiescent

H-mode in the period 118 lt ^ 134 s Results of simulation

calculations are plotted as dotted lines

is shown in Fig 25 These concentrations are derivedfrom measured radiation densities prad(0 t) and fromcalculated radiation rates LFe(Te) on the assumptionthat iron is the dominant metallic impurity (prad =Lpenpene) We notice that although the radiation densitiesdiffer by factors of three to five the concentrations arealmost equal at the time when the quiescent dischargestarts to collapse The large difference in radiation lossesis mainly due to the higher electron density (factor ofmdash 25) additionally the decrease of the temperaturein the late quiescent phase causes a further increase ofthe radiation

So far the ELM activity has been taken to be onlyan indication of low metallic influxes It is foundhowever that ELMs also lead to improved impurityscreening efficiency in the edge region This is inferredfrom the observation that in all discharges with varyingELM frequency the central radiation is inversely corre-lated with this frequency but with a delay of typically50 ms ie approximately the diffusion time In thesecases there is no reason to assume a changing influx ofimpurities across the separatrix Further support for thescreening effect of ELMs is obtained from experimentswith constant low argon gas puff rates [20] In dischargeswith ELMs the argon density in the main plasma is seen tosaturate after about 100 ms whereas it steadily increasesin quiescent discharges The opposite behaviour is foundin the divertor region where the argon density increases indischarges with high ELM frequency which indicatesimpurity retention but during quiescent phases the argondensity is constant

Attempts to simulate the impurity behaviour duringthe quiescent H-phase were initially based on anomaloustransport modelling However no unique descriptionof the transport parameters can be derived from themeasurements and different transport formulationscan lead to similar results Nevertheless it was foundnecessary to reduce the anomalous diffusion coefficientDan by a factor of about four and to postulate substantialinward drift velocities in simulations of the L-H transi-tion [20] On the other hand a consistent analysis ofthe accumulation of metallic impurities in variousregimes of improved confinement in ASDEX [22] ispossible by invoking a combination of neoclassicaltransport and anomalous diffusion Thus it can beconcluded that impurity accumulation is simply theresult of a reduction of the anomalous diffusioncoefficient by which the outward fluxes are decreased

In the following we apply this concept of impuritytransport to the analysis of a more recent discharge inthe new divertor configuration DV-II where quiescentH-phases of up to 160 ms are achieved This configu-ration has better diagnostics than the previous one andin particular 16-channel Zeff measurements (infraredbremsstrahlung) as well as good time and space resolvedTe and i^ profiles are available Some of the relevantsignals are plotted in Fig 26 The global parametersare Ip = 380 kA BT = 22 T neutral beam heating(13 MW Ddeg in D+) for 10 lt t lt 18 s and slightlycarbonized walls The L-H transition occurs at 118 sand the transition back to the L-mode occurs at 134 sas is clearly seen from the C III divertor radiation signalshown in the lower right corner of Fig 26 In theH-phase the line averaged electron density (upperright corner of Fig 26) steadily increases to a maximumof 63 x 1013 cm3 and simultaneously the centraldensity rises reaching its maximum of 90 X 1013 cm3

during the second L-phase In contrast the centralelectron temperature decreases from a maximum ofTe(0) = 25 keV during the first L-phase to 11 keV atthe end of the H-phase Similarly the poloidal betareaches a maximum of 15 at t = 127 s and thereafterdecreases because of the rapidly increasing radiationlosses (at t = 13 s Pingttot = 16 MW Pradtot = 13 MW)Also shown in Fig 26 are the spectroscopic signals ofO VI Cu XIX and Fe XXIII along central chords TheO VI signal is emitted close to the separatrix and isrepresentative of the influx of oxygen which is seen tobe fairly constant for t gt 115 s The Cu XIX radiationis preferentially produced at r = 30 cm this signal isdetermined by influx as well as transport Core radia-tion is represented by the Fe XXIII signal and particu-larly by the soft X-ray intensity In addition the develop-

1976 NUCLEAR FUSION Vol29 NoU (1989)

THE H-MODE OF ASDEX

ment of Zeff on axis and at the half minor radius isshown in the lower left corner of Fig 26 The totalcentral radiation losses are also plotted they reach amaximum of 45 W-cm3 during the second L-phaseThe results of our transport calculations for copper(the new target metal in the divertor) are indicated bythe dotted lines in Fig 26 The calculations are basedon the following assumptions The influx of copper atthe onset of neutral injection rises by a factor of tenduring 10 lt t lt 105 s and then stays constant at alevel of ltACu = 15 x 1019 s1 (6 x 1013 atomscm2-s)The anomalous diffusion coefficient Dan changes froma constant value of 09 m2-s during the L-phase to01 m2-s~ during the H-phase This reduction takesplace in the whole inner region r lt a but not in theSOL zone r gt a In this way reasonable agreement isobtained (in absolute scale) with the measured Cu XIXintensity (ICumax = 0023 W-cm2) For comparisonwith the soft X-ray data the contribution of iron whichaccording to VUV spectra is about equal in concentra-tion must be added We thus obtain 70 of the detectedSX intensity (Isxmax = 75 W-cm2) Normalizing thecalculated and measured SX traces yields the agreementshown in Fig 26 which is satisfactory At the time ofmaximum poloidal beta the central metallic concentration(ncu -I- nFe)ne is again 05

For the estimation of Zeff additional assumptionswith respect to the behaviour of the light elements Oand C must be made As a first approximation weignore accumulation effects and take the contributionof O and C as measured during the Ohmic phase ieZeff(0) - 1 = 13 When the calculated Cu and Feparts are added the dotted curve plotted in the lowerleft corner of Fig 26 is obtained The agreement withthe measured values (bold curve) for r = 0 is notsatisfactory in detail but the systematic trends and alsothe rather high values of Zeff(0) laquo 5 are consistentlyreproduced The measured Zeff traces demonstrate theimpurity accumulation by the inverse behaviour ofZeff(0) and Zeff(a2) From intermediate Zeff channelsthe actual accumulation region is found to be a smallcore zone within r lt 12 cm It is also this regionwhere a sharp rise in Zeff is detected immediatelybefore the transition to the H-phase (see Fig 26)This can be explained by (1) the existence of poloidalasymmetries caused by the sawteeth that trigger theL-H transition and (2) the occurrence of marfes in thetorus midplane Furthermore it should be noted thatthe high central Zeff is of little importance for thevolume averaged quantity Zeff which enters into theratio of the plasma current to the loop voltage In factcalculating Zeff from the corresponding profile measure-

ments yields a relatively low value of Zeff ~32 forthe H-phase whereas Zeff is as high as 45 during thepreceding L-phase

It has been found that the exceptionally good confine-ment properties of the quiescent H-mode cannot beutilized to achieve a maximum plasma energy contentIn particular the metallic influxes from the divertortarget plates (Ti Cu) and additional fluxes from thewalls (Fe) under non-carbonized or poorly carbonizedconditions are too large to keep the central radiationlosses at tolerable levels when accumulation occurs Asin other improved confinement regimes the impurityaccumulation process can be understood by neoclassicalinward drifts which become essential when anomalousdiffusion (caused by turbulence under degraded conditions)is suppressed Although these inward velocities arelower in the present case than for example in thecase of neutral counter-injection where the accumula-tion is strongly increased by the marked peaking of theproton profile [23] they are still high enough (vFe(a2)= 08IH-S1) to produce dangerous core concentrationsof the order of 05 within about 01 s In addition

FIG 27 Total radiation (a) and central radiation density (b)for three quiescent H-phases with various divertor configurationsSolid lines DV-I closed configuration dotted lines DV-II openconfiguration dashed lines DV-II closed configuration The tracesare shifted along the time axis such that the H-L transition occursat the same time point


ASDEX TEAM

600-

500-

i00-20-

15-

( b )

-6 -6 -2 0

Ar= r-r (cm)

FIG 28 Radial profiles of (a) Te and (b) ne in the midplane over the separatrix for ohmically heated and beam heated dis-charges r = rs is the nominal separatrix position according to magnetic signals Vertical bars indicate separatrix positionsdetermined from electron pressure profiles in the divertor chamber using the assumption that neTe = constant along field linesThe question of the exact location of the separatrix is discussed in the text

to accumulation of metals central accumulation oflight elements cannot be excluded and may lead toa further dilution of the protondeuteron densityInformation on this important aspect is expected fromcharge exchange resonance measurements of C VI andO VIII which are planned for the near future Howeverit should be emphasized again that in H-modes withELMs it is possible to achieve steady state operationwith constant poloidal beta acceptable impurity levels(Fig 23(a)) and superior energy confinement comparedwith that in the L-mode (see Section 346)

We have studied the sudden termination of thequiescent H-phase during beam heating with variousdivertor configurations (see Section 42) which lead todifferent developments of the total and central impurityradiation as shown in Fig 27 The solid curve is obtainedin the initial divertor configuration DV-I of ASDEXand the dotted and dashed curves are obtained with thenew divertor topology DV-II under open and closedconditions respectively (The curves are shifted alongthe time axis such that the termination points for thequiescent H-phases coincide) Comparison of the impuritydevelopment shows that the end of the H-phase doesnot coincide with the maximum of total or central radia-

tion The maximum radiation occurs after the H-Ltransition This delay is rather distinct in the newdivertor configuration and is obviously connected withthe rapid shrinking of the density profile in the L-phaseThe actual reason for the sudden termination of thequiescent H-phase and the transition to a secondL-phase is not yet clear The increased radiation leveldoes not seem to be the only reason for it A possiblecause is the continuously rising edge pressure thetransition to the second L-phase is initiated by an ELM

25 Scrape-off layer anddivertor plasma parameters

Various specific diagnostics are available in ASDEXfor edge and divertor investigations The edge electrondensity and the temperature in the equatorial plane canbe measured by using the Thomson scattering systemat the edge The H-mode profiles of Te and n^ at theplasma edge are plotted in Fig 28 together withL-mode and OH results As the diagnostic is limitedto five observation channels which are spatially fixedthe horizontal plasma position was shifted from dischargeto discharge in order to increase the spatial range and


THE H-MODE OF ASDEX

[cm]

1013

9630OH 105s

- - - L 113H 1164

1012

R-Rs [cm]

-2 8

FIG 29 Density profiles in the SOL during the Ohmic phasethe L-phase and the H-phase Hdeg - D+ PNI = 28 MWB = 217 kG Ip = 315 kA

the number of data points In the scrape-off layer (SOL)outside the separatrix the statistical error increasesbecause of the low scattered light intensity and alsobecause of plasma fluctuations (laser pulse length laquo 20 ns)Note the high edge electron temperature (~ 600 eV)a few centimetres inside the separatrix and its steepgradient The H-mode in these measurements exhibitedELMs the data shown in Fig 28 therefore representaverage values as observed in discharges with ELMs

The separatrix position shown in Fig 28 has beendetermined from the signals of flux loops and magneticprobes (nominal position) Its uncertainty of aboutplusmn1 cm is comparable to the radial decay lengthcausing a significant error in the plasma parameters atthe last closed surface Previously the separatrix posi-tion was also determined from the measured pressureprofile in the divertor plasma fan as well as the momen-tum balance along the field lines between midplane anddivertor ie with approximate pressure constancy [24]This procedure yields a separatrix position shifted tothe outside by ~ 1 cm as indicated in Fig 28 At thenominal separatrix position a suprisingly high tem-perature is found especially for the H-phase to obtainconsistency with the measured total power depositionin the divertor chamber a substantial thermal barrieron open field lines would have to be assumed Takingthe pressure corrected separatrix position in Fig 28one obtains values much closer to those expected fromnumerical edge models including a flux limited electronenergy transport into the divertor There is additionalevidence that the actual separatrix position is shifted

further out for example by the instant X-ray emissionwhich occurs when a small target is moved across theseparatrix under plasma conditions where a fast electronminority is present as during lower hybrid heating orcurrent drive [18]

Despite the experimental scatter of the data inFig 28 it is obvious that the radial decay lengths ofthe density and temperature in the H-phase are muchshorter than those during L- and OH-phases Fromdetailed studies of the actual separatrix position weconclude that a radial zone of large density and electrontemperature gradients is located at but inside theseparatrix The exact location of this zone with respectto the separatrix is of decisive importance for H-modetheory

In addition continuous radial edge electron densitieswith high time resolution and accuracy can be derivedfrom measurements of the intensity of light emittedfrom Li atoms which are impact excited by electronsand ions in the SOL For this purpose the Li beam isinjected perpendicularly to the plasma surface in theouter midplane the Li(2p-2s) emission profile alongthe beam is measured at ten spatial points spanning9 cm [25] Figure 29 compares the radial dependenceof the electron density in the Ohmic phase the pre-transition L-phase and the quiescent intervals betweenELMs in the H-phase Most pronounced is the largevariation in the density e-folding length Xn near theseparatrix which ranges from - 2 1 cm in the OH-phaseto - 2 8 cm in the L-phase and to - 1 2 cm in theH-phase A few centimetres further out a more or lessclear plateau is obtained in a region where the electrontemperature has fallen below the ionization level every-where along the field lines Qualitatively these changesare related to changes in plasma confinement Xn islargely determined by the cross-field diffusion in theSOL and by the transit time for particles between themidplane and the divertor target plates Thus a decreaseof Xn in the H-phase reflects a reduction of the cross-field transport coefficient and conversely an increaseof Xn during the L-phase is correlated with increasedperpendicular particle transport Assuming a parallelflow with Mach number M laquo 02 as a first approxi-mation to a SOL with divertor recycling we obtainD = 4000 10000 and 1500 cm^s1 respectively forthe OH- L- and H-phases in the strong gradient partof the SOL

Another important aspect of the SOL density profileduring the H-phase is its invariance with respect toglobal plasma properties Figure 30 illustrates thetemporal behaviour of the density at the nominalseparatrix ns and of the density e-folding length over


ASDEX TEAM

o

c

O

15-

10-

os-

o-

4-

2-

n-

raquo 96301

)bull

L

- - ^

0 (DO 0 bdquo

H

Nl

1

i

idegC11

i

ii

i

o o o

Lm

mdash

11 12 13 t [sJ 14

FIG 30 Temporal behaviour of ampp + i2 the line averaged den-sity ne the Da light intensity of the divertor plasma the separatrixdensity ns and the density e-folding length Xn in the SOL duringand after neutral injection for the discharge of Fig 29

a time span of 400 ms for the discharge considered inFig 29 Upon attainment of the H-phase ns and Xn

exhibit no time dependence even though Hg increasesfrom - 3 4 x 1013 to 5 X 1013 cm3 and j8p + $2increases from - 2 to 28 The density profiles in theSOL during the H-phase are extremely invariant This isparticularly striking since the geometric position of thenominal separatrix shifts over a range of 2 cm as aresult of the increase in poloidal beta and the plasmaposition control

The constancy of the H-mode SOL profile is sporadi-cally destroyed by ELMs which are associated with acatastrophic breakdown of the transport barrier In lessthan 200 s particles are released into the SOL andlead to an increase in Xn by a factor of more than fourSubsequently Xn decays to the pre-ELM values withan exponential time constant of ~05 ms Within afew milliseconds the SOL density profile reassumesits pre-ELM state in both Xn and ns

The relative behaviour of Xn in the various phasesshown in Figs 29 and 30 is universal A limited data-base selected for its parameter extremes (nlt = (18-5)x 1013 cm3 Ip = 220-415 kA Bt = 167-251 kGand PNI = 24-34 MW) shows that Xn(L)Xn(OH)- 13 plusmn 027 and Xn(H)Xn(OH) - 07 plusmn 012 withsingle-null discharges having lower values of Xn(L)With this database it is found that for injection powerlevels which eventually lead to the H-mode nsHeremains roughly constant in both the Ohmic phase and

the L-phase ie the global density profiles exhibitself-similarity in the parameter nsne Since for theDV-I divertor configuration He always decreasesduring the L-phase ns decreases as well In contrastat the onset of the H-phase ns(H) ltx h^ 2Pt

20t

5 (He in1013 cm3 absorbed total power in MW) Hencedepending on the values of He and Ptot ns(H) can beeither greater than ns in the L-phase (as in Fig 29) orless than ns(L) for low densities and high injectionpowers More details on the database are given inRef [26]

The SOL parameters in the midplane have to becompared with those in the divertor chamber Figure 31shows the location and the viewing angle and directionof several different diagnostics The line integratedelectron density in the SOL is measured interfero-metrically with a microwave system The characteristicvariation of the line density during the NI phase isplotted in Fig 32 for an inner divertor chamber Duringan L-discharge the line density increases until it reachesa maximum and then it decreases to the Ohmic levelAt the L-H transition this decrease occurs quickly Onlyrecently when an interferometer with a higher cut-offdensity became available on ASDEX it became possibleto measure the line density across the outer denserdivertor plasma fan The qualitative signature obtainedwith this interferometer turns out to be similar to that

neutralizer plates

infrared camera

HaDQ

FIG 31 Location and orientation of some divertor diagnostics(divertor configuration DV-I) Shown are the angular rangesviewed by different HJDa monitors the chord sampled by theLangmuir probe the location of inside and outside microwavehorns used to measure the electron line density the origin of thereflected flux ltpa at the intersection of the separatrix and theneutralizer plate and the line of sight of the infrared camera


THE H-MODE OF ASDEX

J

L

VUilillililUH V

1bullE 25u

2 20

S 15cat

Z 10c

s ^

sect 0

raquo 9393

10 12 U

t (si

FG 32 Time dependence of the inner boundary layer linedensity the NI phase is plotted on an expanded time-scalebdquo = 03 MA ne = 3 x 70J

cm = 30 MW

found previously ie a sharp decrease of the linedensity at the L-H transition sometimes followed byELMs which cause a strong modulation

The typical variation of the line density as describedabove and as shown in Fig 32 can be analysed as acorollary of the particle confinement variation of themain plasma [27]

The electron temperature and density profiles in thedivertor have been measured with Langmuir probesExamples of these profiles obtained on a shot-to-shotbasis with a static probe in the different confinementregimes are plotted in Fig 33 for two different distancesfrom the target plates The profiles exhibit a sharp peakclose to the separatrix a rapid decrease at the insidewhere the flux surfaces encompass the inner multipolecoil and a broad shoulder on the outside on flux surfaceswhich form the usual SOL This shoulder is sharplycut off at a major radius of 173 cm because the fluxsurfaces at larger radii intersect the shields which formthe divertor throat This shoulder is obviously relatedto the somewhat less pronounced plateau observed indensity profiles on the midplane (Fig 30) The mostimportant aspect of these measurements regardingconfinement is the variation of the peak values whichrise from the Ohmic phase to the L-phase and thendrop again to the low values of the Ohmic phase inthe H-mode

The power flow to the target plate is proportionalto nT32 where T and nt are the values at the targetTaking the values measured with the probe at z = 87 cmwhich is quite close to the target plate we can estimatethe variation of the deposited power for the differentregimes We come to the conclusion that the increaseof the power flux into the divertor chamber in theL-mode is in rough agreement with the increase of theheating power but after the L-H transition the powerflux is sharply decreased although the heating power isthe same as before

Additional information on the divertor plasmaparameters was obtained when the static probe in thedivertor of ASDEX was replaced by a fast movingLangmuir probe When this is operated in the triplemode continuous profiles are obtained along amajor radius line as shown in Fig 34 for L- andH-phases with ELMs At a typical probe velocity ofabout 1 nvs1 many ELMs occur in the H-phaseduring one transit through the divertor plasma fanTherefore if the inidvidual ELMs do not significantlychange the lower envelope of each profile in Fig 34approximately represents the profile shape in the periodsbetween ELMs while the upper envelope connecting

175 165 170 175 165

Rlcml

170 175

FIG 33 Radial profiles of the electron density temperatureand pressure of a divertor plasma at two positions from thetarget plates in the OH- L- and H-phases Ip = 032 MAne = 36 X 1013 cm3 Pm = 31 MW


ASDEX TEAM

1520243 (L 2=0) 20241 (H Z=+1 Cm)

| ri

0

40

gt

20

4

On 2

40

-40

165 170 175 165

R (cm)170 175

FIG 34 Profiles of the divertor plasma fan taken with a fastmoving Langmuir triple probe (velocity = 1 m-s1) along themajor radius (ion saturation current electron temperature densityand floating potential) assuming a Maxwellian plasma with asingle temperature Left Unshifted L-discharge the negative dipin the floating potential (arrow) is supposed to indicate the localseparatrix position Right vertically shifted H-discharge(z = 1 cm) with regular ELMs

the ELM maxima roughly represents an average ELMprofile Comparing L- and H-profiles it should be notedthat the H-profile corresponds to an upshifted single-nulldivertor discharge which is favourable for L-H transi-tion while the L-profile corresponds to an unshifteddouble-null configuration An upshift usually causesnearly a doubling of the ion saturation current anddensity in the upper divertor Except for such differ-ences in the global discharge parameters the mainresults of the static probe measurements are confirmedby the measurements with the Langmuir probe andadditional information for ELMs is obtained Theirradial profile turns out to be even wider in the H-phase

than in the L-phase However a quantitative analysis ofthe individual ELM parameters obtained with theLangmuir probe seems to be incompatible with detailsfrom other diagnostics measuring at different toroidalpositions (see below) One reason for this discrepancymay be the strong asymmetry of the power flow duringan ELM as is discussed in more detail in Section 233Another possible source of error is that the simpletriple-probe theory used for interpretation may not bevalid for such a highly dynamic event

The results from the retractable Langmuir probemay also help resolve the question of the correctseparatrix position in the divertor The magneticallydetermined position is inaccurate within about plusmn 1 cmas in the main chamber and is frequently differentfrom that determined with standard SOL models sincefor example it is located on the wrong side of theprofile maximum However it has been shown [28]that the floating potential profile in the divertor alwaysexhibits a more or less pronounced negative diproughly at the theoretically expected position inside theprofile maximum This dip is attributed to a hot electronminority which leaves the plasma very close to theseparatrix without being reflected at the electrostaticsheath at the target plate This dip therefore providesa direct local determination of the separatrix togetherwith the other triple-probe results The dip in the floatingpotential is clearly seen on the L-profile in Fig 34(see arrow left bottom part) In the H-phase the dipis often masked by ELM perturbations but when thedip is well developed it is at the expected positionThus the observed location of the dip at a differentposition which is sometimes especially pronounced inH-phases seems to be an artefact caused by errors inthe magnetic measurements or by incomplete equilibriummodels used for the determination of the magneticconfiguration Possible reasons are finite currentsaround the separatrix (eg near the X-point) whichare usually omitted in the equilibrium codes or eventhree-dimensional external magnetic error fields asdiscussed in Section 233

Instead of measuring the power load with theLangmuir probes it can be derived from the tempera-ture increase of the target plates during the dischargeby using an infrared camera The power depositionprofile at the outer target plate is shown in Fig 35again for the three confinement phases ie theOH phase the L-phase and the quiescent H-phase (H)shortly after the transition The highest power flux isabout 100 W-cm2 in the Ohmic phase 220 W-cm2

in the L-phase preceding the transition and only35 W-cm2 in the H-phase


THE H-MODE OF ASDEX

90 91 92

FIG 35 Power deposition profiles at the upper outer target plateduring OH- L- and H-phases PN = 3 MW

The total power deposited in the divertor chamber(deposition plus radiation) is 025 MW in the OH phaseand increases to 185 MW in the L-phase As expectedthis variation is in agreement with the increase in heatingpower from 035 MW to 3 MW It is howeversurprising that the power deposited in the divertorchamber in the H-phase is reduced to approximatelythe value found in the Ohmic phase but at invariantlyhigh heating power

Ions from the main plasma which travel along theSOL impinge on the target plates and are partly reflectedas atoms According to the ion temperature at the separa-trix the bulk of the ions are in the energy range of100 eV to a few hundred electronvolts and do notexperience a large change in energy after reflectionThe deposition of these ions from the main plasmacan be measured by using a scanning charge exchangeanalyser Figure 36 shows the deposition profiles ofreflected particles in the L- and H-phases The increaseof the perpendicular diffusion coefficient D whichextends into the SOL (as revealed by the behaviour ofthe SOL density) leads to a broadening of the particleprofile in the L-mode (compared with that during OH)and the decrease of D in the H-mode (between ELMs)causes the particle profile to shrink In addition theincrease of the poloidal beta in the H-phase gives rise toa shift of the deposition maximum From the measuredenergy of the particles their residential time in the SOLcan be calculated using 15 m as the average pathlength from the plasma midplane to the target plateA value of D which best fits the measured profiles isobtained by assuming diffusive perpendicular transportin the SOL The following diffusion coefficients in theSOL are obtained D0H = 4500 cm2 bull s1 DL = 8000 cm2 bull s1

and DH = 3500 cm2-s This agrees quite well withthe values obtained from the analysis of the e-foldinglength Xn

The explosive nature of ELMs leads to an increase ofthe SOL fall-off length in the main plasma vessel as

observed with the Li beam diagnostic and as a conse-quence to a broadening of the particle profiles in thedivertor as seen from the retractable Langmuir probe(Fig 34) This feature is also confirmed by the powerand particle deposition on the target plate as shown in

30

calculated _separotrix

Z mdash

FIG 36 Profiles of (a) the power flux onto the target plate and(b) the particles reflected from the target plates during L- andH-phases between ELMs and at an ELM The displacement of thebackscattering profiles of L- and H-phases is due to the higher ver-tical magnetic field in the H-phase PN = 28 MW


ASDEX TEAM

Fig 36 in comparison with quiescent phases The powerdeposition profile half-width summed over 19 ELMsduring a period of 120 ms (discharge No 10817)increases to 5 cm the profile wing is limited by thedivertor aperture indicating that some power is alsodeposited at the throat The power deposition canreach peak values of several kilowatts per squarecentimetre the total energy deposited during an ELMcan be of the order of 10 kJ ie of the order of 10of the plasma energy content [29] The power pulselength is about 04 ms which is the time resolution ofthe camera Soft X-ray signals indicate pulses as shortas 01 ms Using calorimetry in the new water cooleddivertor a spatially fixed sinusoidal average powerdeposition is found for the ELMs along the outerupper target (Section 233) The infrared camera islocated close to the deposition maximum while theLangmuir probe and the divertor interferometer arerespectively 90deg and 180deg away from it whichintroduces some ambiguity in the comparison of thedata from these different diagnostics Neverthelesseven for qualitative agreement between the results itis necessary to assume that strong local electric currentsflow onto the target in which case the electric sheathmay be located in the electron collecting regime Forthe fast ion deposition (Fig 36(b)) the profile changeis less dramatic but the appearance of a broadershoulder is also evident

In the quiescent H-mode the recycling of hydrogenchanges since the interaction of the SOL with the vesselwall is reduced Furthermore for a plasma with betterparticle confinement less gas influx is required tomaintain the same particle content and to compensatefor the diffusive losses In all regions of ASDEX whereHa monitors are positioned (they are uncalibrated andhence unsuitable for absolute determination of theionization rate) the Ha intensity decreases at the L-Htransition The Ha radiation at locations important forrecycling (divertor chamber and neck stagnation pointtypical wall section) is shown in Fig 5 Because of thereduced recycling and the well localized ionization ofhydrogen in the region with steep gradients the plasmaboundary is sharp and well defined in the H-mode Thetransition to the H-phase can be easily demonstrated bya high-speed movie film

3 CONFINEMENT IN THE H-MODE

31 Power fluxes in the H-mode

The power transported into the divertor chamber isthe main power loss channel in the OH- and L-phases

N I A

10 11

t (s)

FIG 37 Time development of (a) ne and ltfgta and (b) the totalpower flow PDiv into the divertor chambers The dash-dotted linesshow the variation of the normalized transport losses for energyconfinement time changes at the L-H transition (Ip = 0315 MAPN = 35 MW)

in keeping with the anomalous radial heat conductionby electrons across the separatrix The power flux intothe divertor chamber is divided into radiated powervia volume processes (impurity radiation and chargeexchange losses) and power deposited onto the targetplates Another loss channel is impurity radiation andcharge exchange whereby power is deposited onto thewalls around the main plasma Because of the highcleanlines of divertor discharges under both Ohmic andbeam heating conditions the impurity radiation poweris small The process of power transport from the mainplasma to the divertor chamber is explained in terms ofclassical electron heat conduction along the magneticfield lines in the SOL Thus for plasmas under Ohmicand beam heating conditions in the L-regime we havea consistent picture

The situation is totally different after the L-H tran-sition At constant heating power the power transportedto the divertor chamber drops approximately to theOhmic level at the transition This rapid and surprisingreduction of the power flux into the divertor chamberis plotted in Fig 37 which shows both the powerradiated from the divertor plasma and the power trans-ferred to the target plates This sudden decrease of thepower flux into the divertor chamber is not due to asudden deterioration of the magnetic configuration


THE H-MODE OF ASDEX

E

Ul

Ul

80-

70-

60-

50-

40-

30-

20-

10-

0 bull

D 1

bull

itlw deg

fdegl4 Araquo L-type

A A

A

2 3 U

n e [10

p

0

oo

1 8

0

bull OX +

5

cm3]

D+

a

5

A

hrP

PN

6

oD

H-type

= 370 kA= 300 kA

gt 2 MW

7 8

FIG 38 Global energy confinement time versus line averageddensity The solid curves show the Ohmic relation for hydrogenand deuterium plasmas The solid data points are L-type discharges(dots divertor discharges triangles limiter discharges) the opensymbols are H-type discharges at two different currents Crossesdenote TE values deduced kinetically the other symbols are basedon diamagnetic loop measurements (TE)

Particles and energy are still transported onto the targetplates at the location where the separatrix is supposedto intersect them The radial extent of the SOL is evenreduced and the width of the deposition peaks shrinksas shown in Fig 35 However as a consequence ofthe reduced power inflow the parameters of the divertorplasma (density electron temperature Ha radiation)resume the Ohmic values (see Fig 33)

In the periods between ELMs the power flux into thedivertor chamber is also low During ELMs the powerseems to be transported in pulses into the divertorchamber Taking an average over these pulses (egwith a bolometer) it is found that the radiated powerwithin the divertor chamber is somewhat below that inthe pre-transition L-phase and much above the levelduring a quiescent H-phase Regarding the poweraccountability (ratio of the three loss channels bulkradiation + divertor radiation + power to target platesto the power input) there seem to be no seriousproblems during ELMs

After a change in confinement it must be assumedthat a transient reduction of the power loss across theseparatrix occurs Within two to three confinement

times however when the energy content of thedischarge is built up and steady state conditions arerestored the power loss will be the same as beforeThe expected variations of the power flux into thedivertor chamber are plotted in Fig 37 for differentconfinement times In contrast to expectations themeasured power loss remains low mdash at the levelimmediately after the L-H transition The low level ofthe measured power flux across the separatrix cannotbe explained fully by impurity radiation and by thepower required to heat the plasma at the edge

The precision of power accountability is 80-100in the OH- and L-phases but just after the L-Htransition such a precision is not possible At presentwe can only assume the existence of a hidden powerloss channel and we do not know its origin nor do weknow the location where the missing power is depositedand the relevance of the power loss mechanism for thedevelopment of the H-mode Possible reasons for thepower loss are either asymmetries in the radiated powerof the main plasma or toroidal variations of the powerdeposited in the divertor chamber (see Section 233)Hidden losses could be along drift orbits which allowparticles to cross magnetic field lines and to disregardthe magnetic field topology Such a loss channel maybe opened up at the L-H transition where even theplasma edge is collisionless or nearly so It is possiblethat these losses are closely connected with the physicsprerequisites for the L-H transition as discussed inSection 6

32 Global confinement

The global energy confinement time TE is in mostcases determined from the poloidal beta (at its maxi-mum or under steady state conditions) measured witha well compensated diamagnetic loop The results areregularly tested with 3p + f-2 measured by the equi-librium coils and with the poloidal beta of electronsas provided in a quasi-continuous manner by the multi-pulse Thomson scattering diagnostics In some casesthe ion temperature profiles are measured and then afull kinetic determination of j8p is possible In numerouscases transport analysis also provided a consistencycheck for many experimental data

Figure 38 compares the TE values of H-mode plasmasat 300 and 370 kA with those of L-mode plasmas at300 kA for a heating power of gt2 MW (Hdeg injectioninto D + plasmas H-mode with ELMs) the TE valuesare either from diamagnetic loop measurements orkinetically deduced from the profiles At low densityan L-mode discharge with a divertor configuration may


ASDEX TEAM

occur at densities above 3 X 1013 cm3 only H-modedischarges develop In this density range the confine-ment times can only be compared with limiter dataAt the same current T exceeds T by a factor of twoT increases with the plasma current (see Section 34)as in L-mode plasmas Because of the scattering of thedata (predominantly introduced by the irregular natureof the ELMs) a density dependence cannot be deter-mined but a steep or even linear density dependencemdash as in the low-density Ohmic phase mdash can beexcluded

In Fig 38 the H-mode results are also compared withOhmic data For clarity only smooth curves throughthe Ohmic data points are shown The OH results areplotted for hydrogen and deuterium discharges Thehigh current H-mode results agree well with the satu-rated Ohmic values and the Hdeg mdash D + data lie betweenthe hydrogen and deuterium results in the OH-phaseBecause of the difference in parameter scaling thecomparison of OH- and H-mode TE values has nophysical meaning but simply serves to put the absolutevalues of TE into perspective

The improved particle confinement at the L-H transi-tion is obvious from the sudden increase in densitywhich leads to reduced or even zero external gas con-sumption The plasma is then externally fuelled by thebeams only In the quiescent H-mode the rise in thedensity content is higher than the beam fuelling rateby a factor of about two to three under these circum-stances the plasma is refuelled by gas accumulated inthe divertor chamber and the chamber walls Figure 39compares the line averaged density and the externalgas flux of L- and H-discharges During the L-phase

the external gas flux is sharply increased to counteractthe density decrease that would occur without such anincrease

The absolute values of the particle confinement timein the different confinement regimes are difficult toassess Particle transport will be discussed in separatesections dealing with the transport analysis of theplasma in the core and boundary regions and withimpurity transport

Here we summarize the constituents of the particlebalance equation for the different confinement regimes

dNdt = - N T P (2)

where N is the particle content within the separatrixTP is the global particle confinement time of the plasmabound by the separatrix $G is the external gas fluxthrough the valve $B is the fuelling rate of the beamsand $R is the recycling flux In ASDEX the source ofrecycling is the amount of neutral gas stored within thedivertor chamber and in its walls The recycling flux istherfore approximated by

= N0TD (3)

where No is the neutral particle content of the divertorchamber and TD the confinement time of neutral particlesin the divertor chamber which is largely determinedby the conductance of the divertor throats and possibleby-passes

Typical values for the components of Eq (2) arelisted in Table I the quoted rP values have to be takenwith caution but they clearly demonstrate the drastically

6028 laquo 5991

oe

FIG 39 Time dependence of (a) the line averaged density nt and (b) the externalgas flux ltfgtc ofL-type discharges (left column) and H-type discharges (right column)The dashed line indicates the transition from the L-regime to the H-regime


THE H-MODE OF ASDEX

TABLE I ELEMENTS OF THE PARTICLEBALANCE EQUATION

Phase

OH

L

H

dNdt

(s-1)

0

0

2 x 1021

(s-1)

1O21

6 x 1O21

0

V(s-1)

0

8 x 1O20

8 x 102 0

2

2

2

(s

X

X

X

Rb

-)

1O21

102 1

1O21

TP

(s)

OO5

001

015

Particle balance equation

dN N

dt + rp deg +

with N the particle content rp the particle confinement time$G the external gas input 0B the beam contribution and

R the recycling fuellinga Particle flux at 3 MWb The recycling flux is not well known

improved particle confinement of the H-mode Theincrease of the particle content in the quiescent H-phaseis in rough agreement with the beam fuelling rate andthe recycling flux as estimated for the Ohmic phase

33 Transport analysis

To achieve a better understanding of the transportprocesses we made detailed local analyses withmodified versions of the BALDUR simulation code andwith the 11 -D TRANSP analysis code both developedat PPPL [30] For these investigations we took themeasured radial profiles of i^ Te prad and Zeff as wellas computed power deposition profiles from the solu-tions of the equations for current diffusion beam depo-sition and slowing-down of charged particles The ionenergy balance was solved without actual knowledgeof the radial profile of Tt but determining Tj(r) underdifferent model assumptions for the ion heat diffusivityXi(r) in an attempt to fit the results of active and passivecharge exchange analysis and the integral constraintsgiven by 3pJ 3poundqu + 42 and the neutron flux Besidesproviding checks on the mutual consistency of themeasured data this yielded radial profiles of the formallydefined electron heat diffusivity xe = -qÔ^^Te)using the TRANSP code or radial profiles of Te byapplying models for xegt using the BALDUR code

The main result of these studies is that the changes inthe energy confinement from the saturated OH (SOC)regime to the beam heated L-mode and then to the

H-mode are due to modifications in the electron andion thermal transport losses (both conductive andconvective)

mdash The conductive electron loss qe and the electronheat diffusivity xe increase in the L-phase while theelectron heat conduction is the dominating loss channelThe increase in xe is pronounced in the initial phasewhen the beam is switched on After the L-H transitionqe and xe decrease (by a factor of up to two in ELM-free H-discharges) in the main plasma and at least inELM-free H-discharges qe approaches zero near theplasma boundary [31-36]

mdash The conductive ion heat loss q( and the ion heatdiffusivity Xi increase slowly after the OH-L transitionthis increase continues after the L-H transition Even ifXe is kept constant in the analysis during the H-phaseat the level of the preceding L-phase qj and Xi are stillfound to increase after the L-H transition Apart fromradiation losses the ion heat conduction becomes thedominating loss channel in the H-phase The ion heatdiffusivity in ohmically and additionally heated plasmaswith flat density profiles having ^ = (d In Tdr)(d In ndr) gt 1 can be formally described by theassumption of an enhanced (by a factor of two to four)neoclassical conductivity XLCH as given by Chang andHinton [35-38] However a combination of neoclassicaland ^-driven ion transport (see Ref [127]) is alsocompatible with the Tj measurements in all dischargephases (SOC L H) moreover it can explain in aconsistent way the improvement of both the global andthe ion confinement in peaked density discharges withVi 1 [39]

mdash The convective electron and ion losses increaseduring the temperature rise of the L-phase (PconvP= 52 Tk (Te + Ti)(r (E)) with T the particle fluxand (E) the medium energy of the injected neutrals)especially in Ddeg mdash D + discharges with a reducedmedium energy per injected nucleon and increasedtemperatures of the deuterium plasma (see Section 344)For ra lt 07 the dominant particle source comesfrom beam fuelling whereas in the edge region themain particle source is due to the ionization of coldatoms In this case the total convective losses maybecome comparable to either the electron or the ionconduction losses At the L-H transition the convectionlosses decrease because of the strongly reduced particletransport (TP gt TE) which leads to an increase in theparticle content and to a variation of the density profileshapes In H-mode plasmas (density profiles areshown in Fig 63) the energy is transported eventowards the plasma centre by convection


ASDEX TEAM

17005r=2a3

11O H V NI (

115 12 125

X

[m2s]

1-

1-

(

bull

17005

b)

s

IS 11 S2 = 115 s3S 1195 s4U205s551215s

bullXe(a)

0 05 r a 1

FIG 40 (a) Electron diffusivity e and idegn heat diffusivity x-

(= XINC + Xigt Vi) versus time during consecutive OH- L- andH-phases of a Ddeg mdash D+ discharge(b) Corresponding radial profiles of e

and X the Ohmicphase (]) the L-mode (2) and at the L-H transition (3-5)The dots denote Ja) deduced from the profiles of Fig 28 ina quiescent H-phase

We now analyse the local transport behaviour inmore detail Figure 40(a) shows the time dependenceof Xe and Xi at r = 23a in the main confinement zoneof a Ddeg mdash D + discharge and Fig 40(b) shows thecorresponding radial profiles in the Ohmic phaseduring the L-mode and at the L-H transition The valueof xe

H comes close to the xH values although thescalings are different The central hump on the xe(

r)curve in the Ohmic phase indicates losses due tosawteeth these are not present in the H-phase Thedata point xe(a) denotes the value of the electron heatdiffusivity in the steep-gradient edge zone The timedependences of xe at all radii show that the transitionfrom the OH-phase to the L-phase occurs within a fewmilliseconds which is mdash for the bulk region mdash shorterthan the transition from the L-mode to the H-modeThe L-H transition is sharp in the outer plasma zone(r gt 34a) where the transition obviously starts [34 40]qc is strongly reduced The density fluctuation studiesare described in Section 631 It is interesting to notethat these studies also indicate the existence of twotime-scales a rapid drop of the fluctuation amplitude

at the edge and a gradual reduction of the amplitude inthe bulk plasma Since the confinement depends on thefrequency of the ELMs the deduced transport coeffi-cients should be upper limits for the underlying quasi-stationary transport In the quiescent H-phase (H) theelectron heat diffusivity is even more reduced but thecentral and global radiation losses increase during thequiescent phase which leads to large errors in thedetermination of the transport coefficients

The time behaviour of the effective heat diffusivityXeff for both electron and ion transport is in qualitativeagreement with the xe behaviour illustrated in Fig 40(a)Modelling the ion transport with a value of XCH that isincreased by an appropriate factor (a mdash 2-4) in orderto agree with the peak or the average ion temperaturethe magnetically measured plasma beta and the neutronfluxes yields only small changes in the resulting Xivalues at the L-H transition After the L-H transitionhowever the formally defined neoclassical enhancementfactor oc which increases during the L-phase is reducedagain The reproduction of the measured ion tempera-ture profile shapes with the factor a is not satisfactory

3-T

[keV]2-

1-

mdash

(a )

r o )N

t

XCH+X

17005123s

05 ra 1

1

3-

2-

1 -

L (1 15S)

H(1215s)

( b )

OH(ils)

- lt

05 ra 1

FIG 41 (a) Radial profiles of Te (measured with Thomsonscattering) and of Tt simulated with Xi = Xicw + Xiraquo f (given inFig 40) and 3 x xtcw during the H-phase of a Ddeg - D+ dis-charge The points are Tt values measured in a passive CX neutralanalysis of a comparable Hdeg mdash D+ discharge with the same Te

profile but with 40 lower ne values

(b) Radial profiles of ie = (d In Tedr)(d In njdr) during the OH-L- and H-phases of the Ddeg mdash D+ discharge of Figs 40 and 41 (a)


THE H-MODE OF ASDEX

10

FIG 42 Comparison of Te and Tj profiles in quiescent L- andH-phases The T profiles are determined from passive chargeexchange flux spectra measured along five radial chords insuch a way that the deviations of the expected flux spectra from themeasured ones are minimal over the full energy range

Figure 41 (a) shows the measured Te profiles and thecalculated Tj profiles during the H-phase of the dischargeillustrated in Fig 40 with Xi = 3XCH or Xi = XCH + Xigtrespectively The assumption of Xi = 3XCH yields amuch too peaked Tj profile this is also the case forL-mode discharges [39] Since it was not possible tomeasure the Tj profile for the Ddeg mdash D + dischargewith the passive charge exchange technique wecompare in Fig 41 (a) the simulated Tj profile withthe measured Tj values (passive charge exchange) of acomparable Hdeg mdash D + discharge phase with the sameabsolute Te profile and the same n^ profile but with a40 lower Hg value (This lower line averaged densityexplains the lower energy confinement time of theHdeg mdash D + discharge) The ^-mode driven enhancementof Xi yields agreement between the calculated and themeasured Tj profile shapes as is also the case for OH-and L-mode Hdeg mdash D + discharges Figure 41(b) showsfor the L- and H-phases the rje profiles which areclose to the calculated and measured ^ profiles Owingto the strong Tj32 dependence the latter Xi model givesthe increase in Xi from the L-mode to the H-mode (seeFig 40) However the behaviour of the ion heat con-duction losses is similar in the two Xi models since theincreased Xi values are counterbalanced by the reducedTj gradients obtained with the -n model

Because of the difficulty of clearly determining theeffects of the L-H transition on the ion transport wehave used the described comparison of Xi = ot XCH andXi =

XCH + XTJI also for ELM-free Hdeg mdash D + dischargesBasically the same results are obtained with the measuredTe and Tj profiles Figure 42 shows these profiles atthe end of the L-phase and 20 ms after the beginningof the H-phase

A further and rather important indication that theion transport is governed by Trmode driven strongturbulence even in the H-phase is the fact that thetoroidal angular momentum diffusivities xraquo derivedfrom the measured toroidal rotation velocities (themomentum profiles are plotted in Fig 43 for L- andH-phases) can be well described by the theoreticalX values based on rjj-mode driven turbulence for bothL- and H -phases It is important to note that there isa simultaneous improvement of both the ion energyand the toroidal momentum confinement in dischargeswith counter-injection of neutrals in these dischargesa peak of the density profile occurs which results in adecrease of rjj to less than 1 over a large part of theplasma cross-section The experimentally and theoreti-cally derived Xi and x^ values are correspondinglyreduced compared with those in co-injection L-modedischarges [51] The momentum confinement time T^

increases from - 2 5 ms during the L-phase to ~40 msduring the H-phase whereas with counter-injection ofneutrals T^ increases to 120 ms when Xi drops to theneoclassical level

Another example of transport analysis (based onthe BALDUR code) of the pre-transition L-phaseand of an ELM-free H-phase including the steep-gradientzone A close to the separatrix is given in Fig 44 [41]

180 190 200

R (cm)

210

FIG 43 Momentum profiles in the L- and H-phases measured byresonant charge exchange on O7+


ASDEX TEAM

A- L1227s

0 20 A0r (cm)

FIG 44 Profiles of the electron heat diffusivity xegt xê electron

collisionality factor ve the ideal ballooning stability parameterdpdr(dpdr)c and TJ (= d In Ted In ne) in L- and H-phases

The diffusivities xe afid D in the zone A are strongly

reduced in quiescent H-phases (see also Fig 40(b))An exact figure for xe cannot be given because thegradient length in the edge is comparable to the sepa-ration of the diagnostic channels a factor of six maybe typical The confinement in the inner plasma hasbeen shown to improve within 10 ms after the L-Htransition (see also Fig 40(b)) Figure 44 furthershows the electron collisionality factor ie the idealballooning stability parameter (3p3r)(dpdr)c andthe profile parameter rje = d In Ted In n for thissimulation of an Hdeg mdash D + discharge

Another objective of local transport analysis is thedetermination of the scaling relations for the electronheat diffusivity the diffusion coefficient the inwarddrift velocity and the ion heat diffusivity Results fromthese studies [33 39 42 43 44] are presented inSection 347 Another important topic is the searchfor parameters that may be critical for the L-H transi-tion and that may determine the operational limits ofthe H-mode [45 46] These points are closely relatedwith attempts to identify the class of instabilities respon-sible for the anomalous fluxes in various confinementregimes For the ions it is very likely that these insta-bilities are the y modes as described above for the

electrons however no obvious instability could bedetermined so far (see Section 9)

Local transport and ballooning stability studies inH-mode plasmas have been carried out at the beta limit[38 48 49 65] It is found that the discharges belowthe beta limit exhibit H-mode transport and are stable toideal ballooning modes There is no gradual reductionof confinement when beta approaches the limit (hardbeta saturation limit) The degradation of energyconfinement at the beta limit is shown to be due toincreased electron heat conduction and convectionlosses The occurrence of these additional losses closeto the ideal MHD limit suggests that kink and ballooninginstabilities are responsible for them

34 Scaling of the energy confinement timein the H-mode

This section deals mainly with the dependence of theglobal energy confinement time on various externalparameters [52] If not otherwise noted the energyconfinement times are deduced from the poloidal betameasured with the diamagnetic loop and refer to quasi-stationary states obtained by averaging over manyELMs The agreement between the confinement timesobtained from magnetic measurements (TE) and thosecalculated from measured plasma profiles (TE) has beenchecked an example is shown in Fig 39 No correctiondue to radiation is made which is justified forH-discharges with a sufficient ELM frequency wherethe volume integrated radiation power losses arebetween 20 and 30 of the input power and comelargely from the edge

341 Density dependence

The density dependence of ohmically heated ASDEXdischarges shows a linear increase of the global energyconfinement time TE with n for lower densities(He ^ 3 x 1013 cm3) and in the saturated Ohmicconfinement (SOC) regime a levelling-off at higherdensities which is attributed to an increasing contribu-tion of anomalous ion heat conductivity [50 53] In theimproved Ohmic confinement (IOC) regime TE continuesto increase up to the density limit [54] For L-dischargesas well as for neutral beam heated limiter dischargeshowever TE is found to be largely independent of theplasma density Contrary to the Ohmic case howeverthe lack of i^ dependence is exclusively an electrontransport property [31]

Experimental investigation of the density dependencein H-mode discharges is hampered by the large variationin the frequency of the usually observed ELM activity


THE H-MODE OF ASDEX

02 03Io IMA)

04

FIG 45 Current scaling of the energy confinement time for D +

target plasmas (Hdeg mdash D+) in L- and H-modes

which affects both particle and energy confinementIn cases where a quasi-stationary state averaged overthe ELMs is obtained during the injection period thededuced global confinement time does not show amarked Hg dependence over a wide range within theuncertainty of the data (see Fig 38) The interpretationof the non-stationary high density H-discharges is morecomplicated high densities are obtained only by stronggas puffing during the short neutral injection phasewhich in turn leads to a higher ELM frequency andtherefore tends to reduce the rE values At densitiesabove (7-8) X 1013 cm3 only L-discharges seem tobe possible with gas puff refuelling A precise classifi-cation of the discharges into L-modes and H-modes isnot always possible because the density together withthe Ha radiation increase sharply and transitions mayescape observation Phases without any ELMs on theother hand are governed by a long particle confinementtime (see Section 32) To what extent the energyconfinement time of the quiescent H-phase exhibitsa density is still not known

342 Current dependence

An important new parameter which enters thescaling of neutral beam heated plasmas in ASDEX aswell as in other machines [52 55 56] is the plasmacurrent Ip The global energy confinement time TE wasfound to increase linearly with Ip over almost the fullcurrent range accessible in ASDEX (150 kA lt Ip

lt 450 kA) This applies to L- and H-mode dischargesas shown in Fig 45 The TE values for H-dischargesare averaged over ELMs during a quasi-stationarystate At the highest plasma current TE for an H-mode

D + plasma is comparable to the saturation confinementtime of Ohmic discharges With ELMs however atendency of rE to level off at high Ip is generallyobserved Unfortunately it is not possible withinthe ASDEX parameter range to find out whether thebreakdown of the Ip scaling at high plasma currentsis caused by qa approaching a value of 2 or by TE

reaching the saturation level of Ohmic dischargesSince no current scaling is observed in Ohmic

plasmas the transport in the H-phase seems to berelated with that of L-type discharges rather than that ofOhmic discharges We consider the dependence of TE

on Ip under auxiliary heating conditions to be a conse-quence of the Ohmic power input which is negligibleTherefore this dependence which is common toL-plasmas and H-plasmas does not necessarily implyany common trends in microscopic transport and doesnot necessarily represent a contrast between ohmicallyheated and auxiliary heated discharges

343 Power dependence

The ASDEX neutral beam system with eight ionsources is especially well suited for power scan experi-ments since it allows the heating power to be varied infairly small steps The power from one ion source ofabout 04 MW is comparable to the Ohmic heatingpower Additional heating with only one source alreadyleads to a complete change of the electron transportThe dependence of rE on the total heating power Ptotdeduced from power scan experiments with Hdeg injectionis illustrated in Fig 46 The (L-mode) results can be

yj

UJ

60-

40-

-

20-

0-

o

0

L-

^

O

Mode

H

o

bull fraquo

- Mode

w o

ot

FIG 46 Power dependence of the global confinement time forL- and H-discharges (Hdeg - D + bdquo = 320 kA B = 22 T)


ASDEX TEAM

well described by TE ltX pt with w raquo -12 for heatingpowers of up to 35 MW This finding is in qualitativeagreement with the results of other experiments [55]and was confirmed by detailed transport analyses [31]

The power dependence of H-mode discharges hasbeen investigated by operating in a single-null divertorconfiguration This configuration yields somewhatlower confinement values than the double-null configu-ration (see Fig 61) but it reduces the power thresholdfor the L-H transition and therefore permits a scanover a wider power range The results of Fig 46demonstrate that the energy confinement time in quasi-stationary H-phases with ELMs is largely independentof the heating power (TE ltX p-degdeg6plusmndegdeg3)

3431 Power scaling of TE in the quiescent H-mode

A lack of power dependence for deuterium injectioninto deuterium plasmas was reported previously fromDIII-D [11] These findings are in contrast to thosefrom JET [57] and JFT-2M [7] where a degradationof TE was observed in the H-mode as well as in theL-mode Recent results from DIII-D obtained from awider power range (POH ^ P ^ 12 MW) also indicatea power degradation of TE The different results for thepower dependence of TE lead to great uncertainties inthe prediction of the H-mode confinement attainable innext-generation tokamak experiments We try to analysethe power dependence of TE in the quiescent H-modeand to compare it with that of the regular H-mode Itis possible that the H-mode displays intrinsic H-modeconfinement properties because ELMs do not addition-ally contribute to the energy losses The power scalingstudies of JET are for discharges without ELMs butthe published results of ASDEX and DIII-D are fordischarges with ELMs

In ASDEX with Ip = 032 MA and Bt = 22 Tpower scans in the quiescent H-mode could be madefor both Hdeg and Ddeg injection into deuterium plasmasin the restricted power range 175 lt PNI lt 35 MWFor discharges without ELMs an additional difficultyin the TE analysis is that the H-phase does not reach asteady state and is suddenly terminated by a thermalquench due to excessive impurity radiation (seeFig 37) The duration of the H-phase depends on theheating power and increases from 95 ms at 175 MWto 125 ms at 35 MW During the H-phase the particlecontent increases linearly at a rate corresponding totwo to three times the beam fuelling rate The impurityradiation increases nearly exponentially After theL-H transition the poloidal beta increases againbecause of the improved confinement when the

100

80-

60-

40-

20-

WOELMS (D-D+)

Hdeg-D +

-x-N

with ELMs (H -Ddeg )

Po

FIG 47 Global energy confinement time in the quiescent H-mode(H) and in the regular H-mode (H) with ELMs versus heatingpower The curve is a power fit to the D mdash D+ (A) case thehorizontal line is a guide for the eye regarding the H-cases withHdeg ~ D+ (x) The circles are calculated from the Hdeg - D+

Treg values with the radiation correction The T^ values fromthe TRANSP analysis (Hdeg mdash D+J are indicated by squares

impurity radiation starts to affect the energy balance|3p rolls over and already decreases during the H-phaseBecause of the non-steady-state conditions and the centralradiation losses the TE analysis is done in three stepsFirst TE is evaluated according to T^] = E(Ptot - dEdt)to correct for the absence of a steady state Thesevalues can be compared with those from other experi-ments (eg for the purpose of size scaling) Secondthe following relation is used

I -prad (p) p dp dr

[ r T pheat (p) p dp drJo Jo

(1)

Equation (1) corrects for the radiation power emittedin the radial zone where the radiation and the heatingpower densities concur Edge radiation alone does notlead to a correction The TE

2) values should representthe actual transport properties of the quiescent H-modeThere is a certain arbitrariness in the choice of TE

2)

since it strongly varies with time (as is also shown inthe TE traces of Fig 47) We choose the TE

2) values atthe time where T ^ has a maximum (the maximum istypically reached one confinement time after theL-H transition thereafter 3p decreases because ofexcessive radiation)


THE H-MODE OF ASDEX

U13-

_ 010-

ujH

005-

0-

11513

xE(35cmh

XElSOcmly^

PNI=177MW

I

1I v

110 120 130015

010 j ^3 _

HIP

005

11447Tcl35cm)

PW1=348MW

105 110 115 120 125

t(s)

FIG 48 Energy confinement time TE at two radii and replacementtime TE

) for two H-discharges with different heating powers asobtained from TRANSP

In the third step a full transport analysis isperformed (using TRANSP) for two H-dischargesmdash one with the lowest heating power and one withthe highest heating power mdash to have a further checkon the data and the analysis

Figure 47 shows the power dependence of the globalconfinement times TE

I in the H-mode evaluated asdescribed above in comparison with TE values of theregular H-mode with ELMs Since H-phases with ELMsreach a steady state rE is calculated in this case simplyfrom TE = EPtot as described above In the quiescentH-mode TE does indeed show a power dependence Thefollowing scaling results are obtained for the H-phase(based on four data points only) TE

U = 86P-deg4Iplusmn005for Hdeg - D + and T^ = 132P-deg75plusmn0 16- for Ddeg - D + The curve in Fig 47 is the power fit to the Ddeg mdash D +

cases with the horizontal line indicating the resultsobtained with ELMs

Figure 48 shows the time dependence of TE asobtained from the full transport analysis which alsoyields the time dependence of T ^ The confinementtimes are plotted for the OH-phase the L-phase andthe H-phase The results shown are for the cases oflowest and highest power The rE values are obtainedfrom the transport analysis with allowance for radiationlosses and correspond to TE

2) as obtained from Eq (1)

[58] The T^ values obtained from the transport analysisare also plotted in Fig 47

We find in ASDEX the same power dependence ofTE in the quiescent H-mode as in JET Since such adependence is not observed in the regular H-mode itcan be speculated that in this case TE is predominantlydetermined by the energy losses caused by ELMssuperimposed on the heat transport losses so thatthe overall confinement time is independent of powerWe try to analyse this possibility in the following

3432 Effect of ELMs on global confinement

Since ELMs are external modes the global confine-ment is affected A discharge with frequent ELMsfollowed by quiescent phases is shown in Fig 20 Assoon as ELMs set in the particle and energy contentsdecrease It is difficult to assess the energy losses perevent From the changes in the slope of the j8p trace(Fig 20(a)) we conclude that rE

LM (for losses duringperiods of frequent ELM events with low amplitude)is about 110 ms

The energy lost during an ELM event can be deter-mined in three ways First Aj8p can be measureddirectly by using the equilibrium coils which areplaced within the vacuum vessel and have a sufficienttime response Typically 5 of the energy content islost in an ELM event (Fig 20(b)) Second the energyloss can be determined via the effect of an ELM eventon the plasma profiles i^ and Te are reduced in therange from the plasma edge to r ~ 15 cm (see Fig 16)The relative amplitude increases approximately linearlywith the radius with An^ne raquo ATeTe 10 atr = 30 cm Assuming that the Tj profile is affected byan ELM event in the same way as n and Te the energyloss can be integrated it is found that about 8 of theenergy is lost Third the energy loss of an ELM eventcan be evaluated by measuring the power flux into thedivertor chamber and onto the target plate with a peakpower density of about 1 kW-cm2 and a width of about4 cm (see Fig 36) The period of increased energyloss during an ELM event is approximately 04 msthe energy loss is found to be about 10 kJ which is inrough agreement with the other estimates The particleloss per ELM event is typically 1 x 1019 correspondingto ANeNe laquo 5

The repetition time of ELMs depends on the heatingpower At low power ELMs appear erratically and theELM period is not well defined At high power therepetition time of ELMs becomes constant (about 6 ms)and the ELM period is better defined Figure 49 showsthe distribution of the ELM frequency at the low and


ASDEX TEAM

111

Qgt 0

n

2 8

PN1= 12 MW

I I I

Id

32 MW

I2 4 6 8

Time between ELMs (ms)

10

FIG 49 Frequency distribution of the ELM period for low andhigh powers

high power ends of the scan It was not possible todetermine the amplitude distribution of ELMs Thelow power high frequency ELMs are clearly smallerin amplitude Assuming a constant ELM amplitudeAEE of 6 and a repetition time tELM = 6 ms weobtain a confinement time for the ELM losses alone

TELM _ EApoundtELM = 100 ms For large amplitude

singular ELM events the equivalent confinement timeis T|L M = 110 ms estimated for the integral effect offrequent low amplitude ELMs which dominate a lowpower (see Fig 20(a)) Because of the agreementbetween these data we assume that the losses dueto ELMs are largely independent of power under theconditions of our H-mode power scans Superimposingthe ELM losses onto the intrinsic and power dependenttransport losses we have calculated the power dependenceof the global confinement time Ti = (TE

2))- + (AEE)ti[MThe results obtained in this way (open circles in Fig 49)are also plotted in Fig 47 They agree roughly with themeasured TE data as obtained for the regular H-modewith ELMs

We conclude that the global energy confinement timedecreases with power when the H-mode is operated inthe quiescent H-phase as in JET However this con-clusion has a rather weak experimental basis becauseoperation in the H-mode without ELMs is limited onASDEX The lack of power dependence in the regularH-mode with ELMs could be due to the power depen-dent microscopic transport losses in addition to thosecaused by ELMs

The ratio of TE in the quiescent H-mode betweenJET and ASDEX (both with Ddeg - D+) as determinedfrom 3p without radiation correction is about 20which is a factor of two more than the ratio of thecurrents indicating an additional approximate scalingwith the major radius

344 Plasma species dependence

The confinement properties of neutral beam heatedASDEX discharges have been studied with hydrogendeuterium and to a smaller extent helium target plasmasTransitions to the H-mode have been obtained in allcases with some differences in the operational range(see Section 4) Figure 50 shows the density depen-dence of TE for Ddeg - D + Hdeg - H+ and Hdeg - D +

H-mode cases For comparison OH results are alsoshown As in the other confinement regimes theenergy confinement time of deuterium is superior tothat of hydrogen TEVIP(Ddeg - D+) = 023 ms-kA1T |7 I P (H 0 - D+) = 016 ms-kA1 TÎ P (Hdeg - H+)

= 011 ms-kA1 The power dependence of TE forHdeg mdash H+ is plotted in Fig 51 for L- and H-modesThe isotope effect on rE in both L- and H-phases hasbeen confirmed also by injection of two successiveNI pulses mdash one with hydrogen and one with deuteriummdash separated by an Ohmic phase these pulses wereinjected into a single deuterium discharge for both

100-

50-

I =03 MAP N I gt 2 MWNl

o Ddeg-raquoA Hdeg-raquo

0 2 I 6 8 10

ne (1013 cm3)

FIG 50 Density dependence of TE in the H-mode for Hdeg mdash H+Hdeg ~ D+ and Ddeg mdash D+ Ohmic results (fitted curves) are shownfor comparison


THE H-MODE OF ASDEX

60-

20-

02 MA

0 1 2 3

PNI CMW]

FIG 51 Power dependence of L- and H-mode results forHdeg - H

the L-phase (PNI = 12 MW) and the H-phase(PN = 155 MW) The ratio TpoundTpound[L] is 142 andTETJE [H] is 153 Although it is primarily the ion

mass which is different in these cases it seems thatthe superior confinement properties of deuteriumplasmas are a consequence of the electron transportsince electron heat losses dominate the energy balancein these discharges

345 Toroidal field dependence

The effect of the toroidal magnetic field B on theconfinement of neutral beam heated ASDEX dischargeswas investigated in a few series of experiments in whichB was varied in the range 16T lt B lt 26T whileall other plasma parameters were kept constant Theresults of various Bt scans are shown in Fig 52 Theydemonstrate that the toroidal field does not signifi-cantly affect the global energy confinement in both theL-mode and the H-mode

346 Summary of the TE scaling results

In the scaling studies we investigated the role of theexternal parameters r^ Ip Ptot and Bt and of the atomicmass Aj of the target plasma The scaling for TE can besummarized as

TE = C ne0 x IJ x Pdegt x Btdeg x A

Generally the confinement results for the H-mode aregiven by a combination of microscopic transport andenergy losses through an MHD process In the above

scaling results the parameter scaling of the impact ofELMs on the energy losses is partly included

The above scaling relation has been obtained fromthe outcome of well prepared and controlled single para-meter scans We have also constructed scaling relationsfrom a larger database in which not only the results ofoptimized scenarios are included We have divided thedatabase into two groups representing discharges fromshots No 4000-12000 and from shots No 17000-20000which makes it possible to assess also long term aspectsin the development of the confinement The followingresults have been obtained for Hdeg mdash D +

Early series rpound (ms) = 100 Ip057 P-deg50 n^032

Late series rpound (ms) = 090 Ip070 P-deg41 r^022

where Ip is in kA Ptot is in MW and ^ is in 10l3 cm3

The scaling result of the total data bank (154 datapoints) is

_H _ Q lt)g7 jO67plusmnOO7 p-O3OplusmnOO5 jjO221006

Figure 53 shows a histogram of the data versus theratio of T and the predicted values of the Goldston[59] scaling and the Kaye-Goldston [60] scaling TheH-mode results are typically a factor of two above theL-mode scaling results A factor of two is also obtainedin the comparison of the H-mode confinement timeswith an ASDEX L-mode database

347 Scaling of transport coefficients

Local (flux surface averaged) transport has beenanalysed by computer simulations of a series of

50-

Emdash 30H

10-

H-TYPE

_ g 1 1 bull

L-TYPE

IP= 295-315 kA

mdashr~15

1 1 1 1 1 120 25

B [ T ]

FIG 52 Variation of the energy confinement time with the toroi-dal field for L- and H-discharges The different symbols belong todifferent series of experiments


ASDEX TEAM

FG 55 Histogram of the rE values of the H-mode normalized

with respect to the predicted values

ASDEX L- and H-discharges The coefficientsobtained are for tangential co-injection of hydrogeninto deuterium target plasmas and for injection powersmuch higher than the Ohmic input power before theauxiliary heating The following empirical scaling rela-tions give a good fit to the measured profiles of theelectron density and the electron and ion temperaturesand to the poloidal beta in the L-regime the H-regimewith ELMs and the H-regime [33 42 43]

Xe(r) (cm2-s-) =

D(r) = 04

vin(r) = 05 D(r) Te(r)dr

where Co is a regime dependent factor CL = 62 x 105CH = 25 x 105 and C j = 13 x 105 Bt is in kGand qBt = r (BpR)~ with the major radius R in cmThe outstanding features of xe are the inverse Bp scalingand the lack of a density and temperature dependenceThe thermoelectric type relation for the anomalousinward drift is found to work in the above regimes[44] and is applied instead of the Ware pinch

4 OPERATIONAL RANGE OF THE H-MODE

The H-mode can be produced over a wide parameterrange and in ASDEX it is the L-mode which is limitedto small regions of the operational space For the H-modea threshold beam power is required and it is onlyaccessible in a density window The H-mode is achievedin hydrogen deuterium and helium discharges in single-null (SN) and double-null (DN) divertor plasmas witheither neutral injection (co- and counter-injection) orion cyclotron resonance heating For NI the powerthreshold depends on the plasma configuration thespecies the NI geometry the location of the gas inputvalve (divertor dome fuelling is superior to gas puffinginto the main plasma vessel) and on circumstances thatare less controllable such as the wall and recyclingconditions or the unpredictable occurrence of a largesawtooth in the L-phase which triggers the L-H transi-tion The configurational aspects of the L-H transitionare considerable The H-mode is most easily accessiblein the SN divertor configuration The lowest powerthreshold for the L-H transition ever observed onASDEX was obtained with counter-NI In this casea total power of 11 MW (60 NI power and 40OH power) was sufficient to trigger L-H transitions at420 kA 380 kA and 300 kA in a DN configuration atthe higher currents and in an SN configuration (verticalposition Az = -4 cm) at the lower current SN operationat 420 kA did not further reduce the power thresholdThe low power injected in these cases however didnot allow the H-mode to be maintained for more than10 ms after which time the occurrence of ELMscaused the plasma to switch back to the L-mode Evenat high powers the H-mode developed only for rathershort phases (a few ten milliseconds) and mostly collapsedbecause of a strong increase of radiation or because ofMHD problems H-mode studies with counter-NI aretherefore of a preliminary nature

41 Parameter dependence of theH-mode power threshold

Study of the power threshold Pthr for the H-mode is ofimportance because such a study may reveal the inherenttransition physics furthermore there seem to be crucialdifferences between the various experiments In JET[61] and DIII-D [62] it is observed that Pthr increaseswith the toroidal field in DIII-D it is found that Pthr

increases also with the density For JFT-2M an increaseof Pthr with current is reported [7] In particular theunfavourable dependence of Pthr on Bt and mayjeopardize the prospects of high fieldhigh density


THE H-MODE OF ASDEX

0 100 200 300 400 500

ltmdashmdashbullbullbullbullbullbull

( c )

10 20B (T)

30

FIG 54 Operational diagram for H-mode plasmas giving thepower threshold versus (a) line averaged density ne (b) plasmacurrent Ip and (c) toroidal field B

devices being able to operate in the H-mode Figure 54shows the operational range of H-discharges versus thesetting parameters of the discharge ie the density inthe OH plateau phase the current and the toroidal fieldThe power threshold is approximately 11 MW in theexperimentally accessible range no current or fieldlimitation has been observed The operational range ofthe H-mode is however restricted by a lower densitylimit (approximately 17 x 10l3 cm3) It is of impor-tance that the H-mode can be accessed at all currentlevels even up to the highest values Ip = 490 kAThese discharges are of interest because at qa = 2(B = 186 T) the highest densities are achieved onASDEX The quality of these low qa H-phases ishowever degraded possibly because of the increaseddensity A confinement time of 50 ms is obtained atn = 7 x 1013 cm3 and Ip = 480 kA

In contrast to the results of other experiments nopronounced dependence of Pthr on Bt Ip or rig has beendetected A weak dependence of Pthr on the density

cannot be excluded This could be understood fromconsiderations that the power threshold may be causedby the necessity to raise the edge electron temperature(or a related quantity) above a limiting value The actualsensitivity of P ^ on Hg may depend on recycling controland on the actual geometrical conditions which maybe less favourable in an expanded boundary topologythan in a closed divertor The aspects of recyclingcontrol will be discussed in Section 42

Because of the linear (or even steeper) increase ofPhr with B as observed in other experiments we havestudied this aspect in great detail Figure 55 showsHa radiation traces measured in the upper outer divertorchamber which serve as monitors for confinementphases at various toroidal fields and constant plasmacurrent Ip = 290 kA The power is scanned during thedischarge in three pulses In all cases the H-mode isrealized in the third pulse at Pot = 22 MW In thecase of the lowest Bt value the H-mode develops alreadyduring the second pulse at Ptol = 165 MW Fromthis observation it may be concluded that there isindeed a B dependence of Pthr which is not distin-guishable in a scatter diagram of all data (Fig 54(c))However we should point out that the sawtooth ampli-tude at the edge increases when B is lowered (in acase where Ip = const) as indicated for example bythe sawtooth modulation of Ha during the first pulseUnlike in the other cases the L-H transition is triggeredin this case by a sawtooth at the lowest field valueBt = 17 T leading to a Bt dependence of Pthr whichhowever is actually given by a secondary process

08 10 12 14 16 18

FIG 55 Temporal evolution of the HJDa radiation in the divertorchamber for three NI pulses with different beam power levelsThe variation of B from discharge to discharge is indicated

NUCLEAR FUSION Vol29 Nol l (1989) 1997

ASDEX TEAM

3-o L - Mode

H - Mode

B (T)

FIG 56 Operational diagram giving the power threshold as afunction of B The data points are the results of a detailed singleparameter scan carried out for this purpose

In a second scan the power in the three pulses wasreduced to 06 10 and 17 MW No H-phase appearedin the range 17 T lt Bt lt 27 T

Figure 56 summarizes these results in an operationaldiagram A linear relation between Pthr and Bt can beconcluded from Fig 56 (solid line) The slope of the line

iS a = ((PMax - PMin)PMin)((BMax BMin)BMin) lt 0 7

The slope of the boundary in Fig 54 is a = 0 Thecomparable values are a = 11 for DIII-D [62] anda = 37 for JET [61]

Because of the importance of the Bt dependence ofPhr we have also studied the duration of the L-phasepreceding the L-H transition in a B scan The ideabehind this investigation is that a potentially favourableB dependence of Pthr would also be indicated by ashortening of the L-phase when Bt is decreased Nosuch dependence has been found (see Fig 57)

Figure 58 exemplifies in single parameter scans thelack of an Ip dependence of P^ Plotted is the rise of3p (as deduced from plasma equilibrium) for the lowpower L-cases and the high power H-cases at threecurrent levels The L-H transition occurs at PNi mdash 2 MW(DN discharges) There is a lower density thresholdfor the development of the H-mode about 3 x 1013 cm3

(see Fig 59) which might slightly increase with thecurrent The results shown in Fig 59 are also obtainedfrom DN discharges There is also an upper densitythreshold for the development of the H-mode whichmdash under ASDEX heating conditions mdash is about7 x 1013 cm3 At high density achieved under theunfavourable conditions of gas puffing the H-modeedge conditions obviously cannot be maintained withthe given heating power A similar observation was

150

10CH

2Q

bull bull

16 18 20 22 24

B (T)

FIG 57 Duration of the L-phase preceding the L-H transitionversus toroidal field

25

20-

~ 15 bull

a

lt

10

5

0-

L

r

H-type

8

W L-type )pound

= 200 kA

300 kA

380 kA

PN CMW]

FIG 58 Increase in j3p + IJ2 (from plasma equilibrium) versusNI power For clarity the L-mode data points are omitted thetransition to the H-phase is indicated

made in PDX [63] With pellet refuelling under condi-tions of low edge cooling the upper density thresholdcan be increased (see Section 53)

The power threshold clearly depends on the divertorconfiguration and on the isotope mass of the targetplasma and the beam For the L-H transition lesspower is required in the SN configuration than in theDN configuration Figure 60(a) shows the data fromFig 54 sorted according to the plasma configuration


THE H-MODE OF ASDEX

Imdash_gtlaquo

LUP

70-

60-

50-

30-

20-

10-

0-

bullbull

4 V

bull bull bullL-type

3 1 2 3

V 1

ao

irftv

ON

6ooP0 Q 0

8tradedegc f i o o 0 ^0 X

bull

[101

tP aaa a

a a

^

Sraquoodego deg00 g

bulldeg Pbull 0 Ip

DN

PN

5 6

3cm3)

H-type

o

N

= 370 kAc 300 k A

gt2 MW

7

FIG 59 Energy confinement time versus line averaged density forL- and H-mode discharges (DN configuration) The vertical linesdenote the density threshold the dashed lines separate the datapoints plotted for two different current values

sCL

o

2 4 6

fie (1013crrv3)

FG 60 H-mode operational diagram for discharges with(a) various configurations (SN DN) and (b) various injection gases(Hdeg Ddeg) The power threshold is lower for the SN configurationand for Hdeg - D +

PN| (MW)

FIG 61 Increase in 3pl versus NI power showing the loweringof the power threshold with the SN configuration The SN TE valuesare lower mostly because of a smaller plasma cross-section

Pthr is about 15 MW for the DN configuration and11 MW for the SN configuration Figure 61 showsthe rise of 3p (deduced from diamagnetism) from asingle scan under controlled conditions a H-mode inthe SN configuration can be obtained at a power whichgives L-mode plasmas in the DN configuration (Therise of 3P is weaker in the SN configuration becausethe plasma minor radius is smaller) In the SN con-figuration also the lower density limit is reduced fromtypically 3 x 10l3 cm3 to 17 x 1013 cm3 Thepower requirements for the H-mode are reduced in theSN configuration only when the ion grad-B drift isdirected to the X-point otherwise Pthr is even higherThis aspect will be discussed in Section 93

Another scaling parameter for Plhr is the isotopemass of the target plasma and the beam Figure 60(a)also shows cases with Hdeg injection into H + (SN con-figuration) Pth is increased by a factor of nearly twoThe isotope effect on P ^ was confirmed under con-trolled conditions a hydrogen pulse and a deuteriumpulse were consecutively injected into a single D +

discharge at low power At Ptot = 1 3 MW thehydrogen pulse did not produce the H-mode whilethe deuterium pulse caused an L-H transition at alower power Ptot = 115 MW It is interesting tonote that the improved confinement with deuterium(see Section 344) has a positive effect also on Pthr

The question of whether the H-mode can only berealized under divertor conditions has been examinedon ASDEX with various limiter configurations iepoloidally closed ring limiters poloidal arc limitersplaced on either the high or the low field side


ASDEX TEAM

without insertsDV-I

with inserts

Pumping panels

DV-II Limiter

I Ti-sublimator

FIG 62 The different divertor configurations of ASDEX with which H-mode studieswere carried out The structures of DV-I were radiation cooled those of DV-II are watercooled The cross-section of the toroidal graphite belt limiter in ASDEX is also shown

mushroom limiters and a toroidally closed belt limiterplaced on the bottom side of the plasma The limitermaterial was iron in all cases and in a second versiongraphite The experiments with auxiliary arc limitersor with mushroom limiters showed that the H-mode isquenched at a separatrix-limiter distance of 25 cmirrespective of the limiter position (at the low or thehigh field side) In a recent analysis of belt limiterdischarges L-H transitions have been detected Theresults are presented in Section 43

A specific limitation for H-mode confinement studiesis the high beta stability limit In spite of its superiorconfinement the H-mode seems to have the same lowbeta limit as the L-mode [64] However this resultmay be an indication that different mechanisms areresponsible for the stability limit at high beta and for

the gradual degradation of confinement in the L-regimealready at low beta

H-mode plasmas conform to the beta limit scaling0MAX = CIpaBt [15] with C = 28 for a thermalplasma or with C = 35 when plasma rotation andbeam pressure are included At the beta limit ASDEXdischarges generally do not disrupt but the confinementdegrades irreversibly during NI causing beta to dropafter it has reached a maximum [65]

In conclusion the operational power range withinwhich the intrinsic confinement properties of theH-mode can be studied is small The H-mode can beestablished only at a power of more than 11 MWand because of the good confinement a relatively lowpower of 3 MW brings the plasma up to the beta limitClose to and at the beta limit the confinement proper-


THE H-MODE OF ASDEX

ties are additionally influenced by superimposed stabilityeffects

42 Study of the H-mode undervarious divertor topologies

The various divertor configurations which have beenrealized on ASDEX and explored for their impact onthe development and properties of the H-mode areshown in Fig 62 The H-mode was discovered inthe previous divertor configuration DV-I withoutinserts which had a closed divertor chamber Theonly connection between the main plasma vessel andthe divertor was through the divertor necks with avacuum conductance of 7 x 105 L-s1 for molecularhydrogen Many of the results described in this paperhave been obtained in this configuration In the config-uration DV-I with additional inserts around the centralmultipole coil the cross-section of the divertor neckwas further reduced In this configuration the vacuumconductance of the divertor neck was 32 x 105L-s~This modification did not cause any changes in thethreshold power and the confinement properties of theH-mode The modification of the divertor to the DV-IIconfiguration [66] was necessary to enable long-puseheating to be performed Since the modified divertorhad to be water cooled an additional and rather compactinsert was installed in the previous divertor chamberNow the divertor chamber is no longer well separatedfrom the main plasma vessel since by-passes establish aparallel conductance of 6 x 105 L-s1 These modifi-cations had a strong impact on the power thresholdwhich increased to more than 26 MW (the present limitof the long-pulse injection system on ASDEX) for theDN configuration and to twice the previous valuefor the SN configuration ( -2 4 MW) Clearly thecompeting edge effects which make sufficient edgeheating impossible are intensified in this geometryIn contrast to our previous experience sawteeth do notdisappear during the H-phase which also indicates thatedge heating is less effective Furthermore the qualityof the H-mode confinement is degraded and after theL-H transition the increase in beta is only 50 of thepreviously obtained values The main reason for thisconfinement degradation is a higher ELM frequencyA tentative explanation of the new situation is thatafter the L-H transition the edge density quickly risesowing to the higher recycling through the by-passeswith the consequence that the edge temperature doesnot increase sufficiently to stabilize the H-mode beforethe increased edge pressure gradient gives rise to anELM Because of these unfavourable aspects the new

FIG 63 Density profile development in the quiescent H-mode forvarious divertor configurations Each case starts with the lastL-mode profile just before the L-H transition There is a successiverise in density The profiles are measured by Thomson scatteringwith a repetition time of 17 ms (a) DV-I closed configuration(b) DV-II open configuration (c) DV-II closed configuration

divertor chamber was again separated from the mainplasma vessel as much as was technically possible

To study the role of the recycling gas in more detailonly the upper divertor chamber was closed Thismeasure reduced the H-mode power threshold to theoriginal level for upper SN discharges The effect ofrecycling on the parameter dependence of the H-phasewas studied in quiescent H-phases in the DV-I andDV-II configurations with open and closed divertorThe variation of the density profile shape and theincrease of the electron temperature or density at theplasma edge were found to depend sensitively on theprevailing recycling conditions Under closed divertorconditions the density profile broadened moderately butremained peaked throughout the quiescent H-phaseThe most peaked profiles were obtained in DV-I andthe broadest ones in the open configuration of DV-II


ASDEX TEAM

1 2 3 4 5

ne (1013crrv3)

FIG 64 Edge electron temperature versus edge density(raquo 25 cm o 5 cm x 75 cm bull 10 cm inside the separatrix)

for the L-phase and the H-phase(a) Edge profiles for the quiescent H-phase (H) and after theonset of ELMs (H DV-I)(b) Profiles for the preceding L-phase (Lt) and the subsequentL-phase (ty and for the quiescent H-phase (DV-II)The dashed curves follow the excursion of the parameters75 cm inside the separatrix

In this case even hollow profiles were obtained Theprofile development during the quiescent H-phase isshown in Fig 63 beginning with the L-phase in eachof the cases The density builds up successively Theprofiles are measured every 17 ms The variation ofthe edge temperature and density at the L-H transitionis plotted in Fig 64 for the closed DV-I configurationand the open DV-II configuration Data points areshown from r = 375 cm to r = 30 cm in steps of25 cm (see the various symbols) The plots of theL- and H-profiles in the quiescent phase (H) and inthe phase with ELMs (H) in Fig 64(a) document thestrong rise in edge temperature with a modest rise indensity In the open divertor configuration (Fig 64(b))the rise in edge temperature is modest but the densityincreases strongly The profiles are shown at the end ofthe L-phase preceding the L-H transition at the end of

the quiescent H-phase and at the beginning of the secondL-phase The dashed lines show a plasma cycle fromthe L-phase to the H-phase and then to the phase withELMs in case (a) and to the second L-phase in case (b)From our studies with various divertor configurations wecome to the conclusion that the development of the densityprofile depends on the actual recycling conditionsThis may explain some of the differences in the densityprofile shape in the H-mode as observed in variousexperiments [61 62] The study of various divertorconfigurations demonstrates that the edge pressurealways increases after the L-H transition whether itrises mainly via the density or via the temperaturedepends on the recycling conditions

43 Limiter H-mode of ASDEX

The discovery of the H-mode under limiter conditionsin JFT-2M [7] and in other experiments (see Section 8)stimulated thorough analyses of limiter dischargeson ASDEX an axisymmetric belt limiter had beenused in these discharges Figure 60 shows the shapeand position of this limiter in a poloidal cross-sectionThe limiter material is graphite In limiter dischargesthe multipole coils were not in operation

10

FIG 65 Line averaged density along two chords Ha intensityemitted in the midplane and 3pW and ^^ for a limiter dischargeThe transition to the H-mode is indicated by the vertical line(Because of incomplete compensation fif can only be used forrelative measurements)


THE H-MODE OF ASDEX

These toroidal limiter plasmas showed L-typeconfinement in all cases investigated Therefore nodetailed analysis of the discharges was carried outA recent study showed that in some of these dischargesthere were indeed L-H transitions which had previouslynot been noticed Figure 65 shows the density the Ha

measured in the plasma midplane and the poloidal betaestimated from plasma equilibrium and diamagnetismThe dashed line indicates the transition to the H-modeAt this transition both the density and the energy con-tent increase the recycling decreases the edge electrontemperature increases and ELMs set in which showthe characteristic changes in density edge electrontemperature and horizontal plasma position in theH-phase the high-Z impurity radiation increases Theincrease in beta after the L-H transition is typicallyonly 10 (in divertor discharges it is 100) Thesmall increase in beta after the L-H transition inimiter discharges of circular cross-section has alsobeen observed in other experiments

The only new information from the limiter H-modedischarges on ASDEX is that the H-mode can also berealized with a bottom limiter and not only with aninside limiter Although the relevance of this findingis not studied here it should be mentioned that the iongrad-B drift was away from the limiter (see Section 93)

5 USE OF OTHERHEATING AND REFUELLING TECHNIQUES

FOR H-MODE PLASMAS

51 ICRF heating

Plasmas in the H-mode can also be operated with acombination of NI and ICRF with either of thembeing the main heating method It is also possible toproduce an L-H transition with ICRF alone [67]

511 Hydrogen minority heating

We have succeeded in producing the L-H transitionon ASDEX with hydrogen minority heating only inthe upper SN configuration (ion grad-B drift towardsthe X-point) at a coupled power of 18 MW Thedrastic changes of the SOL (discussed in Section 25)give rise to a sudden change of the coupling conditionsIn the experimental period from 1984 to 1986 one ofthe generators then invariably terminated the operationthis was due to voltage breakdown in one of the vacuumtransmission lines with the consequence that this H-modewas only transient [67] Subsequently the ICRF system

(cm)

MoV ctldiv)

(QU)

FIG 66 H-mode discharge in experiments with 10 hydrogen

minority heating (PNI = 187 MW PICRH = 19 MW)

was upgraded to withstand higher voltages and can nowbetter cope with the changes in the SOL parameters atthe L-H transition Since the heating power requiredfor attaining the H-mode is higher in the DV-II config-uration than in the DV-I configuration (see Section 42)no H-phases were achieved with ICRH alone TheH-mode was only obtained with additional injectionof deuterium into deuterium plasmas with a minimumpower of gt34 MW (PNI = 187 MW PIC gt 16 MW)Figure 66 shows an example of a 025 s long H-phaseobtained with NI -I- ICRH The L-H transition wasclearly triggered by ICRH and ended because of thehigh density The variation of the antenna resistanceduring the H-mode can be explained by the occurrenceof eigenmodes due to the density increase [68] Theconfinement time is degraded by frequent ELMs sothat it is only 20-30 higher than for the best L-modedischarges In some cases where the density rise issmaller owing to stronger ELM activity the H-modecan last for the whole ICRH pulse length (05 s)


ASDEX TEAM

512 Second-harmonic hydrogen heating

With second-harmonic hydrogen heating the H-modehas so far only been achieved with the DV-I configura-tion and in combination with NI It is of interest tonote that it is easier to achieve the H-mode with theion grad-B drift away from the X-point This isthought to be due to the greatly reduced impurityradiation under this condition

52 Lower hybrid heating and beam current drivein the H-mode

The combined operation of lower hybrid heating andNI has been studied on ASDEX in a wide parameterrange [69 70] The use of lower hybrid current drivein combination with the H-mode however was limitedto a very narrow density range The upper density limitfor lower hybrid current drive was at Hg = 2 x 1013 cm3

for the 13 GHz system This value was only slightlyabove the lower density threshold of h laquo 17 x 1013 cm3

for the H-mode which was regularly exceeded by thefast density rise immediately after the L-H transitionDuring the H-phase lower hybrid powers of up toabout 1 MW could be transmitted mdash the same levelas was achieved in Ohmic target plasmas The L-Htransition never caused failures in the RF transmissionThe power coupling remained comparable to that inthe L-mode for the whole duration of the beam pulseup to 04 s Nearly half of the total plasma current inthe target plasma was driven by lower hybrid heatingWith neutral beam heating the loop voltage dropped tozero and the total current was driven non-inductivelyThe strong density rise during the H-phase howeveragain led to an increase in the loop voltage The electrontemperature profile was peaking during lower hybridcurrent drive The central temperatures rose to valuescomparable to those of the subsequent H-phase

After the L-H transition a pedestal in the electrontemperature was formed close to the periphery and theradial profile of Te(r) assumed the same shape as inthe case of an L-H transition from an Ohmic targetplasma

Under conditions without inductive current drive theplasma current could be kept constant at 150 kA by NI(otherwise it decays with its LR time) with the beamdriven current regular H-phases could be achieved

53 Pellet refuelling in the H-mode

Pellet refuelling of H-mode discharges was alsopossible on ASDEX with the use of a centrifuge for

multi-pellet injection [71] The small pellets contribute1 x 1013 cm3 each to the volume averaged densityTheir penetration depth is small owing to the highelectron temperature at the plasma edge Neverthelessthe deleterious edge cooling of standard gas-puffrefuelling could be avoided and the upper density limitfor the H-mode was raised from Hg = (7-8) x 10l3 cm3

to 12 x 1014 cm3 The density profiles are still broadand more characteristic of the standard H-mode than ofpellet refuelled discharges The high density pelletdischarges however are plagued by frequent ELMswhich are probably responsible for the low confinementtime of TE laquo 40 ms (not corrected for radiation)

6 PHYSICS ASPECTSOF THE L-H TRANSITION

The L-H transition can be viewed as a bifurcationphenomenon in the sense that the properties of thefinal state (eg the confinement properties) differwidely while the properties of the initial state (theplasma parameters of a discharge just before theL-H transition compared with those of a dischargeremaining in the L-mode) can hardly be distinguishedfrom each other experimentally [72] Figure 67compares a few typical diagnostic traces of twoconsecutive discharges mdash an L-discharge followed byan H-discharge Operation close to the power thresholdoccasionally yields L- and H-discharges with identicalexternal parameters for the plasma and the beam Thearrows indicate the moment of transition The tableauof diagrams in Fig 67 contains traces which documentthe variation of the external parameters such as thecurrent the density and the horizontal plasma positiontraces which illustrate the recycling conditions in themain plasma and in the divertor chamber the impurityconditions (main plasma radiation iron radiation andloop voltage) and the development of the energy contentof the two discharges Within the amplitude of therandom fluctuations the plasma parameters at theL-H transition are identical with those of dischargeswhich remain in the L-mode throughout the pulseThis comparison shows that the search for the decisiveparameter causing the plasma to carry out the L-H tran-sition will not be easy This search has to concentrateon the plasma conditions at the end of the L-phaseFor an understanding of the physics of the L-Htransition only the L-phase should be considered andthe structural elements of the fully developed H-phase(such as the changed profiles or the steep edge gradients)should not be included For an understanding of the


THE H-MODE OF ASDEX

Ic

cQJ

4-

2-

r

JO

JQ

11 12

o

c

cQJ

curr

d

[asm

a

01

d

Vol

t

a oo

u)

JO

3co

d

da

rb

u)

co

d

dcccot_

4-

2-

bull

AU

-

m

o-

o-

0-

Jp

UiX u l

FB )

Fe X

bull L (6124)

- H (6125)

lasma

I

1

If Main plasmaij

Oivertor

i bull bull i 1

t

r u

S 2-co

Zn

S o

-2-

2-

1-

bull 1 -

11 12 11 12

Us)

FIG 67 Comparison of plasma parameter variations during the NI phases of two consecutivedischarges the first being an L-discharge and the second an H-discharge The arrow indicatesthe L-H transition (H^CH (Htradev) = Ha radiation in the main plasma vessel (divertor chamber))

full extent of confinement improvement during theH-mode however these modifications may also betaken into account because the confinement continuesto evolve and improve during the H-phase

61 Role of the edge electron temperature

A minimal heating power is required for the L-H tran-sition and the H-phase develops after an L-phase Thisbehaviour points to the existence of a threshold which

has to be surpassed for the H-mode to develop In theinitial phase it takes some time before the plasma issufficiently heated if the power is too low the thresholdis not reached at all These observations indicate that itmay be the electron or the ion temperature or a relatedquantity such as pressure temperature gradient electricalconductivity or collisionality which is responsible forthe sudden change in confinement The search for thecrucial parameters first concentrated on the electrontemperature because it was observed that no H-mode


ASDEX TEAM

o 0

mo

^ 6

1 2 -

8672

8671

-J

10 11 12 13 14 15

t (sJ

FIG 68 C III line radiation and edge electron temperature of twodischarges into which methane was injected during the NI phasefrom 114 s to 124 s (No 8671) and from 122 s to 132 s(No 8672) The impurity radiation cools the plasma edge andaffects the L-H transition Ip = 038 MA ne = 4 x lO13 cm3PN = 30 MW

611 Addition of impurities

Artificial impurities have been introduced in dischargesto study in detail their detrimental effect on the develop-ment of the L-H transition Figure 68 compares twocases with methane injection into the discharge at thebeginning of the NI pulse (solid curve) and during theH-phase (dashed curve) When methane is injected atthe beginning the edge electron temperature is keptlow and the L-phase is prolonged When the impuritypulse is switched off the electron temperature risesand the transition to the H-phase occurs By contrastwhen methane is injected during the H-phase the edgetemperature is reduced and the H-L transition occursat about the same Te value (Without methane injectionthe H-L transition occurs 30 ms later at about the sametemperature) When neon (high Z) is used instead ofmethane smaller amounts of it are sufficient to suppressthe H-mode

When one considers these results one may beinclined to correlate the suppression of the H-modein limiter discharges with excessive impurity (andrecycling) cooling at the edge

develops shortly after opening of the plasma vesselwhen the walls have not yet been cleaned and theplasma suffers from excessive impurity radiation Wedescribe now some experiments which indicate theimportance of the electron temperature (or a relatedquantity) for the L-H transition In these experimentsthe electron temperature ECE diagnostic has been usedsince this is the only diagnostic which gives a continuousreading with sufficient time resolution In the course ofthese experiments we came to the conclusion that it isprobably the electron temperature of the plasma peripherywhich determines the development of confinement [72]In the following diagrams we therefore plot the varia-tion of Te at the outermost channel located at 31 cmin the midplane on the high field side where measure-ment with the ECE diagnostic is possible Because ofthe horizontal plasma shift during the discharge themeasuring point is about 7 to 8 cm away from theinner separatrix

6-

EV

CO

gt-8-c

o Hbull L

PNI = 2M MWI P = 380 kA

ARL [cm]

FIG 69 Variation of the edge electron temperature when theoutside poloidal limiter wing is moved to the plasma surfaceThe data points for ARL = 0 are obtained from limiter dischargeswithout energized divertor coils


THE H-MODE OF ASDEX

8-

E L

A H-type (Divertor)+ L-type Divertor)bull L-type (Limiter)

N

2

IMW]

FIG 70 Variation of the edge electron temperature with thebeam power in limiter discharges and in L- and H-type divertordischarges Ip = 038 MA ne = 3 X JO13 cm3 (H)ne lt 2 X JO13 cm3 (L) and ne = 5 X 1013 cm3 (limiter)

612 Development of the electron temperaturein limiter discharges

Different limiter configurations have been inves-tigated as discussed in the previous sections Alllimiter discharges showed a deterioration of the energyconfinement even in the parameter range of the H-modeExceptions were a few belt limiter discharges asdescribed in Section 43 Figure 69 shows the variationof the electron temperature at r = 31 cm when theoutside limiter wing is moved towards the plasmasurface (The limiter position was changed from shotto shot the divertor coils were deactivated only inARL = 0 discharges) At a plasma-limiter distanceARL of lt 25 cm (roughly one to two density ortemperature fall-off lengths in the SOL) the edgetemperature decreases sharply and the H-regime issuppressed The edge temperatures are a factor ofabout three lower in limiter discharges than in H-typedivertor discharges These results are also supported byThomson scattering measurements at the edge and asimilar decrease of the edge ion temperature is observed

In Fig 70 the variation of the edge electron tem-perature (r = 31 cm) with the beam power in limiterdischarges is compared with that in L- and H-typedivertor discharges A linear increase of Te with PNI isobserved for the L- and H-type divertor dischargeswhile the limiter discharges show a very weak depen-dence on PNI The comparison indicates that the diver-

tor configuration allows the edge temperature to evolvewithout constraints In limiter discharges howeverthere seems to be a mechanism (eg impurity erosionfrom the limiter increasing with beam power) whichkeeps the edge electron temperature largely indepen-dent of the beam power thus constituting an additionalboundary condition L-type divertor discharges (obtainedby operating below the density threshold) also exhibit alinear increase of the edge electron temperature buteven at the maximum available injection power Te

remains below the threshold for the L-H transitionThe low density case indicates that the H-mode mightultimately also be accessible but at a higher power

613 Post-beam pulse H-phase

An interesting technique to unravel the crucialparameters for the L-H transition is to heat the plasmawith a power just below the power limit Operationunder such marginal conditions increases the sensitivitybecause already small parameter changes which hardlyaffect the global plasma conditions have an impact on the

E

FIG 71 Line averaged density at the plasma centre (z = 0) andalong the chord z mdash a2 HaDa radiation in the divertor chamberand electron temperature at two radial positions The H-phase(between dashed lines) occurs after switching on the NI pulseduring a phase of elevated temperature


ASDEX TEAM

transition conditions This technique has been success-fully applied in different investigations

For beam heated plasmas it is a common observa-tion that the electron temperature rises transiently whenthe beams are switched off [73] In the short phasefollowing the beam pulse when the orbiting beam ionsstill heat the plasma (slowing-down time ~ 15 ms) theheating per particle is suddenly improved when theflux of cold electrons injected with the beam atoms isterminated This phenomenon has been dubbed post-beam pulse electron temperature rise [73] Figure 71shows such a case with medium heating power wherethe H-phase develops shortly after the beam pulse isswitched off During beam heating the particle confine-ment is of the L-type The H-phase is short becausethere is no auxiliary heating power but it is longenough to be interrupted by a few ELMs

614 Comparison of L-H and H-L transitions

Because of the confinement sequence OH-L-H-L-OHthe plasma properties at the L-H transition in the initialbeam phase can be compared with the H-L transitionafter the beams are switched off The comparison isonly meaningful when the conditions for the two tran-sitions are rather transparent with a longer L-phasepreceding the L-H transition and with an H-L transi-tion that is not disturbed by ELMs Such a case isshown in Fig 72 The H-L transition occurs 40 msafter the beam pulse is switched off in a phase wherethe plasma is cooling down As indicated in Fig 72the transition back to the L-phase occurs roughly at thesame peripheral electron temperature as the transitionto the H-phase All other plasma parameters and alsothe plasma profiles are widely different at these twomoments This observation indicates that it could bespecifically the edge electron temperature which hasto surpass a certain threshold for the L-H transitionto occur

615 Sawteeth as H-mode trigger

An interesting feature of the L-H transition is that itcan be initiated by a sawtooth crash (see Section 23)Detailed measurements with good time resolutionshowed that the triggering of the H-mode by a sawtoothoccurs when its thermal wave arrives at the plasmaedge This trigger mechanism which has also beenobserved by other authors [5] is the most convincingevidence of the role of Te at the plasma periphery (orof a parameter depending on it) in the L-H transition

Generally the transition to the H-mode occurs undernon-stationary plasma conditions when the edge electrontemperature is still increasing At low q and low injec-tion power the L-H transition can be triggered by asawtooth In Section 41 it is described how sawteethcan affect the dependence of the threshold power onthe toroidal field A sawtooth triggered L-H transitionis shown in Fig 12 in comparison with an L-typedischarge (The only difference between the twodischarges is the vertical shift the H-discharge is anupper SN discharge and the L-discharge is a lowerSN discharge) Figure 12 shows the edge temperatureand the variation of the line averaged density r^ duringthe NI pulse for the two cases Sawtooth disruptionsappear as sharp drops in the density signal As shownin Fig 12 (arrows) the heat wave of a sawtoothincreases Te at the periphery but after its passageTe decreases again

A sawtooth which causes the L-H transition alsoraises the temperature at the edge Afterwards howeverthe temperature does not decrease as in the case of anormal sawtooth but it remains at the high level andin the course of the H-phase it increases further as aconsequence of the improved confinement The heatpulse is dissipated in the plasma periphery Actually

t Is]

FIG 72 Peripheral electron temperature line averaged densityalong two chords and HJDa radiation in the divertor chamberduring NI heating the L-H and H-L transitions are indicatedby arrows


THE H-MODE OF ASDEX

10 11

FIG 73 Line averaged density Ha radiation in the divertorchamber and ECE electron temperature during an L-dischargewith large sawteeth Two sawteeth give rise to a short H-phase

a sawtooth which triggers the L-H transition usuallydoes not give rise to a thermal or particle pulse at theneutralizer plate as a normal sawtooth would do Sucha case is shown in Fig 73 where the line averageddensity i^ the Ha radiation in the divertor chamberand the electron temperature Te are plotted at fourdifferent radii of an L-discharge with large sawteethand a heating power close to the power threshold Thesawteeth modulate Te in the known form of a reductionwithin the q = 1 surface and a pulse-like variationoutside of it caused by the thermal wave travelling tothe plasma surface The plasma density is modulated ina similar way The sawteeth also modulate the Ha signalin the divertor chamber causing a signal rise therewhich is very conspicuous during the beam heatingphase Two examples of sawteeth which behave differ-ently are also shown in Fig 73 namely large sawteeth(only one is documented by the Te diagnostic) whichcause an L-H transition Comparison of the parametervariation caused by a sawtooth in the L-phase with thatof a sawtooth triggering the H-phase reveals a distinctdifference in the outer plasma zones but a rather similarbehaviour in the plasma core A regular sawtooth givesrise to a fast pulse-like temperature variation in theplasma periphery the energy pulse travels across theseparatrix along the SOL into the divertor chamberand causes an increase of the Ha radiation there Asawtooth correlated with an L-H transition leads to a

slow decay of the temperature in the plasma peripheryand a reduction of the divertor Ha radiation

Although the results presented above indicate thatthe L-H transition is connected with the high edgeelectron temperature it is not clear whether it is thetemperature itself or a related quantity which causesthe L-H transition The different relative variations ofTe and ^ at the edge which depend on the recyclingconditions (see Section 42) may indicate that a suffi-ciently high edge pressure is of importance

62 Formation of a transport barrierat the plasma edge

In the previous section the effect of a high electrontemperature at the plasma edge has been discussed Ata sufficiently high Te value a transport barrier developsjust inside the separatrix which impedes the outflow ofenergy and particles and initiates the H-phase [40] Thedevelopment of the transport barrier has been studiedby applying the same techniques as described abovenamely operation under marginal power conditions inthe L-mode but with large sawteeth The parameterchanges in the plasma boundary have been monitoredby the soft X-ray (SX) diode array with high time andspace resolution capabilities As an example two tracesare shown in Fig 74 Diode 1 views the SOL anddiode 2 views mainly the plasma inside the separatrixThe distance between the two viewing lines is 25 cmWe compare the parameter changes due to two con-secutive sawteeth mdash a regular one in the L-phase and asawtooth which causes an L-H transition The dynamicsof the L-H transition becomes evident from Fig 74since the two events occur in sequence and only 50 msapart The thermal wave of a sawtooth during theL-phase causes Te to increase first in the main plasmaperiphery and subsequently in the SOL where the Te

variation modulates the SX signal This signal variationafter a sawtooth event is well known

The SX traces shown in Figs 74 and 75 are obtained withtwo SX cameras with different viewing geometries The edgechannels shown in Fig 74 are vertical (see insert in Fig 74) andthose shown in Fig 75 are tilted (see insert in Fig 76) Theadvantage of this viewing geometry is that the actual position ofthe separatrix at the tangent point mdash obtained from equilibriumcalculations mdash is known with higher accuracy ( mdash 05 cm instead ofmdash 1 cm as in the midplane) The disadvantage of the tilted channelsis that they measure the signals from both the plasma edge and theX-point (for the SN configuration it is the X-point formed by theouter separatrix) while the vertical chords are terminated at thevessel wall This difference in viewing geometry may be the reasonwhy the SOL signal is zero in Fig 74 but decreases to a finitelevel in Fig 75


ASDEX TEAM

2 0

Plasma

A2 1

H mdash25 cm

10 ms

FIG 74 Soft X-ray radiation during the L-phase with largesawteeth Diode 1 views the SOL diode 2 views mainly theplasma within the separatrix One sawtooth sth(H) gives rise to atransient H-phase

Te (keV)

t (s)

FIG 75 Time evolution of (a) the ECE electron temperature(measured by electron cyclotron emission) (b) the line averageddensity (c) the Da radiation in the divertor (d) the reflected fluxlttgta from the neutralizer plate and (e) four SX traces from theplasma edge (The ECE traces are interrupted by a chopper)

The large sawtooth which triggers an L-H transitionsth(H) gives rise to a totally different behaviour Theedge electron temperature does not show the transientvariations caused by a passing thermal wave TheL-H transition occurs during the sawtooth rise whichis initially still measurable At the instant of transitionthe signal of the SX diode viewing the SOL sharply

decreases Within the separatrix the sawtooth triggeringthe H-phase causes a continuously rising signal Justafter the transition an ELM occurs an ELM alsoterminates the short H-phase

Figure 75 illustrates the same sequence of sawteethas shown in Fig 74 with further SX channels Alsoplotted are the electron temperature in the main plasmafor four radial positions the line averaged density Hethe Ha radiation in the divertor chamber and the atomflux 0a emerging from the target plate Supplementingthe information of Fig 74 Fig 75 shows that thesawtooth triggering the L-H transition has a large Te

amplitude at the edge and the peripheral Te valueremains high throughout the H-phase whereas thesawteeth in the L-mode show an evanescent behaviourAlso plotted in Fig 75 are the power and particlefluxes into the divertor chamber which are due to asawtooth and which modulate the Ha radiation andthe atom flux ltjgta in a pulse-like fashion The differentbehaviour of these divertor signals is clearly indicated inthe case of the sawtooth which triggers the L-H transi-tion because now the power and particle fluxes into thedivertor chamber associated with the sawtooth areblocked and Ha and ltfgta decrease The density duringthe H-phase rises

1-

units

)

p

0

001-y

r0I y

Single-Nu

s

SX-lntensityNS

- bull

1 Plasma

-5 -10 -20

r-re (cm)

-30

FIG 76 Radial profiles of the SX radiation (2 fim Be filter) inthe L-phase before the L-H transition and shortly afterwards atAt = 20 ms Ip = 375 kA B = 22 T ne = 33 x W3 cm3PNt = 08 MW The insert depicts the observation geometry

2010 NUCLEAR FUSION Vol29 No II (1989)

THE H-MODE OF ASDEX

FIG 77 Temporal development of the edge electron pressuregradient during the L-phase (circles) and during the quiescentH-phase (squares) The profiles are measured every 17 ms Afterprofile No 8 the plasma transits back to a second L-phase

The formation of a transport barrier as discussedabove leads to reduced outflow of energy and particlesinto the divertor chamber improved confinementproperties of the the plasma and steep gradients at theplasma edge with subsequent occurrence of ELMs

The drastic changes of the plasma profile at theedge as monitored by the SX diagnostic with the bestspatial resolution are shown in Fig 76 The SXradiation is given by the product of certain functionsof rig and Te A steep electron pressure gradient causesstrong radial variation of the SX radiation The profilesof Fig 76 have been obtained just before the L-Htransition and 50 ms thereafter

The electron heat diffusivity in the edge transportbarrier xe is about 5 X 103 cm2-s as calculatedfrom the steep Te gradient in Fig 28 and the poweroutflux This value is plotted in Fig 40(b) togetherwith Xe as obtained from the transport analysis

The radial extent of the edge transport barrier hasbeen estimated from the rise in the edge pressureFigure 77 shows the pressure gradient as it developsbetween the separatrix and 10 cm inside the separatrixThe pressure gradients during the preceding L-phaseare shown for four time points (solid points) The firstprofile measured after the L-H transition is denotedby 1 The period between the succeeding profiles is17 ms The pressure gradient rises at the edge thelargest change occurs 5 cm inside the separatrix andthere is no further change ~ 10 cm inside the separatrixFrom these results and from similar observations inother quiescent H-phases it becomes obvious that theedge barrier first develops at the separatrix and sub-

sequently expands inwards The change in gradientcaused by the transport barrier seems to reach typically8 cm inside the plasma This distance is longer thanthe shear length at the separatrix and also longer thanthe banana width of thermal particles at the edge

63 Microscopic turbulence in H-phases

631 Density fluctuations

Neutral beam injection produces complex changes ofthe density turbulence as observed by collective laserlight scattering The scattering system uses a 100 mW119 m continuous wave CH3OH laser and homodynedetection with a Schottky diode (for a detailed descrip-tion see Refs [74 75]) The wave number range is25 cm1 lt kx lt 25 cm1 with a resolution ofplusmn125 cm1 and can be scanned in a single plasmadischarge Five chords with different distances fromthe plasma centre can be accessed per discharge(Fig 78) The spatial resolution is plusmn16 cm perpen-dicular to the laser beam and chord averaged along theline of sight in the dominant wave number rangekplusmn lt 10 cm1

In the Ohmic phase the fluctuation spectra are foundto be consistent with the assumption of a density gradientdriven drift wave turbulence in a wide range of para-meters [74 75] During NI heating the L-phase is ingeneral characterized by an increase of the total scatteredpower compared with the Ohmic phase as well as a

view A-Aentrance

A - windows

0degodegodegexit

windows

FIG 78 Poloidal section of ASDEX showing the beam pathsinside the plasma vessel in the different chords and the windowarray The distances from the plasma centre are 0 cm 105 cm25 cm for the horizontal chords and 30 cm 395 cm for thevertical chords The scattered beams are schematically indicatedby dashed lines


ASDEX TEAM

24942

SCATTERED SIGNAL POWER

18

FIG 79 Scattered signal power Ps measured in the equatorialchannel for kx = 3 cm1 The frequency channel is 55-400 kHzAlso plotted in the lower part are the line density the NI monitorand the Da signal in the upper divertor chamber

S SCATTERED SIGNAL

SIGNAL

LINE DENSITY

23463

H

116 118t (S)

120 122

FIG 80 Scattered signal power Ps measured close to theseparatrix at the transition from an L-phase to a quiescent H-phaseat lcplusmn =3 cm1 (outer vertical chord) Also plotted are the Da

signal in the divertor and the electron line density 30 cm fromthe plasma centre

dramatic broadening of the frequency spectra [74] Inaddition sawtooth activity strongly affects the scatteringsignals at low kx [75] Coherent MHD modes duringadditional heating as observed with Mirnov coils atfrequencies up to 25 kHz are obviously associatedwith low wave number density fluctuations asobserved on the FIR scattering signal

In quiescent H-phases the total scattered powerdecreases significantly to about the Ohmic level This

is illustrated in Fig 79 which shows the temporaldevelopment of the frequency integrated scatteringsignal in a sequence of transitions OH-L-H-L-OHwithin one shot The scattering signal of Fig 79 wasrecorded at kx = 3 cm1 It was measured in theequatorial plane where the scattering system viewsmainly poloidally propagating fluctuations The lowlevel of the scattered signal in the quiescent H-phaseappears even more striking since it occurs during apronounced increase of the mean electron densitycharacteristic of this phase which is also shown inFig 79 A similar behaviour was reported from amicrowave scattering experiment on PDX [76] OnASDEX a clear decrease of the scattered power duringtransitions to quiescent H-phases was also observed atthe plasma boundary near the separatrix where thescattering system views mainly radially propagatingfluctuations This is illustrated in Fig 80 which showsscattering signals measured when the scattering beamaxis was located 1 cm inside the separatrix A similarbehaviour of the scattering signals was observed whenthe plasma position was shifted inside so that thescattering beam axis was located 05 cm outside theseparatrix A comparison with density profiles measuredwith the lithium beam probe in the separatrix region(see Fig 81) rules out the possibility of explaining thereduced level of the scattering signals during the quies-cent H-phase in Fig 80 simply as the result of a densitydrop andor a decrease in the density gradient lengthIn the sampling time interval of 1 ms the scatteringsignal power Ps decreases simultaneously with the drop

E 2u

POSITION OF LASER BEAMAXISPOSITION OF SEPARATRIX

2ms AFTER L-H TRANSITION6 ms BEFORE L-H TRANSITION

23445

FIG 81 Electron density profiles in the separatrix region beforeand shortly after the L-H transition (measured by a lithium beamprobe)


THE H-MODE OF ASDEX

-50 -25

T (us)

FIG 82 Cross-correlation Junction of fluctuations in the Ha lightbetween a signal channel and other channels at different separa-tions for L- and H-phases The poloidal distance varies between6 and 36 mm

of Da in the divertor chamber The rapid drop of thefluctuation level at the edge is in clear contrast to theslower decrease of the core fluctuation level At theL-H transition the frequency spectra broaden showinga distinct increase at the high frequency end this maybe due to an increase in the poloidal rotation velocityof the plasma In H-phases with ELMs the scatteringsignals are dominated by these modes and behaveirregularly

Further investigations are necessary to obtain aconclusive picture of the density fluctuation behaviourat the L-H transition At present it cannot be decidedwhether the lower fluctuation level during quiescentH-phases is the cause or the consequence of theimproved confinement It should be kept in mind thatthe density fluctuation level cannot be directly relatedto the transport since the potential fluctuations andphase angles are not known

632 Fluctuations of the Ha light emission

Density fluctuations at the plasma edge have beeninvestigated in regions of sufficient neutral hydrogendensity by observation of fluctuations of the Ha lightemission [77] Cross-correlation functions and cross-power spectra have been calculated for pairs of channelsseparated in the poloidal direction by an integer multiple

of 6 mm A significant difference between L-mode andH-mode discharges is observed (see Fig 82) Whilethe cross-correlation functions for the L-mode aresmooth and decay rapidly with increasing distancethose for the H-mode oscillate and decay much moreslowly with increasing distance Correspondingly thecross-power spectra decrease monotonically in theL-mode and show a broad maximum (around 20 kHz)in the H-mode The coherence between different channelsin the frequency range of the maximum is much higherin the H-mode and decreases slowly with increasingpoloidal distance The phase difference between twochannels increases rapidly with the distance as expectedfor modes with short poloidal wavelength These resultsalso indicate that the key to the L-H transition may befound at the plasma edge

I W 21895H laquo 21696

Miriiov activity

-4-

10 14 Ms) 18

f= 30 kHz

(= 82 kHz

fe222kHz

f 1 MHz

18

FIG 83 Comparison of the broadband magnetic fluctuationamplitude in the L- and H-modes


ASDEX TEAM

633 Magnetic field fluctuations

A set of coils mounted on a pneumatically drivenmanipulator has been installed on ASDEX The mani-pulator can be used either to scan the probe over adistance of 8 cm in the radial direction within 150 msduring a discharge or to change the fixed position ofthe probe between discharges

The radial poloidal and toroidal components of thefluctuating magnetic field are measured simultaneouslyA slotted graphite casing is fitted around the probe toprovide electrostatic shielding of the coils whilemagnetic fields can still penetrate A passive high-passfilter is employed to attenuate the dominant coherentmagnetic fluctuations due to Mirnov oscillationsThe amplifier output is monitored by a frequencycomb [78 79] consisting of a splitter whose output isprocessed by a set of eight bandpass filters each withAff = 0 1 The RMS amplitude of the coil output issimultaneously measured at eight frequencies in therange of 30 kHz to 1 MHz

From experiments involving sawtooth perturbationof the incoherent magnetic field fluctuation amplitude[80] it is concluded that the observed magnetic fluctua-tions are generated within a few centimetres of theseparatrix In addition there is a significant increasein the ratio of the toroidal magnetic field fluctuation tothe radial magnetic field fluctuation as the probe movestowards the separatrix Further support for this conclu-sion is provided by recent experiments on TEXT wheremagnetic field fluctuations measured outside the limiterradius have been found to be correlated [81]

Figure 83 shows the magnetic fluctuation amplitudein discharges with the same nominal conditions ofIp = 380 kA Bo = 217 T and i^ = 29 x 1013 cm3with 26 MW of Hdeg injection into deuterium (Nos 24895and 24896) The separation between the separatrix andthe magnetic probe is 10 cm Previously broadbandradial and poloidal magnetic field fluctuations duringthe H-mode were observed in ASDEX with probe coilslocated 17 cm from the separatrix [82]

The upper traces of Fig 83 correspond to a dischargewhich remained in the L-mode and the lower tracescorrespond to a discharge which made a transition tothe H-mode The coherent magnetic fluctuations att = 15 s are in the range of 15-25 kHz These fluctua-tions have been identified with mn = 41 Mirnovoscillations in the discharge which remained in theL-mode and with mn = 32 Mirnov oscillations in thedischarge which made a transition to the H-mode Athigher frequencies the broadband magnetic fluctuationsare of smaller amplitude during the H-mode After the

L-H transition a sharp decrease in amplitude of thef = 82 kHz component occurs (see Fig 84) despitethe increase in the amplitude of the coherent magneticfluctuation as measured by the f = 30 kHz channelThis difference in behaviour suggests that the mechanismresponsible for the generation of coherent fluctuationsis not directly linked with the instability generating thefluctuations at higher frequency Further investigationsare required to determine whether the stabilization offluctuations in the low frequency range is the cause orthe consequence of the transition to the H-mode

The observed amplitude increase of the radial andtoroidal components of the magnetic field fluctuations inthe higher frequency channels after the L-H transitionsuggests that a different mode has been destabilized Acomparison of the time dependence of the amplitudesat f = 30 kHz and f = 606 kHz (see Fig 85) demon-strates that this process is independent of the presenceof coherent magnetic fluctuations Preliminary measure-ments with the probe positioned 4 cm from the separatrixshow an even more dramatic increase of the toroidalcomponent at high frequencies The steep pressure

l=380kA B=236T q=30

f-30kHz

U82kHz

(=222 kHz

f 606 kHz

14 10

Time (s)14

FIG 84 Frequency dependence of the broadband magneticfluctuation amplitude at the L-H transition


THE H-MODE OF ASDEX

24896

FIG 85 Relation between the broadband magnetic fluctuationamplitude the sawteeth and the emission of Da radiation in thedivertor

(MA

)

Euo

ic

wcD

xij5e

04-

02-

o-

08-

u^

J

6

9JLT

) 02

m =

5 J

04

mdash ^ j ^ p _ _ _

06 08

t(s)

1

-8(A

)u

o

bull0

10

FIG 86 Variation of the hard X-ray radiation ltfgtx during theinitial discharge phase when the current is ramped up andrational q surfaces cross the plasma surface

r-8

a

mpoundurgtO

0)IC

A-

3-

-

1-

n -u

5982 J

mdashJ J

itiik

W^^VÂ

idisruptive

I p = 300 kA

Bt = 22 T 2e

10 ii 12 13

t Is]

U

FIG 87 Time evolution of the hard X-ray radiation with neutralinjection and at the L-H transition The line averaged density isgiven for reference

gradient at the plasma boundary in the H-mode isthought to play a role in the generation of thesefluctuations

634 Confinement of runaway electrons

The confinement of runaway electrons dependssensitively on the quality of the magnetic configurationThey are measured via the hard X-radiation ltigtx whichis emitted from a molybdenum target hit by runawayelectrons The target is placed outside the plasma inthe midplane on the low field side Runaway electronsare produced in ASDEX during the first 50 ms in thedischarge breakdown phase they are accelerated duringthe current ramp-up phase and are gradually lost duringthe plateau phase thus defining a runaway confinementtime TR from the exponential variation of $x The transientincrease of $x indicates increased runaway electronlosses [83]

Figure 86 shows the variation of $x during thecurrent ramp-up phase The transit of rational q-surfacesacross the separatrix leads to increased runaway electronlosses because the magnetic configuration is somewhatdisturbed The radial magnetic field component whichdevelops in the configurationally unfavourable situationof a rational q-surface at the plasma edge is too smallto affect the bulk plasma When the plasma currentand the toroidal magnetic field are chosen such that arational low-q surface remains close to the plasmasurface during the plateau phase runaway electronsare quickly lost The sensitivity of the runaway electronconfinement to disturbances of the magnetic fieldconfiguration is highlighted by the fact that in sucha case the sawteeth strongly couple to the runawayelectron population leading to strong sawtooth modu-lation of the hard X-radiation

The confinement of runaway electrons is sharplydegraded with auxiliary heating At the L-H transitionhowever the confinement of runaway electrons is againimproved The increase of the hard X-radiation in theL-mode and the sudden reduction at the L-H transitionare plotted in Fig 87 together with the line averageddensity According to this plot the L-phase is a stateof high magnetic turbulence while the L-H transitionagain leads to a quiescent phase

Analysis of the runaway confinement time TR yieldsa radial correlation length of about 1 mm and afluctuation level BB of ~ 2 x 104 together with theparameter dependence of TR this indicates that resistiveballooning modes are the inherent turbulence As aconsequence of this analysis we conclude that resistiveballooning modes can be stabilized under the specificedge conditions at the L-H transition


ASDEX TEAM

7 MHD STABILITY ANALYSISOF H-MODE DISCHARGES

It is of considerable interest to compare the measuredMHD activity with theoretical calculations since inthis way more insight can be obtained into the physicalmechanisms that govern the high poloidal beta phaseof the H-mode One tool for this investigation is theGA-3D-CART code [84] which is based on the large-aspect-ratio expanded MHD equations at finite poloidalbeta j3p laquo Roa and is capable of treating the linearand non-linear evolution of ideal and resistive MHDinstabilities (Section 71) Furthermore free-surfaceinstabilities related to the ELMs are studied in theframework of resistive MHD equations (Section 72)

Investigations of ideal and resistive ballooning modeshave been stimulated by the observation of a hard betasaturation near the maximum attainable beta which isclose to |SC = 28 Ipa Bt [ MA m T] [85 86] Itis termed hard saturation because it is distinguishedby the absence of both sudden disruptions and gradualdeterioration of the confinement over an extendedrange of beta To explain this within the framework ofMHD instabilities ballooning mode stability analyseshave been performed on ASDEX which are discussedin Section 73

71 Medium m-mode stability

The linear MHD equations of the CART code aresolved for realistic ASDEX equilibria and plasmaparameter profiles [87 88 89] Before performingthe stability calculations we determine the plasma andmagnetic field configuration by solving the free-boundaryequilibrium problem

R2 div + Mo

JJOO = mdash (1R2)1

Mo

+ 4TT2

dldV

= 0

for the poloidal fluxes of the magnetic induction (fluxfunction ^) and the current density on the basis ofgiven profiles of pressure p and toroidal current I asfunction of ra = (VVp)12 embedding the plasma inthe internal conductor system of ASDEX Here ()denotes the usual flux surface average and Vp is thetotal plasma volume The magnetic field is then given by

Transport analyses (see Section 33) yieldedprofiles of the total plasma pressure p(r t) = pth

+ 12 (pStrade + p^1) and - by solving the poloidalfield diffusion equation mdash profiles of the currentdensity j t (r t)

We generally find that the global MHD activity ismainly caused by tearing modes or pressure drivenmodes External kink contributions are weak for ourcases (Ay lt 10) as can be shown by moving theconducting wall closer to the plasma surface A changein the driving mechanism for the instability withincreasing pressure is indicated by the t scaling of thegrowth rates as shown in Fig 88 It turns out thatlow 3P discharges scale as 7735 as expected for tearingmodes whereas for high j3p discharges an interchangemode scaling 7 ~ 17m is found

Usually large poloidal mode numbers (m lt 5)are obtained which clearly exceed the qa value at theboundary of an equivalent circular discharge at finitebeta qa laquo qa(l + e2 (1 + O5(3pi + f2)2)) so thatthe resonant surface m = q should lie close to butinside the separatrix (qa = 5Bt r

2(27r RQ [Q j t rdr))An example is the high j3p discharge No 1804103p ~ 192) with qa = 34 and a measured value ofm = 4 n = 1 It turns out that a simulation of theseresults with constant vacuum resistivity rj is impossibleThis problem can be resolved by noting that smallvacuum resistivities increase the effect of the perturbed

yco

101

10-2

106 10-5104 10-3

B =1

X V 0 + x0J

FIG 88 Growth rates of medium-m resistive modes normalized

to the Alfven frequency as a function of the plasma resistivity tp

the resistivity outside the separatrix is fixed at tv = 10~2) for a

medium value of the poloidal beta 0p = 11 (No 16996) and

a beta limit value fip = 21 (No 17005) The influence of the

plasma resitivity model is also indicated The dashed lines

represent the scalings yugtA mdash t]35 and r)3


THE H-MODE OF ASDEX

0A-Z[m]

02-

00-

-02-

-04-

(a)

i i i l l it irHil iTiT-ljrirKTifrl i

12 14 16 18 20 R[m]

BeBe

00015

0001

00005

0

-00005

-0001

(b)

50 100 150 200 250 300 350

FIG 89 (a) Perturbed magnetic flux contours for the unstable n = 1 mode of a discharge with 33c = 10The solid line shows the magnetic separatrix

(b) Comparison of the calculated magnetic fluctuation amplitude with measurementsThe vertical dashed lines indicate the limited poloidal range covered by Mirnov probes

current density on the evolution of the correspondingmagnetic flux if we assume that the ratio of the convectionterm and the resistivity term depends only weakly onvt Of = (1TRlaquoA) X (I7rrp

2)j uA = Bp(rp2 nm fx0)

0-5

= Mo Since

a stronger attenuation of the high-m contributions atthe plasma surface than in the case with large rj isexpected On the other hand experimental data indi-cate a very effective insulation between the conductingwall and the plasma surface since high m-numberspersist close to the vacuum vessel We have thereforeincreased 17 exponentially from its value at the plasmaboundary to a high value near the wall (if waii = 01)This treatment naturally leads to stronger effects at theinner side of the torus where the equilibrium magneticflux is lower than at the outer side As can be seen inFig 89(a) for discharge No 18041 (3P = 19) thisprocedure leads to the required large m-values as wellas to the correct mode asymmetry ie a smaller poloidalwavelength at the inner side of the torus

For an even more detailed comparison with experi-ments we have performed non-linear calculations forwhich superposition of all Fourier components of theexpansion in the toroidal direction is required Inpractice it turns out that three Fourier componentsare sufficient The non-linear evolution is started with

the corresponding linear n = 1 eigenfunction Highern-values are obtained by convolution with the n = 1contribution The amplitudes for the initial eigenfunc-tions have to be chosen such that the evolution remainsin the linear phase for a few Alfven times Usuallysince the Strauss equations in high beta ordering donot lead to true saturation in the non-linear phaseforced saturation by an effective pressure diffusionterm has been used The evolution is stopped as soonas the calculated perturbed magnetic field at the out-board side of the torus reaches the measured amplitude

In Fig 89(b) the numerical results for the perturbedmagnetic field Be versus the poloidal angle at a fixedtoroidal position after saturation in the non-linear phaseare compared with the measured Mirnov signals Becauseof the large outside-inside amplitude ratio non-lineareffects are stronger at the inner side of the torusComparison with data in the experimentally testablepoloidal region shows reasonable agreement for thephases as well as the amplitudes

The deviation of the observed soft X-ray waveforms from pure proportionality to sin (nltgt) can beregarded as a measure of non-linear effects This givesthe possibility of comparing the investigated saturationmechanism and the corresponding n gt 1 contributionswith the data We have compared the measured timeevolution of soft X-ray traces for discharge No 18041with calculations of the line integrated squared perturbedpressure There is no frequency doubling in the central


ASDEX TEAM

channel indicating a weak m = 1 contribution inagreement with experiment Our results show that thephase differences of the various traces are reproducedwith good accuracy For this special case it turns out thatthe ratio of the n = 2 contribution to the n = 1 con-tribution is less than 10 These effects turn out to bestronger at the inner side of the torus mainly becauseof the large ratio of outside-inside amplitude

In summary global MHD stability calculations havebeen performed for H-mode high poloidal beta dischargeson ASDEX It is shown that at high j8p the dischargesare subject to a pressure driven tearing instabilitywhereas at low j3p the instability is mainly of the tearingtype When the vacuum resistivity is exponentiallyincreased from its value at the plasma surface to ahigh value near the conducting wall we find highpoloidal mode numbers for the analysed high j8p

discharges in agreement with experimental observationsNon-linear calculations with forced saturation by aneffective pressure diffusion term predict amplitudes ofthe non-linear contributions to the n = 1 eigenfunctionsof the order of 10 The calculations of Bd versuspoloidal angle and line integrated perturbed pressureare in reasonable agreement with experimental datafrom soft X-rays

However no clear correlation between the observedn = 1 mode activity and the beta limit or the betadecrease after maximum beta is reached can be foundin the experiments [85] The strong m = 2 modesometimes observed during beta decay does not seemto be a prerequisite for this decay If such a mode ispresent its contribution to the beta decrease can beascribed to the presence of magnetic islands (seeSection 232) Finally energy losses due to ELMs arealso present in medium beta H-mode discharges withouta beta decrease and are therefore not responsible forthe additional losses at the beta limit

72 Resistive MHD simulations of ELMs

The experimental evidence concerning ELM activityis described in Section 233 and can be summarizedas follows

mdash Only the outer part of the plasma is influenced byELMs

mdash The observed time-scale corresponds to the idealMHD time-scale

mdash There is no pronounced (m n) precursormdash ELMs are characteristic of H-discharges and are

relatively independent of the value of the safetyfactor at the surface and of the poloidal beta

Therefore it seems necessary to begin a theoreticalstudy by addressing the question of possible free-surfaceinstabilities in the framework of resistive MHD A smallviscous term xV2v is included in the momentumbalance to obtain smooth profiles For numerical con-venience the continuity equation is replaced by p = ctIf the velocities are low the corresponding error isquite small The simulation is restricted to cylindricalgeometry Details of the numerical method and thecode are found in Ref [84]

The L- and H-discharge profiles displayed in Fig 90have been used as experimental data The aspect ratioRa is 40 and the resistivity is const rj = 106Typically the value of the safety factor varies fromunity on axis to 3 at the boundary The parameters forthe H-discharge are q0 = 12 qa = 28 and pp = 18

The linear stability analysis yields a survey ofpossible instabilities related to ELMs Clearly a global(m = 1 n = 1) type mode is not involved (q0 gt 1)According to the analysis there is a large number ofunstable modes localized near the surface such as(m = 3 n = 1) (m = 8 n = 3) and (m = 15 n = 5)The resonant surface at r = rs is defined by qs = mnThe growth rates scale as rm and hence these insta-bilities are basically pressure gradient driven For theprofiles of the H-discharges these modes are morepronounced owing to the large gradients near thesurface

Free-surface modes are studied in a system wherethe main plasma is surrounded by a force free

FIG 90 Pressure and current profiles of (a) an L-discharge and(b) an H-discharge The gradients are stronger at the surface


THE H-MODE OF ASDEX

6

6-

4-

2-

bull H - Mode

L - Mode

100 101 102 103 104

ra

FIG 91 Growth rate of an m = 8 n = 3 mode (normalizedto the Alfvin time) versus the location of the resonant surface(ra = 1 denotes the plasma boundary) Die upper curvecorresponds to the H-discharge and the lower curve to theL-discharge

(currentless and pressureless) plasma with highresistivity 77 up to a perfectly conducting wall atr = rw This system has stability properties similar tothose of a plasma-vacuum system but it yields a morerealistic description New instabilities are found whenthe resonant surface is outside the plasma These modesare a mixture of kink modes and resistive interchangemodes and are both current driven and pressure gradientdriven Their growth rates saturate for TJ ~ 104 to103 It is emphasized that the ideal peeling mode isstable Hence these new instabilities can be consideredas resistive peeling modes If the resonant surface istoo far outside the plasma the mode becomes stableas indicated in Fig 91 Again this surface mode ismore pronounced in H-discharges For a sufficientlyclose wall rwrp lt 11 this free-surface instability isstabilized

The non-linear evolution of the free-surface modeinstabilities has been analysed by numerical simulationIt is of great importance to find out whether suchlocalized modes are easily stabilized and saturate orwhether they grow significantly when there are changesin the equilibrium For this purpose we have studiedup to 36 modes corresponding to wave numbers m and nwith resonant surfaces in the region 07 lt rsrp lt 11Here the resistivity follows the temperature profile asTJ ~ 1j with 17 = 106 on axis and TJ = 17 = 103

outside the hot plasma (rrp gt 1) The wall is placed atrwrp = 11 It is found that for H-type profiles thesurface modes interact and enhance each other theplasma expands radially in about 20 is (150TA ~ 20 s)

This is shown in Fig 92 The mode dominant inthe linear phase amplifies other modes such as the(m = 3 n = 1) mode to make their contributions equalA mixture of these modes yields the observed incoherentstructure In contrast for L-discharges it is impossibleto obtain the non-linear growth of the correspondinginstabilities in a time-scale of up to 400 xs The linearinstabilities are too weak and too localized and aretherefore easily suppressed by local changes in theequilibrium

It is concluded that in H-discharges non-linearMHD modes may lead to an expansion of the plasmaby about 4 cm radially ie 10 of the plasma radiusand to a shift of an internal plasma ring to the separatrixwhere the energy and particles are transported to thedivertor The experimentally measured energy which istransferred to the divertor plates during one ELM eventcorresponds to the energy in an outer plasma ring of3-4 cm width Thus within this model we arrive atthe following scheme for repetitive ELMs Strongpressure and current gradients near the plasma surfaceinduce free-surface MHD instabilities The plasma isenlarged by 4 cm (10 of the radius) in about 20 fisA small plasma ring is shifted to the separatrix andthe energy and particles are carried into the divertorAfterwards flatter profiles lead to MHD stability butthe intrinsic H-mode transport again builds up stronggradients at the plasma edge

t = 0

FIG 92 Contour plots of the pressure for the non-linear evolutionof free-surface modes


ASDEX TEAM

0 02 01 06 r Q 10 0 02 0A 06 r 0 10

FIG 93 Radial dependence of the pressure gradient p normalized to themarginally stable gradient pM due to the ideal ballooning modes according tothe a(s) criterion (1) a large-aspect-ratio expansion (2) and an exact solution (3)together with the pressure and q-profiles used for a Ddeg mdash D+ discharge(No 17005) and an Hdeg ~ D+ discharge at ampmax

This simulation has been performed in a straightcylindrical geometry The pressure gradient drivenresistive instabilities which combine with kink-typemotions stand for resistive ballooning modes withwave number m mdash 3-20 Similar instabilities can beexpected to occur in toroidal geometry Toroidaleffects enhance the coupling especially with kinkmodes (see Section 71) The divertor geometry ofASDEX has not been taken into account ie the shearclose to the separatrix is increased in relation to thismodel but ergodization of the field lines near theseparatrix may again diminish the effect of theX-points

73 Ballooning stability calculations

As a first result of our calculations of ideal ballooningmode stability of MHD equilibria reconstructed fromASDEX experimental data [38] it is found that in aplasma configuration with a relatively small aspect ratio(A laquo 4) toroidal curvature the large differential displace-ment of the magnetic surfaces at high poloidal beta andthe effects of local and global shear in the neighbourhoodof the separatrix play an important role in the derivationof quantitative results In general accurately calculatedMHD equilibria and a correspondingly careful treatmentof the stability equations are required

731 Ideal ballooning modes

In an ideal ballooning mode stability analysis ofASDEX equilibria the corresponding Sturm-Liouvilleproblem has been solved for magnetic surfaces withvolume values 0 lt V lt Vp where Vp is the totalplasma volume For a particular magnetic surface theballooning equation for the unstable mode u dependingon the poloidal angle 6 can be written in the form

3PC2(0))u = 0

This ballooning equation is conceived as having anexplicit dependence on the local poloidal beta and animplicit dependence (through the coefficients S Qand C2) on the total equilibrium To obtain informationon the presumably attainable marginal value we havemodified the explicitly appearing local poloidal betaon the basis of a given equilibrium configuration untila marginal solution of the ballooning equation with apoloidal beta value j3M was obtained

Figure 93 shows the calculated beta ratioV0M = P^PM (Wim m e prime indicating ddiraquo) asa function of ra for a Ddeg mdash D + discharge and anHdeg mdash D + beta limit discharge (0 = amp) at the time ofmaximum beta Besides a general evaluation of the


THE H-MODE OF ASDEX

05-

FIG 94 Time evolution of the pressure gradient p normalized tothe marginally stable gradient pu due to ideal ballooning modes(large-aspect-ratio expansion) for Ddeg mdash D +

above ballooning equation we have also performed alarge aspect ratio expansion of the coefficients S C andC2 Although we have assumed circular flux surfaceswe have taken into account the correct differentialdisplacement of the magnetic surfaces due to the toroidalcurvature the poloidal beta and the internal inductanceJ- This treatment is different from that discussed inRef [91] where the normalized pressure gradient aand the shear s are the only free parameters of theproblem Our treatment is also different from thatdiscussed in Ref [92] where a special functional formof the differential displacement was assumed Exceptin the neighbourhood of the magnetic axis we findthat the results of our large aspect ratio expansion arein good agreement with those of the complete treatmentthese refined approaches yields however 33M valuesabout 20-30 lower than those given by the simplea-s criterion when p = dpd^ is in the vicinity of themarginal limit (see Fig 93) Broader current densityprofiles with higher q0 values are more susceptible toballooning instabilities owing to their lower shear andvice versa For given q profiles this can be demon-strated by variation of the 33M profile rather than byan increase of its maximum value which is alwaysbelow 09 for the range 08 lt q0 lt 12

The time development of the ideal ballooning stabilityaccording to the large aspect ratio expansion in theDdeg mdash D + beta limit discharge is illustrated in Fig 94At the time of maximum beta (about 126 s) the dischargereaches a normalized pressure gradient pp^ = 08in the region 05 lt ra lt 09 This is also the regionwhere additional increased plasma losses start accordingto the TRANSP analysis (see Section 33) causing a

decrease of beta in the period 128-138 s During thistime the ppM = 08 region shrinks only slightly butthe maximum value of pp^ stays below 09 When ageneral evaluation of the ideal ballooning equation ismade for 015 lt ra lt 085 a region with ppvvalues between 07 and 085 is obtained for the periodof the beta decrease

To keep the plasma close to marginal ideal ballooningstability the current profile has to flatten on a time-scale that is smaller than the resistive time-scale forcurrent redistribution assuming a time independentflat Zeff profile The computed internal inductance alsodecreases more slowly than the measured one Betteragreement of the time-scales has been obtained byusing neoclassical resistivity together with a sawtoothmodel and with the measured or inferred Zeff profiles(from consistency checks with radiation profiles andspectroscopic measurements) [38]

When bootstrap and beam driven currents are takeninto account it is found that only small changes in thecurrent the safety factor and the shear profiles occuron time-scales much shorter than the resistive time of400 ms It is found that ideal ballooning stability is leftalmost unchanged by the non-ohmically driven currentsin the pre-transition L-phase in the H-phase with andwithout ELMs and at the beta limit [10] Figure 95presents an example for the analysis of ideal ballooningstability in an H-discharge with neoclassical resistivity

FIG 95 Pressure gradient normalized to the critical value forideal ballooning modes versus radius in L- and H-phases withOhmic bootstrap and beam-driven currents included A denotes thewidth of the steep gradient zone


ASDEX TEAM

107

71

14th Flux Surfacera laquo 067

- 0002 0005 0010 Re7

FIG 96 Branches in the complex y plane for the 14th flux surface (ra = 067) and the7th flux surface (ra = 088) The latter surface corresponds to the one that is most unstable toideal ballooning modes The numbers at the curves label the various toroidal mode numbers

and Ohmic bootstrap and beam driven currents takeninto account During the L- and H-phases the plasmais stable and even at the beta limit it is still marginallystable to ideal ballooning modes

Finally it should be remembered that as noted inSection 33 in discharges with j3max lt 08j3c the ppUvalues remain significantly below unity the maximumvalues being smaller than the corresponding globalj8j3c ratio

In ASDEX H-mode discharges the resistivity is verysmall but finite so that actually the modes to be studiedare resistive ballooning modes In addition thedestabilizing potential of ideal ballooning modesturns out to be too small to account for the hard j8p

saturation These circumstances motivated us toextend the investigations to resistive ballooning modesin the framework of the one-fluid MHD theory

732 Resistive ballooning modes

In this approach we have assumed infinite parallelelectron heat conductivity ie constant temperature ona flux surface However as pointed out in Ref [91]the mean free path of the electrons in ASDEX is ofthe order of 103 cm The mean free path thus turns outto be much larger than the parallel wavelength of theresistive ballooning mode Nevertheless the ballooningmodes cannot be stabilized by finite electron heatconductivity as shown in Ref [94] in the context of

the Braginskij two-fluid model In line with these argu-ments we believe that electron heat conduction doesnot qualitatively change our results and so we postponethe investigation of extended dissipativekinetic effectson ballooning modes

On the basis of the resistive hydromagnetic equationswe revisited the resistive evolution of velocity andmagnetic fields in the high-m stability limit For theFourier approximation of this set which leads to theresistive ballooning equations of Ref [95] we thenperformed a numerical solution by applying a varia-tional method to the corresponding boundary valueproblem in four dependent variables with real andimaginary parts of the growth rate as parameters Thestationary values of the corresponding Lagrangian Lare associated with the growth rates of resistiveballooning modes Their actual values are uniquelydetermined by the experimental input of p(V) I(V)and T7(V) and by the magnetic field configuration(see Section 71)

For purely growing modes resistive effects areusually significant only if the parameter n2TArR issufficiently large (TA is the Alfven time) In regionsclose to the plasma centre the required values for nmay exceed 100 If we allow overstable solutionshowever we find that much smaller values of n areassociated with unstable modes Our calculationsshow that the critical n-value strongly depends onthe compressibility Thus we find that for n lt r^ the


THE H-MODE OF ASDEX

R o ( 7 gt

G005 bull bull

00

Resistive Growth Rates

ra = 0867

03

FIG 97 Resistive growth rate (= Re(y)) versus the pressure

gradient scale factor Cp (= dpMdp) The curve relevant to ASDEX

is the solid line

compressibility term in the resistive ballooning equationsdominates whereas for n gt nlt the resistivity termstake over

Accordingly we find that with decreasing cpcv thecritical n-value decreases Figure 96 presents examplesof the 14th flux surface (rrp = 067) and of the 7thflux surface (rrp = 088) which is most unstable toideal ballooning modes the corresponding branchesin the complex 7-plane for discharge No 17005are plotted The numbers specify the correspondingvalues of n The bifurcation to overstability occurs atric laquo 396 for the 14th surface and at 1 = 135 for the7th surface Figure 96 demonstrates that for these fluxsurfaces the n values can be significantly decreased ton = 140 and n laquo 60 respectively before the ballooningstability limit (Re 7 = 0) is reached This result agreeswell with our expectations for reasonable n-values inthe context of a hydromagnetic approach

10

06-

02 bull

00

00

Toroidal

current IIp

1mdash1mdash1

^

025 05 075

Volume VVp

Toroidal current density JT(Rraquo z = 0)

10 I 14 16 I8 20

10

06

02

00

V PPO

bull bull bull bull

Plasn

1mdash^ mdashmdashmdashj

1a pressure pPO

025 05 075

Volume VVp

0075Pressure Volume

I Window

increasedpressure gradient

085 09 095 10 VVp

10

FIG 98 Toroidal current and plasma pressure as functions of the normalized volume VVp for discharge No 17005

(Ip is the plasma current p0 is the pressure on the magnetic axis and Vp is the plasma volume) Pressure profile

steepening in the plasma edge region as indicated in the enlarged pressure volume window results in the radial

current density distribution shown in the upper right corner


ASDEX TEAM

To investigate the signatures from resistive ballooningmodes we calculated the normalized growth rate 7as a function of the pressure gradient scale factorCp = dpMdp (VpM = (dpMdp)Vp with pM(p) beingthe modified pressure profile) which was chosen suchthat Cp = 1 reproduces the equilibrium values at theglobal maximum poloidal beta [96] Results for Re7versus Cp are shown in Fig 97 for n = 100 all curvesrefer to the 7th flux surface The effect of compressibilitycan be seen in Fig 97 by comparing the dotted curveand the short-dashed curve which are for the totallycompressible case (yT mdashbull 0) and the incompressible case(7T ~ degdeg)gt respectively In agreement with theoreticalexpectations the incompressible plasma is more stablefurthermore a pressure gradient threshold appears

There is a strong increase of the growth rate whenthe poloidal beta approaches its maximum ieCp = 1 (see Fig 97) This is due to the transitionfrom a region where resistivity effects dominate(Cp lt 1) to a region where the growth rate is essen-tially controlled by the pressure gradient (Cp gt 1)These regions are separated by the knee in the dottedcurve which furthermore defines the transition pointsfrom purely growing modes to overstable modes

All results discussed above refer to A-like solutionswhich can be approximated by invoking the A criterionof resistive ballooning modes [97 98] ie thesemodes are fed by energy from the ideal region Inaddition to these solutions we also find electrostaticbranches [99]

Dispersion relations for such modes can be derivedin a limit where the growth rate is much larger thanthe sound frequency Since these modes are driven byenergy from the resistive layer we expect them to beof importance in regions of large resistivity or close tothe plasma edge There the corresponding growthrates for these modes are comparable with those of theA branch Inspection of the dispersion relation revealsthat the growth rate of these modes decreases withincreasing plasma pressure (|3) therefore in regionswhere the plasma pressure is low but the pressuregradient is large (H-mode) we expect electrostaticmodes to be important

To prove these statements we have performedcalculations with a modified increased pressuregradient in the plasma edge region Figure 98 showson the left side the unmodified profiles of the toroidalcurrent IIp and the plasma pressure pp0 as functionsof the normalized volume VVp The small pressure-versus-volume window on the pp0 profile near theplasma boundary is shown enlarged on the bottomright side This insert illustrates how the pressure

10

10-2

103dpdevalue of ASDEX

^ ^ 1 1

5 x 1 0 -4 105 15 1 0 5

FIG 99 Ideal and real resistive ballooning growth rates in

ASDEX obtained by applying an increased pressure gradient

in the plasma edge region

gradient is successively steepened on the particularmagnetic surface with VVp = 0925 Growth ratecalculations based on a correspondingly scaledsequence of plasma equilibria are shown in Fig 99The results demonstrate that despite an increasedpressure gradient ASDEX is unstable but is far fromthe second region of stability that the A-like modesand the electrostatic modes have comparable growthrates and that for even smaller beta values electro-static modes may dominate A-like modes

To summarize the increased energy losses at thebeta limit are connected with resistive ballooning insta-bilities but the anomalous losses observed far belowthe beta limit are caused by other instabilities

8 COMPARISON OFH-MODE PROPERTIES ON ASDEX

WITH THOSE FOR OTHER EXPERIMENTS

The H-mode has also been observed in divertorexperiments on JET [8] DIII-D [6] PDX [5] PBX[100] and JFT-2M [7] A very important point is thatthe divertor on JET DIII-D and JFT-2M has an openexpanded boundary configuration and the plasma cross-sections are elliptic These are the topological charac-teristics envisaged for reactor-grade tokamaks regardingpower exhaust ash removal and high current capabilityThe accessibility of the H-mode even in a not fullyoptimized geometry has been demonstrated on JET


THE H-MODE OF ASDEX

which was originally not designed as a magnetic limiterconfiguration

H-mode operation under limiter conditions has beendemonstrated on JFT-2M [7] TFTR [101] DIII-D[102] and JIPP-T2 [103] These studies clearly showthat the high edge shear specific to the divertor config-uration is not the determining factor for L-H transitionand improved confinement However it is found thatthe improvement of confinement is poor for a circularlimiter plasma Only with an elliptic cross-section isthe energy confinement time of limiter dischargesclearly improved as shown on JFT-2M and DIII-DThese experiments indicate that the magnetic configu-ration and the enhanced shear may nevertheless beof importance On the other hand results for limiterdischarges in the H-mode also indicate the importanceof recycling control for good confinement (recyclingcontrol is a necessity in other good confinementregimes such as the supermode [104] the IOC regime[54] and the improved regime with counter-NI [105])

The phenomenology of the H-mode development isthe same in all cases [106] With the exception of theoccurrence of the Ohmic H-mode in DIII-D a shortL-phase succeeds the H-phase and the transition israpid and distinct In the H-phase both particle andenergy confinement improve leading to a rise in densityand beta The transition to the H-phase is clearly indi-cated by a sudden drop in the Ha radiation emittedfrom the high recycling zone (in the divertor chamberaround the X-point or in front of the limiter)

We now compare the H-mode results from ASDEXwith those from DIII-D (The plasma geometry para-meters of DIII-D are R = 169 cm a = 64 cm andK lt 20) In some aspects the DIII-D results arecomplementary to those of ASDEX for exampleregarding the discovery of the Ohmic H-mode [102]and of the H-mode initiated by ECRH [107] onDIII-D From these results (together with the H-modeobtained with NI or ICRF heating) it is clear that thedevelopment of the H-mode is connected with the plasmaproperties and is rather independent of the characteristicsof the heating technique

81 Agreement between the observationson ASDEX and DIII-D

In the H-mode of DIII-D energy confinement timesof up to 160 ms have been obtained in pure D + plasmas(Ip = 1 MA PN1 ~ 5 MW) in the L-mode TE ~ 70 msAs in the regular H-mode of ASDEX with ELMs nodistinct scaling of TE with power (for Ddeg mdash D+) Kg

and B was observed on DIII-D no power dependencewas found in the range 3 lt PNI lt 6 MW For theOhmic H-mode discovered on DIII-D however adegradation of rE with heating power was also observedTE increased linearly with Ip (for q95 gt 3) The opera-tional range for this H-mode is large but a powerthreshold and a density threshold have to be exceededFor Ip = 21 T the critical heating power is 3 MW (onASDEX 12 MW) the critical density is ~ 2 X 1013 cm3which is similar to that of ASDEX single-null plasmasAs on ASDEX the power threshold is larger in thedouble-null configuration than in the single-null con-figuration It is also observed that the ion grad-B driftto the X-point reduces the power threshold (this impor-tant aspect has also been observed on JFT-2M andJET) The power threshold is increased by operatingwith hydrogen or helium plasmas instead of deuteriumFurthermore on DIII-D the power threshold withcounter-NI is 20 lower than that with co-NI

Another interesting common observation is that theH-mode is quenched when the plasma current isramped up (although it can be obtained at any constantcurrent level) This observation is not yet understood

The transition to the H-phase is frequently triggeredby a sawtooth after the L-H transition steep pressuregradients develop at the edge Although some uncer-tainty remains because the gradient length is comparableto the accuracy with which the separatrix location canbe determined it is concluded that the steep pressuregradient is inside the separatrix because of the develop-ment of an edge transport barrier On DIII-D further-more a decrease of the density fluctuation level insidethe separatrix is observed (by microwave reflectometry)At the L-H transition the SOL and also the powerdeposition profile at the target plates shrink Thepower deposition profile is reduced and mdash as onASDEX mdash the degree of power accountability isworse than under OH- and L-mode conditions Afterthe L-H transition the plasma profiles broaden andthe electron temperature develops an edge pedestal ofapproximately 300 eV

On DIII-D it is found by transport analysis thatnot only does the confinement improve at the veryedge but also the heat diffusivity (single-fluid treatmentbecause of high density) in the zone 05 lt p lt 1decreases by a factor of three after the L-H transitionand agrees approximately with the Ohmic diffusivityvalues

ELMs are also observed on DIII-D in the H-phaseThe power and particle losses are 10-20 of the particleand energy content mdash somewhat higher than on ASDEXThere is clear evidence on DIII-D that ELMs are


ASDEX TEAM

pressure driven instabilities which occur when the edgepressure gradient reaches the limit of the first stabilityregime Because of the circular topology of the ASDEXplasma the critical pressure for ballooning instabilitiesmay be lower on DIII-D resulting in lower ELMamplitudes

82 Disagreement between the observationson ASDEX and DIII-D

An important difference between ASDEX and DIII-Dis the parameter dependence of the threshold power forthe H-mode On DIII-D Pthr = 06 neBt(MW 1013 cm3T Hdeg - D+) On ASDEX only a weak dependenceon these parameters is observed The density depen-dence may be the result of the sensitivity of the H-modeto recycling control (because the recycling flux increaseswith He) and this dependence may be different in theexpanded boundary configuration and in the closeddivertor configuration

A dependence of the threshold power on the toroidalmagnetic field is also observed on JET No reason forthe different observations on ASDEX can be givenConfigurational and machine-specific effects cannot beruled out On JFT-2M the threshold power is found todepend on the plasma current which is not seen onany other experiment

Contrary to the observations on ASDEX thedevelopment of an extremely broad density profile hasbeen observed on DIII-D which can even become veryhollow The edge density rises strongly and the edgeplasma remains collisional even in the H-phase Thisdifference does not seem to be of a fundamental natureOn ASDEX the density profile shape is found to dependon the recycling and the wall conditions and becomesbroader with a more open divertor structure and ahigher recycling rate (see Section 42)

The differences in the impurity development duringthe H-phase may be a consequence of the differentdensity profile shapes in the two devices On ASDEXthe electron density profile is peaked and there is astrong increase of the central impurity radiation OnDIII-D the impurities are concentrated in the edgeregion where the density profile peaks Impurities seemto be carried to the radial zone of maximal density byneoclassical effects Furthermore central impurityaccumulation may be prevented by sawteeth whichare generally present in the centre of DIII-D H-modeplasmas but are absent on ASDEX On DIII-D themagnetic turbulence as measured by probes outside theplasma clearly decreases after the L-H transition Thisdecrease is generally used to signal the transition A

rather sophisticated variation of the magnetic fluctuationlevel at the L-H transition has been seen on ASDEXthe signal can decrease but also increase dependingon the frequency range the field component and thebehaviour of the coherent MHD phenomena

9 DIFFERENT THEORETICAL MODELSFOR THE H-MODE

In this section we discuss some of the theoreticalmodels put forward to explain the L-H transition andthe good confinement in the H-mode and we comparethe predictions with experimental data from ASDEXThe comparison is mainly qualitative this is partly dueto the nature of the models but it also reflects thedifficulties in carrying out edge measurements ofsufficiently high spatial resolution to match the steepgradients forming in the H-mode

The transition to the H-mode clearly begins at theplasma periphery where the most pronounced para-meter changes occur The first task of relevant theoriesis therefore to explain how the conditions for the H-modecan lead to changes in the linear or non-linear stabilitybehaviour of transport inducing modes in the boundaryzone These theories ought to provide explanations for(1) the abruptness of the transition (2) the possibilityof two different equilibrium solutions for the same valuesof the externally controllable parameters at least overa limited parameter range and (3) the hysteresisobserved in the comparison of the L-H transition withthe H-L transition

Historically in all these models the poloidal divertorgeometry was considered first often however they donot strictly depend on this geometry A class of thesemodels starts from the high-q high-shear region in thevicinity of the separatrix which also exists mdash to asmaller extent mdash at the boundary of non-circularlimiter tokamaks Other models involve particle lossorbits or the predominant direction of the poloidal heatflux in the SOL and would also hold if the first plasma-wall contact were with an appropriately located limiterFor a quantitative comparison we also have to takeinto account that the shear conditions of the actualASDEX geometry significantly differs from the simplemodel equilibria used in some of these calculations andalso from the equilibria in open divertor configurationsASDEX was designed so that deviations from a circularcross-section geometry are localized as much as possibleat the plasma boundary therefore ASDEX has a muchsmaller spatial region where the flux surface averaged


THE H-MODE OF ASDEX

shear and the safety factor q are visibly influenced bythe presence of the stagnation points

In addition to the formation of a density and tem-perature pedestal the H-mode on ASDEX gives riseto a reduction of the electron diffusivity in the plasmainterior This has been demonstrated both by TRANSP-type analyses and by simulations in which explicitswitching to different diffusivity was used to model theL-H transition in the plasma interior From the stand-point of a purely local transport theory however itshould be possible to explain this reduction of theelectron diffusivity as a consequence of the dependenceof the diffusivities on the plasma parameters Somesuch models have indeed been proposed albeit generallyonly in a qualitative form

91 H-regime theories involving SOL physics

The behaviour of the SOL of divertor tokamaks isdistinctly different from that of conventional limiterdevices Thus for given energy and particle flowmultiple solutions may exist for the density and tem-perature distributions along the field lines intersectingthe target plates Thus it would seem to be promisingto study the SOL physics in order to find the origin ofthe LH-mode bifurcation It is not possible howeverthat the steep radial gradients in the edge region arecaused only by a modification of the transport alongthe field lines since even complete suppression ofparallel losses will only produce conditions equivalentto those prevailing anyway on closed flux surfaces

The first and most detailed model was suggestedby Ohkawa et al [108] It consists of two elementsRadial transport in the SOL is assumed to be reduced(below the transport across closed field lines) by theelectrical contact of the open field lines with the targetplates and the consequent suppression of weakly unstableelectrostatic and electromagnetic modes On the otherhand energy losses along the field lines can besuppressed by the formation of a potential distributionwith a local minimum giving rise to a thermal barriersimilar to the one proposed for mirror machines Forthe formation of a potential minimum the plasmadensity has to increase strongly towards the targetplate The L-H transition would thus coincide with astrong increase of the ionization rate in the vicinity ofthe target plate According to this model the steepgradient zone would lie outside the separatrix and themidplane electron temperature in the SOL would beincreased during the H-phase

In experiments however a drop of the Ha radiationin the divertor chamber is clearly observed The validity

of a theoretical model also depends crucially uponwhether the observed steep gradient zone lies inside oroutside the separatrix The required accuracy of theexperimental results can be questioned because thelocation of the separatrix in the plasma midplane isdeduced from equilibrium calculations which givesthe separatrix position in the midplane to no betterthan plusmn1 cm (corresponding to one density e-foldinglength Xn in the SOL) Nevertheless the experimentalresults from ASDEX indicate that the high temperaturezone and the steep gradients are located inside theseparatrix (see Section 25) this also leads to moreconsistency between the various SOL and divertorplasma measurements Other experiments in the H-modealso confirm the location of the steep gradient zoneinside the separatrix [5 109]

Even a simple gas dynamic model combined withSpitzer heat conductivity is capable however of yieldingtwo solution branches for the SOL parameters [110]The high density branch [111] as well as the low densitybranch [112] have been identified as the regionscorresponding to the H-regime The predominantexperimental evidence however is that a zone ofhigh radial thermal resistance is located inside theseparatrix An outstanding feature of the L-H transi-tion in the SOL as a consequence of this edge barrieris the sudden reduction of the power flow into the SOLwith a consequent decrease of the plasma parametersin the SOL and in the divertor region

92 Models of high shear zone effects

In a poloidal divertor configuration the safety factorq diverges logarithmically and the flux surface aver-aged shear diverges inversely linearly with the distancefrom the separatrix This is expected to have conse-quences for the linear stability and the saturationamplitude of ideal and resistive MHD instabilities

In particular the stability of ideal MHD ballooningmodes in the vicinity of a separatrix has been thoroughlyinvestigated for a simplified model geometry [113114] In this model the parameters determining thepermissible pressure gradients are the proximity to theseparatrix the location of the stagnation point in thepoloidal plane and the normalized current density Aparameterized in the form A = rV27r RBp TJ (77 isthe electrical resistivity) in the separatrix region ForX-points located more on the high field side of theseparatrix centre (as is the case for ASDEX PDXDoublet III JET JFT-2M) the limiting pressuregradient of the first stable region shows relatively littledependence on the current density and the separatrix

NUCLEAR FUSION Vol29 NoU (1989) 2027

ASDEX TEAM

16

FIG 100 (a) Forced L-H and H-L transitions by currentramp-up and decay The Ha radiation in the divertor chamberindicates the regime transitions(b) The density and j3pX are plotted for reference

distance The lower limit of the second stable regimeon the other hand strongly decreases with increasingcurrent density and decreasing separatrix distanceultimately leading to a coalescence of this limit with thefirst stable regime for sufficiently large values of AFor stagnation points situated closer to the low fieldside (as in the old JT-60 configuration) on the otherhand even interchange modes can become unstableand the first stability limit of ballooning modesbecomes sensitive to the current density near theseparatrix In particular this stability limit passesthrough zero as a function of A before reaching thepoint of possible coalescence with the second stableregime

On the basis of these theoretical results Bishop[115] developed a scenario for an L-H transition inwhich the pressure gradient of the one solution branchcorresponding to a low edge temperature (and hencelow edge current density) is limited to the first stableregime and the second branch corresponding to ahigh edge temperature passes through the coalescencepoint into a pressure gradient regime that is not limitedby ballooning modes

For a complete explanation of the L-H transitionwith this model the pre-transition L-mode phase wouldhave to be close to the ballooning limit The measuredelectron pressure gradient at the edge (normalized in

the form of a = -2fi0 Rq 2p7Bt2) is a = 007 in the

L-mode and a = 035 in the H-mode The pressuregradient at the edge may be close to the ideal ballooningmode stability limit in the H-mode but it is far fromthis limit in the preceding L-mode The required edgecurrent density A would have to be above 07 nearthe X-point to reach the second stability regime ForZeff = 18 an edge electron temperature of 500 eVwould be required (see for comparison Fig 27) whichis close to the upper limit of the experimental errorbars for H-regime conditions (an additional contributionto it could however come from the bootstrap current)

In a dynamic model of the L-H transition the highedge current density would however have to be estab-lished before the L-H transition which is not supportedby experimental measurements The MHD behaviouras described in Section 23 indicates a broadening ofthe current density profile but only after the L-H transi-tion when the m = 1 activity slowly disappears (seeFig 13) It is also not clear whether the change of thecurrent density profile can happen fast enough in thecase of a sawtooth-initiated L-H transition

Specific experiments have been performed on ASDEXto study the effect of current profile changes on theH-mode Figure 100 shows the plasma current whichwas ramped up and down in the beam phase the lineaveraged density and the Ha radiation in the divertorchamber used to monitor the confinement regimesWhen current is added in the edge region the H-modeis suddenly quenched when current is removed fromthe edge region the H-mode reappears Under steadystate conditions the H-mode can be maintained at acurrent level well above the critical one indicating thatthe results in Fig 100 are not due to a current limit forthe development of the H-mode Thus the favourableeffect of the edge current density on the developmentof the H-mode is not confirmed although the inter-pretation of the dynamic experiments as presented inFig 100 is not unambiguous

Even if the model of Ref [113] cannot quantita-tively explain the L-H transition on ASDEX it stillcontains some valuable elements For example theobserved ballooning stability of separatrix boundequilibria with the X-point in the bad curvature (lowfield) region could provide an explanation for thedifficulties experienced on JT-60 in connection withthe H-regime and better agreement between theoreticalstudies and experiments might be obtained if resistiveballooning modes were taken into consideration Alsothe increasing confidence in the existence of the boot-strap current may bring a substantial new element intothis model since in this case the high edge current


THE H-MODE OF ASDEX

density (which is a prerequisite for high pressuregradients in this model) can be due not only to theincreased electron temperature but also to the increasedpressure gradient itself

The high edge temperatures and the bootstrap effectsin the H-regime give rise to uncommonly high edgecurrent densities and hence steep current densitygradients These are conditions known to drive inconventional geometries tearing or kink modes withresonant surfaces in or just beyond the steep gradientzone (see also Section 23) It has been shown in ananalysis by Hahm and Diamond [116] that at least fora linear model of highly localized high-m high-nmodes the consequences will be different in a scenarioin which the shear introduced by the geometry of theflux surfaces strongly dominates that originating fromthe current density distribution In this case the modesare found to be strongly stabilized mdash a point which weshall further discuss in connection with models forconfinement changes in the plasma interior

The authors of Ref [116] also studied the possibleimpact of the separatrix geometry on resistive fluidturbulence which is possibly the cause of Ohmic andL-mode transport in the outer plasma zones Theyspecifically considered incompressible resistive ballooningmodes and impurity gradient driven rippling modes asthe reasons for anomalous electron heat conduction andparticle transport respectively In both cases the maineffect of the separatrix geometry is a reduction of thecharacteristic radial scale length of the resulting fluidturbulence due to the high shear and consequently areduction of the contributions to the electron heatdiffusivity the diffusion coefficient and the runawayloss rate It has been shown recently by Burrell [117]that the specific stabilization mechanism of resistiveballooning modes (the increase of the diamagnetic driftfrequency) suggested by the authors of Ref [116] cannotbe responsible for the L-H transition since the associateddiffusivity would actually increase during the formationof the temperature and density pedestal Since howeverexpressions suggested by Callen et al [118] for resistiveballooning mode driven turbulence yield reasonableagreement with the magnitude and profile shape of theelectron heat diffusivity in the outer plasma zones ofL-discharges the search for other stabilizing mechanismsshould be continued

93 Effects of the discontinuity between open andclosed flux surfaces on plasma transport

In the proximity of the plasma boundary the radialparticle and energy transport can be modified through

losses of charged particles to the target plates Modelsbased on this effect have been stimulated by the dis-covery of the H-regime and they frequently referspecifically to the axisymmetric divertor geometryHowever for the flux surface structures used in thesemodels to be applicable it is only necessary that thecontact between the plasma and the target plates beaxisymmetric with the contact located on the top orthe bottom or at the high field side of the plasmaboundary These theories therefore are not invalidatedby the discovery of the limiter H-mode

The first theory of this type and the one that hashad the best experimental verification [119] is thework by Hinton [120] who showed a strong dependenceof the Pfirsch-Schluter ion energy transport across theseparatrix on the location of the X-point The sinkconstituted by the target plates induces an additionalheat flow along field lines adding to or subtractingfrom the parallel Pfirsch-Schluter flow and thereforealso increasing or decreasing the radial heat flux for agiven radial ion temperature gradient For a given heatflux through the separatrix parallel fluxes give rise toflat ion temperature gradients while anti-parallel fluxescause steep gradients Since the direction of the parallelPfirsch-Schluter heat currents depends on the ion grad-Bdrift steeper gradients will develop if the latter is in thedirection to the X-point In the symmetric DN configu-ration with two X-points these geometric effects shouldcancel each other At high heating power these aspectsalso play no role because the heat transport under colli-sionless conditions is not affected by the X-point topology

Ion heat conduction is not considered to be thedominating energy transport process across the separa-trix but it will contribute to the power balance at theedge and its strength may be decisive for the attainmentof the high edge temperature values associated with theH-regime In a more recent work Hinton and Staebler[121] showed the existence of a similar effect onparticle transport which could be even more significantbecause convective energy losses may indeed be adominating term in the power balance

Unlike the stability conditions of ideal ballooningmodes which also introduce geometric constraints theneoclassical transport effects described above predictthe kind of up-down asymmetries for which there isstrong experimental evidence

In experiments the H-mode can be obtained both inthe SN and the DN configurations The SN configura-tion is achieved by vertically displacing the toroidalplasma column a few centimetres utilizing a radialmagnetic field The SN topology has major advantagessuch as lower power and density thresholds (see


ASDEX TEAM

E

I1 ( b )

bull mdash mdash

10 15 20

t(s)

FIG 101 L-H transitions of two consecutive shots (Nos 15564and 15565) for a DN discharge (a) and an SN discharge (b)The vertical displacement of the SN discharge is 1 cmIp = 031 MA B = 22 T PNI = 35 MW

Section 4) in the SN configuration with hydrogeninjection into a hydrogen plasma and PNJ gt 25 MWthe H-phase can be achieved by refuelling into themain plasma vessel (in the DN topology the refuellingmust be done in the dome) Furthermore with the SNconfiguration the H-mode can be achieved even in adirty plasma (for example when operation is resumedafter the vessel has been vented) in which case thedevelopment of the edge electron temperature isimpeded by impurity radiation and the available heatingpower is insufficient to produce the H-mode in theDN geometry

In the SN configuration the L-phase preceding theL-H transition is always observed to be shorter thanthe DN configuration at the same plasma and beamparameters Two subsequent discharges mdash one in theDN configuration and the other in the SN configura-tion mdash are compared in Fig 101 The verticaldisplacement is 1 cm in the case shown in Fig 101(b)and corresponds to a typical (density or temperature)density e-folding length in the SOL Plotted are the lineaveraged density and the HaDa radiation in the divertorchamber The drop in the HaDa radiation and thesimultaneous rise in density (until ELMs set in) markthe transition to the H-phase In the DN topology thepre-transition L-phase is 150 ms and in the SN topologyit is only 45 ms

The most important aspect of Hintons theory is theexpected impact of the ion grad-B drift direction on theL-H transition which is indeed observed experimentally[119] Figure 102 shows an operational diagram of theH-mode regarding the power and the vertical plasmaposition (which determine the plasma configuration)Centred (z = 0) plasmas are DN discharges whileplasmas shifted upward (downward) are upper (lower)SN discharges (open circles indicate L-discharges andarrows indicate the ion grad-B drift direction) Aspredicted in Ref [120] at high beam power theH-regime can be obtained irrespective of the symmetryof the stagnation points or the direction of the ion grad-Bdrift even when the plasma edge becomes collisionlessFigure 102 gives the same information as Fig 60(a)illustrating that in the DN configuration more powerthan in the SN topology (eg the cases at z = 4 cm)is required to produce the H-mode provided the iongrad-B drift direction is correct For positive verticaldisplacements when the ion grad-B drift direction istowards the stagnation point H-discharges are obtainedwhile in the lower SN topology with the ion grad-Bdrift direction away from the stagnation point onlyL-discharges are obtained at medium heating powerlevels

When the toroidal field is reversed (with the directionof the plasma current being the same to maintain theco-injection geometry) plasmas in the upper SN con-figuration are L-discharges while plasmas in the lower

(b)2 (cm)

4-

2--

o--

-2-

-4-bull

0 bull VB-drift

0 lt bull

O 0 0 bull 10 bull

0

bullVB-drift

PN (MW)

FIG 102 Operational diagram for L- and H-discharges(Hdeg injection into D+ plasmas) z is the vertical plasma positionz gt Oin the upper SN configuration z = Oin the DN configurationand z lt 0 in the lower SN configuration PNI is the beam powerinjected into the vessel The arrows indicate the ion grad-B driftdirection The curve in (a) denotes the operation boundary betweenL- and H-discharges and (b) indicates the plasma configurationThe solid points are for H-discharges and the circles forL-discharges


THE H-MODE OF ASDEX

( b )

2-

FIG 103 Electron and ion collisionality parameters deducedfrom the measured profiles The transition from the plateau to thecollisionless regime is indicated PNl = 33-35 MW B = 22 T(a) Ip = 031 MA (b) Ip = 038 MA

SN configuration mdash with the ion grad-B drift towardsthe (lower) stagnation point mdash mostly turn out to beH-discharges (Only a few discharges with a reversedfield have been carried out since the reversed magneticforces pose an additional risk for the machine)

As mentioned above besides ion heat conductionalso convection and charge exchange cause losses inthe boundary zone Only if the edge neutral density iskept low mdash which is probably the case in the divertorconfiguration where recycling occurs predominantlywithin the divertor chamber mdash can neoclassical or onlymoderately increased ion heat conduction be prevalentin the region adjacent to the separatrix

The detrimental role of increased recycling and gaspuffing has indeed been observed experimentally Inboth PDX [5] and ASDEX it is found that gas fuellingfrom the divertor dome instead of from the mainplasma vessel facilitates the L-H transition Excessivegas puffing could quench the H-phase in PDX whichwould lead to low confinement

In ASDEX the H-mode is obtained with hydrogenneutral injection into hydrogen plasmas if the sourceof the external gas flux that is required to maintainconstant density is moved from the main plasma intothe divertor chamber Results obtained with variousdivertor geometries as summarized in Section 42further revealed that at low power with a closeddivertor configuration the H-phase can only beobtained when the molecular hydrogen backflowfrom the divertor into the main plasma is reduced

The detrimental effect of the proximity of a materiallimiter is discussed in Section 612 The transition tothe H-phase is prevented by a poloidal limiter placedat a distance corresponding to about two SOL e-foldinglengths At this distance impurity erosion may still below while the local neutral density at the limiter isalready increased (in the Ohmic phase by a factor ofapproximately five) As in the case of the electrontemperature the ion temperature increases after theL-H transition (see Fig 7) at r = 35 cm Tj risesfurther from 07 keV in the L-phase to 1 keV inH-phase A steep Tj gradient develops at the edgeFigure 103 shows the ion and the electron collisio-nality parameters u and vl deduced from the electronand ion temperature profiles measured just before theL-H transition and 100 ms after it The results areobtained in the closed divertor configuration DV-I Theion collisionality parameter at the plasma edge isslightly above unity in the L-phase and clearly dropsbelow unity after the L-H transition The electroncollisionality parameter at the plasma edge is aboutunity in the L-phase and about 04 in the H-phase

These measurements indicate that the electrons andions are nearly collisionless even at the plasma edgeIn the pre-transition L-phase the collisionality para-meters are close to unity In the various divertorconfigurations studied (with different relative changesof i^(a) and Te(a) after the L-H transition) je(a) isgt 1 in all cases in the L-phase At r = 095a vl islt 1 in all cases In the closed divertor configurationvl drops to below 05 after the L-H transition even atthe plasma edge In the open configuration vl (a) remainsbetween 1 and 2 in the H-phase while vl (095a) isabout 05 Neither the rise of q at the plasma edge inthe separatrix configuration nor the very likely increaseof Zeff near the plasma edge have been considered inthe calculation of the collisionality The quoted vl valuesare therefore lower boundaries Despite these uncer-tainties it is possible that the collisionality regime atthe plasma edge changes at the L-H transition

Many features of the L-H transition are in qualitativeagreement with Hintons theoretical model for theL-H transition low recycling conditions are requiredand mdash as long as the plasma periphery is still collisional(at low beam power) mdash an asymmetric topology ofthe SN configuration In an SN discharge the H-modedevelops at low heating power shortly after the NIpulse is switched on in hydrogen plasmas and evenunder dirty operational conditions if the direction ofthe ion grad-B drift is towards the stagnation pointIf the L-H transition occurs at a critical gradient(which also requires a critical ion temperature gradient)


ASDEX TEAM

Hintons model predicts the existence of a powerthreshold

Particle transport across magnetic flux surfaces islinked with the momentum balance of the differentspecies and is intrinsically ambipolar in the innerregions of axisymmetric devices This is not true inthe near-boundary zone where electrons and ions canexchange momentum not only with each other but alsowith neutrals and with waves escaping from the plasmaor with material walls (for particles on loss orbits)In this situation quasi-neutrality is enforced by theappearance of a radial electric field which modifies thetransport of one or both species so that the net chargeloss out of the plasma is stopped Thus there is someanalogy to collision induced transport in the interior ofstellarators in which case there are sometimes twosolution branches for particle transport which differ inthe sign of the radial electric field

The possible influence of electric fields on theL-H transition was first pointed out in Ref [122]where a model of particle losses for the boundary zoneis presented In this model it is assumed that the ionsare lost through neoclassical orbit effects and that theelectrons are lost when they stream along braided fieldlines Both forms of transport depend on the radialelectric field the quasi-neutrality condition of radial flowis expressed by a relation between the gradient para-meter X (weighted sum of logarithmic density and tem-perature gradients) and the particle flux Fp In generalthe relation has three roots for r p ( ) but at low valuesof X only the high flux branch exists (with F mono-tonically increasing with X) and at high values of Xonly the low flux branch exists For the L-H transitionscenario it is assumed that during the pre-transitionL-phase the gradients increase until the high fluxbranch of the solution is no longer valid and a suddentransition to the low flux branch takes place TheS-shape of the Fp(X) relation also leads to a hysteresiseffect in the transition with the H-L transition occur-ring at lower values of X compared with the L-Htransition

At least in a qualitative sense this L-H transitionmodel reproduces many experimental observations verywell The transition in the boundary region is suddenand exhibits hysteresis character Its primary effect is adrop in the charged particle flux crossing the separatrixBefore the transition sufficiently steep gradients arerequired (these will become even steeper after thetransition) and thus the transition is certainly sensitiveto the magnitude of additional power losses such ascharge exchange or ion heat conduction losses asdiscussed by Hinton As energy transport mechanism

the model considers only convection which howevermay indeed be dominant in this zone during the L-phaseAfter the L-H transition because of the reduction ofthe particle flux and in particular the form of itsfurther dependence on X (Fp decreases with increasing X)the plasma cannot regain thermal equilibrium onlythrough convection effects In fact we observe areduction of the power flux into the separatrix and aloss of power accountability indicating that in the edgeregion the parameters indeed reach values at whichnew loss channels may open up (one of them beingELMs)

The critical element of the model presented inRef [122] is that it identifies (as for stellarators)the good confinement branch as the branch havingpositive radial electric fields (Er) However limiterbias experiments on ISX-B (the relevance of which forthe L-H transition can of course be questioned) haveshown that particle confinement is improved by anegative bias Recent measurements of the poloidalrotation of the plasma in the separatrix region ofDIII-D [123] also give results which are in contrast tothose predicted by the model of Ref [122] since theyshow that the H-phase is associated with more negativeEr values In this model no changes of the turbulentfluctuation level are required for better confinementcontrary to experimental observations (see Section 63)On ASDEX no measurements of the Er field at theplasma edge have yet been made The only indicationof a change of Er comes from the asymmetric broadeningof the scattering spectra as described in Section 63

A different approach to incorporating Er fields into anL-H transition model was made by Shaing et al [124]who used a neoclassical model of turbulence driventransport In this case the sensitivity of the results toEr arises from the shear in the E X B induced toroidalvelocity which can affect the frequency spectrum ofthe transport producing turbulence In particular forthe resistivity gradient driven turbulence it isexplicitly shown that a negative Er branch wouldcorrespond to a narrower spectrum and a reducedsaturation level The resulting turbulence induced ionand electron fluxes are intrinsically ambipolar so thatthey by themselves do not determine the value of Er-in the region near the edge Er is determined by thenecessity of balancing the non-ambipolar ion lossesinduced by momentum exchange with neutrals and theEr field modified orbit losses For low neutral densityand an ion collisionality parameter v lt 1 this leadsto a more negative Er field which reduces the amountof ambipolar losses With both v gt 1 and v lt 1Er becomes less negative Shaing et al [124] identify


THE H-MODE OF ASDEX

the two Er regimes with the H-mode and the L-moderespectively The observed improvement in confinementwould then be primarily due to the change in theanomalous transport contributions which are necessarilyambipolar but depend on the prevailing Er field Thistheoretical model is in line with the existing evidenceof the Er field behaviour in other devices anotherpoint in favour of this model is that the L-H transitionindeed reduces the type of anomalous losses that areprobably responsible for the transport in the L-phaseSo far however no catastrophe-type transition scenariohas been demonstrated with this model On the basisof our experimental evidence we consider such aproof to be essential in any theory on the L-H transi-tion in the plasma periphery

94 H-mode transport in the plasma interior

Transport analysis indicates that the overall improve-ment of the confinement in the H-mode probably takesplace in two steps a sudden increase correlated withthe development of an edge barrier and then a gradualimprovement which is determined by diffusiveprocesses that may lead to profile changes in the plasmainterior The processes can perhaps be explained interms of a continuous parameter dependence of thediffusivities throughout the OH- L- and H-phasesSince there is no first-principle transport model whichcorrectly reproduces both the global parameter scalingand the temperature profiles only qualitative investiga-tions have been made so far

The general trends of confinement at the L-H transi-tion in the inner plasma zones are however notinconsistent with the predictions of the standard modelof strong electrostatic turbulence driven by drift waves[125 126] and by rj modes [127] As discussed inSection 33 the ion heat transport in all confinementregimes of ASDEX can be well described by a combi-nation of neoclassical contributions and ^ mode drivencontributions to the heat diffusivity A conspicuousfeature of the H-regime is the flattening of the densityprofiles in the plasma interior where actually noimprovement of the ion energy confinement has beenobserved An increase of rjj would actually lead to anenhancement of this transport channel which is howeverlimited by the approach of Ln = (d log ndr)1 to themajor plasma radius Ro according to recent theories[128 129] On the other hand an increase of Ln wouldreduce the contributions of dissipative and collisionlesstrapped electron modes to the electron heat transportin agreement with experimental observations While theagreement between ion heat transport and predictions

for the Tji mode is satisfactory even quantitatively theabove statements concerning the electron heat diffusivityhave been verified only in a qualitative sense Themost serious objection to this electrostatic turbulencemodel concerns its implied unfavourable isotope depen-dence which is in contrast to the observed trend of xe-

In the H-mode the steep gradients of the pressureparticle density and current density are moved to theregion directly at the edge thereby the free energy inthe bulk plasma is reduced which may lead to animprovement of the transport conditions there Thespecific edge structure in the H-mode may thus permitthe formation of a type of plasma profiles with betterconfinement aspects One profile which will clearlyshow a significant change after the L-H transition isthat of the current density The most direct contributionto this change comes from the associated high edgetemperatures the electrical conductivity in the plasmaperiphery in the H-mode is about the same as it is inthe plasma centre during the OH-phase Added to thisshould be the bootstrap current that is associated withthe steep pressure gradients in this zone (possiblymodified by the presence of the plasma boundary seeRef [130]) The calculations of Hahm and Diamonddiscussed in Section 92 indicate that the plasma shouldindeed be capable of accommodating a higher currentdensity gradient in the high shear region so that adisplacement of the current to the edge region has agenerally beneficial effect upon the stability to currentdriven modes Improved MHD stability in the bulkplasma is indeed observed in the H-mode because them = 1 mode and the sawteeth disappear without beingreplaced by m = 2 mode activity What is unclear ishow the improved stability to macroscopic modes isconnected with the microscopic turbulence Manystudies of this subject have been published Thisproblem is also discussed in conjunction with thedegradation of confinement in the L-mode and theobserved resistance of the electron temperature profileto any changes by auxiliary heating [130] A controver-sial point in this respect is the problem of the associatedtime-scales because the penetration of current densityperturbations should proceed on the resistive skin timewhereas the observed adjustments of the electron heatdiffusivity seem to proceed on a much shorter time-scale

In general resistive-type fluid turbulence as consid-ered in Ref [116] should be reduced by giving theplasma profile a temperature pedestal The confinementcould thus improve at least in the outer zones of thebulk plasma (corresponding approximately to theregion q gt 2) where this type of transport has some-times been postulated to dominate A further mechanism


ASDEX TEAM

by which resistive fluid turbulence (but possibly alsoother modes) might be reduced was suggested byShaing et al [124] in the context of his neoclassicalmodel of turbulence driven transport (see Section 93)namely that the radial field changes associated with theL-H transition propagate inward owing to viscousdamping of the resulting velocity shear in the cor-responding flow

Two attemps made to test some of these ideas bysimulation calculations have been reported in the litera-ture One investigation [111] started from semi-empiricalexpressions that were however chosen to reflect thebasic dependences expected from different types ofturbulence in different plasma parameter regimes Thecalculations were carried out in an attempt to obtain aquantitative fit of discharges on PDX and on ASDEXBy assuming an external trigger for the H-mode(argued to correspond to a sudden plugging of thedivertor and acting through a rise in the respectiveedge densities) it was indeed possible to follow intime a complete experimental discharge scenario witha fair fit to the profiles and the average plasma para-meters The main effect of the L-H transition on theinterior plasma could be reproduced by applying atransport that had a favourable density and temperaturedependence and which was introduced to simulate theOhmic confinement behaviour over the whole plasmacross-section With additional heating the Ohmictransport characteristics are assumed to dominatethe outer zones

Similar results were obtained in calculations ofSheffield [131] these were made without reference tospecific discharges but took into account in a quantita-tive way the best present knowledge of local transportcoefficients From these studies it follows that modesof the resistive fluid turbulence type may account forthe improvement in transport beyond the immediateedge zone after an L-H transition

10 SUMMARY

In ASDEX the H-mode develops during the auxiliaryheating pulse after a preceding L-phase At the L-H tran-sition both the particle content and the energy contentrise the divertor Ha radiation decreases within 1-2 msindicating an improvement of the confinement Duringthe H-phase the plasma profiles broaden and steeppressure gradients develop at the edge A new instabilitydevelops in the H-phase which is dubbed edge localizedmode (ELM) because it affects the plasma periphery itleads repeatedly to particle and energy losses ELMs

can be suppressed by moving the plasma closer to theouter wall In this way a quiescent H-mode (H-mode)is achieved which has even better confinement proper-ties than the H-mode with ELMs but which is verysusceptible to impurity accumulation After terminationof the auxiliary heating pulse the plasma remains inthe H-phase for a short time (~30 ms) then it returnsto the L-mode and gradually (within - 100 ms) againto Ohmic conditions

The neutral heating efficiencies for both electronsand ions are better in the H-phase In the case ofthermal neutrons the fluxes are higher by a factorof three to four in the H-phase Bootstrap and beamdriven currents amount to nearly 50 of the totalcurrent

Typically NI heating is applied to sawtoothingOH target plasmas In this case the sawtooth periodincreases and the duration of the m = 1n = 1 precursoris prolonged If L-H transitions are triggered bysawteeth their period increases further During theH-phase the sawteeth often disappear At higher power( -1 5 -2 MW) after the first sawtooth crash them = 1 mode remains at a quasi-stationary levelwithout giving rise to sawtooth relaxation processesIf the L-H transition occurs during such a phase them = 1 amplitude is drastically reduced but then it mayagain appear in fishbone-like bursts In all scenariosthe m = 1 mode provokes an m gt 4n = 1 satelliteMirnov oscillation (of the same frequency)

During the L-phase also an m gt 3n = 1 mode isoften observed It propagates in the opposite directioncompared with the m = 1 mode and at a lower angularvelocity (lower frequency) The m gt 3n = 1 mode islocated inside and near the separatrix and vanishesafter the L-H transition within a few milliseconds

The ELMs are a new MHD phenomenon of adisruption type so far they have been observed onlyin H-type plasmas The most prominent manifestationsof ELMs are the sudden change of the equilibriumposition due to the loss of energy and a spike in theHa emission from the divertor chamber indicatingincreased power loss During ELMs the edge local-ized m gt 3 mode reappears it does not howeverhave the character of a precursor

The impurity development in the H-phase is deter-mined by reduced plasma-wall interaction improvedparticle confinement and possibly ELMs whichrepresent an additional loss mechanism When ELMsare present quasi-steady state conditions regarding theplasma particle and energy content and impurity con-centration can be established in the H-phase WithoutELMs no steady state develops and in this case the


THE H-MODE OF ASDEX

H-phase is already terminated during the beam phaseby a transition to the L-phase Accumulation of high-Zimpurities can be described on the basis of classicalimpurity accumulation theory

Various edge and divertor diagnostics are availableon ASDEX to analyse the plasma parameters beforeand during the H-mode

The transition from Ohmic heating to neutral injec-tion generally leads to an L-mode which at the edge ischaracterized by a significant increase of the radiale-folding lengths in the SOL an increase of thepower and particle fluxes into the SOL and the divertorand hence a substantially intensified divertor recyclingand power load These changes are consistent withstandard models of the SOL and the divertor when theincreased fluxes are properly taken into account andwhen the values of the radial anomalous transportcoefficients are taken to be twice as high as beforewhich is qualitatively in keeping with the worsening ofthe bulk confinement

At the L-H transition the midplane edge gradientssteepen significantly causing a reduction of the radialdecay lengths by a factor of more than two The Ha

signals drop everywhere indicating a global reductionof hydrogen recycling In the divertor the recyclingand power load are strongly reduced to roughly Ohmicvalues the plasma profiles in the divertor chamber arenarrower in accordance with the reduced SOL widthof the main plasma Obviously the power and particleinputs into the SOL and the divertor are decreased bya significant factor and the edge cross-diffusion coeffi-cients are reduced to a fraction of the Ohmic value inthe quiescent H-phase Because of the steep gradientsand the narrow profiles the error in the determinationof the separatrix position in the midplane and divertor(of the order of plusmn 1 cm) which is already a problemin the OH- and L-modes becomes severe in theH-mode since the SOL width is of the same orderIn the divertor the profile maxima sometimes seemto move to the side of the separatrix where the fieldlines are not connected with the main plasma vessel mdashin contradiction to standard edge models Furthermorein the H-mode the position of the thermal barrier relativeto the separatrix has to be considered The followingpoints seem to be relevant in this context An indepen-dent determination of the position of the separatrix inthe divertor which relies on the observed very narrownegative dip (caused by fast electrons) in the floatingpotential always gives a separatrix position that isapproximately the expected one and that is sometimesin contradiction to the position determined magneticallyIn the midplane an independent measurement of the

separatrix position on the basis of the soft X-ray emis-sion from a radially moving target again relying onfast electron dynamics gives a radial position of theseparatrix that is at the end of the error bars from themagnetic determination In addition the assumption ofapproximate pressure constancy along field lines betweenthe midplane and the divertor (which may be questionedfor the H-mode but is probably correct for the OH-and L-modes) also requires that the true separatrixposition be outside that calculated from magnetic signalsfor all three phases This is true without exception inall cases that have been studied in detail

It is therefore concluded that during the H-mode theedge region is well described by the standard SOL theoryif significant reductions of the anomalous radial transportand of the instantaneous power and particle fluxesacross the separatrix are taken into account No specificthermal barrier along open field lines (apart from aweak standard flux limit) is required Thus it shouldbe noted that the region of strongly increased edgeelectron temperature is clearly inside the correctseparatrix in accordance with a perpendicular thermalbarrier in the adjacent high shear region while theseparatrix temperature itself remains at moderatevalues The quiescent H-mode is frequently interruptedby sudden increases of the energy and power flux intothe SOL and the divertor that are produced by ELMsand that cause temporarily extreme recycling andpower load conditions in the divertor The radial widthof the SOL during an ELM is even larger than in theL-mode The time averaged power loss approaches thelevel of the input power but the amount of missingpower is higher than in other regimes Detailed ana-lyses seem to be impossible because the process ishighly dynamic and shows obvious deviations fromsimple fluid behaviour In addition time averagedtarget plate calorimetry shows an approximate toroidalsymmetry in the OH- and L-phases but a pronouncedtoroidal asymmetry during ELM activity making localELM measurements questionable This asymmetry alsoimplies that ELMs always occur with roughly the sametoroidal phase angle probably as a consequence ofmode locking to small resonant external magnetic fieldperturbations In fact a sideward shift or tilting of thedivertor triplet coils within the mechanical tolerancesof several millimetres already causes the formation ofmagnetic islands of several centimetres width at rationalsurfaces near the edge and ergodization around theseparatrix Except for the observed phase lockingthere is as yet no clear indication of a direct influenceof the edge perturbation on the H-mode physics


ASDEX TEAM

After the L-H transition the power flow patternchanges The power flux into the divertor chamber isreduced approximately to the OH-level no satisfactorypower accountability is possible The energy confine-ment time increases after the L-H transition by a factorof about two The linear current scaling of the energyconfinement time remains during the H-phase no cleardependence on Bt or h is observed No power depen-dence of the energy confinement time is observed duringthe regular H-phase with ELMs The analysis indicatesthat the lack of power dependence is due to a combina-tion of power losses via ELMs which decrease withincreasing power and via the intrinsic transport losseswhich increase with increasing power In the H-phasethe energy confinement time increases linearly with theisotope mass

The main results of the local transport analysis arethat the electron heat diffusivity and the particle diffusioncoefficient increase from the OH-phase to the L-phaseand decrease after the L-H transition changing typicallyby a factor of two in both cases The L-H transitionobviously starts near the plasma boundary where theelectron heat diffusivity and the diffusion coefficientare even more reduced than in the plasma centre Inohmically heated and additionally heated plasmas withflat density profiles having ^ gt 1 over the entireplasma the ion heat diffusivity is increased by a factorof two to four compared with the neoclassical valuesThis increase is in agreement with the theoreticalexpectations for r mode driven ion heat diffusivitiesAt high ion temperatures convective losses have to betaken into account Scaling relations for the diffusivitieshave been given and the parameters critical for theL-H transition have been identified and compared withtheoretical models

The operational range for the H-mode is large howeverit is necessary to have a density and a heating powerabove a certain threshold ie n gt 17 X 1013 cm3

and Ptot gt 11 kW The threshold conditions dependon the plasma configuration (for the DN configurationhigher density and power are required than forthe SN configuration) as well as on the drift directionof the ions (less power is required when it is towardsthe X-point) and on the ion species of the plasma andthe beam The power threshold shows a weak depen-dence on the density the toroidal field and the currentA decisive factor for the development of the H-modeis the control of recycling gas Backflow of molecularhydrogen out of the divertor chamber should beprevented The H-mode can be achieved with ICRHin the minority mode under lower hybrid (with NI)and beam current drive conditions with additional

pellet refuelling and in the limiter configuration witha bottom rail limiter

Because of the L-phase preceding the transition andthe existence of a power threshold efforts to explorethe mechanisms for the L-H transition have concen-trated on parameters which are affected by auxiliaryheating There is experimental evidence that the electrontemperature at the edge (or a related quantity such aspressure resistivity or collisionality) plays an importantrole Most convincing is the observation that the H-phasecan be triggered by a sawtooth event Detailed studieswith good time resolution show that the L-H transitionoccurs when the thermal wave reaches the periphery

At the LmdashH transition an edge transport barrierdevelops which impedes the flow of particles andenergy across the separatrix The location of the steepgradients leads to the assumption that the edge barrierdevelops at the separatrix but inside of it

At the instant of the L-H transition the densityfluctuation level at the edge suddenly decreases thedecrease of the bulk fluctuation amplitude proceedsmore slowly The confinement of runaway electrons alsostrongly increases at the L-H transition The increasedrunaway losses in the L-phase are ascribed to the effectsof resistive ballooning modes The magnetic fluctuationlevel can decrease after the L-H transition There arehowever a number of unexplained observations andno direct connection has been found so far between themagnetic turbulence as measured from the outside andthe confinement properties of the bulk plasma

The MHD stability of ASDEX H-mode dischargeshas been investigated with respect to both the linearand the non-linear evolution of ideal and resistiveMHD stabilities as well as ideal and resistive ballooningmodes using free-boundary equilibria The existenceof pressure driven resistive modes at j3p gt 1 mayexplain the fact that the m lt 5 MHD modes observedin the H-mode have large inside-outside asymmetriesof B resonant surfaces close to the separatrix andm values increasing with beta Because of the locationof pressure and current gradients near the plasma edgeit can be assumed that ELM instabilities are caused bypressure driven resistive modes with resonant surfacesnear the separatrix but outside of it These modes canlead to transport of plasma across the separatrix bykink-type motions so that energy and particles aretransported to the divertor

For calculations of ballooning mode stability onASDEX detailed informations on toroidal displacementsof the magnetic surfaces and on local and global shearnear the separatrix are needed Ideal ballooning modesare not unstable even at the beta limit where a sudden


THE H-MODE OF ASDEX

saturation of beta is followed by a slow decreaseDuring this decrease of beta there is a broad region ofppM values between 07 and 09 When the values ofthe pressure gradient p decrease the current profilealso becomes flat which can be explained by thebroadening of the Te profile by the increasing Zeff

(due to impurity accumulation) and by the effect of thebootstrap current The growth rate of resistive ballooningmodes strongly increases near the beta limit and thesemodes may lead to the observed increased energy lossesin this region Compressibility and resistivity are thedominating destabilizing processes depending on themode number overstable solutions are also observedElectrostatic ballooning modes are of similarimportance near the plasma boundary of H-dischargeswhere the plasma pressure is small but p is largeOur calculations show that mdash despite the increasedshear in this region mdash p is high enough for resistiveballooning modes to become unstable but it is far fromthe second region of stability

Comparison of ASDEX results with those fromother experiments in particular those from DIII-Dshows agreement between them in many respectsfor example the general occurrence of an L-phasebefore the L-H transition the simultaneous improve-ment of the confinement times of energy and particlesthe possibility of triggering the H-phase with a saw-tooth the development of a transport barrier at theseparatrix but inside of it the sharp reduction of theedge density fluctuation level and the importance of theion grad-B drift direction The H-mode is achieved inboth limiter and divertor configurations and with variousheating methods

Compared with the ASDEX results a strongerdependence of the power threshold on B and n isfound on DIII-D and a clear correlation betweenmagnetic fluctuations and bulk plasma confinementis observed

The comparison of experimental observations withtheoretical models of the H-mode can only be qualita-tive Theoretical explanations are needed for thesuddenness of the L-H transition to prove the simul-taneous existence of two equilibrium states for thesame set of external parameters and to explain theobserved hysteresis in the L-H transition

The general agreement on the location of thetransport barrier mdash at the separatrix but inside of it mdashseems to rule out bifurcating solutions for the paralleltransport in the SOL The achievement of the H-modein the limiter configuration seems to indicate that theincreased shear in the edge region does not have astrong impact The hypothesis that the L-H transition

is triggered by the plasma edge entering the secondstability regime seems to contradict the L-phase stabilityanalysis Even close to the L-H transition the L-modeplasma is far from the first stability limit

Theories based on mechanisms arising from thediscontinuity between open and closed flux surfacesand plasma transport reproduce some salient H-modefeatures such as the role of the ion grad-B drift direc-tion the suddenness of the transition and the observedhysteresis effects In one of these theories the effect ofa change in the radial electric field on turbulent transportis considered to reconcile the neoclassical transporteffects with the observed sharp drop in the fluctuationamplitude

Generally the improvement of the bulk plasmaconfinement is connected with the reduction of freeenergy in the bulk plasma when the steep gradients areshifted to the edge region The role of the modifiedplasma current profile has also been studied and it isfound that the higher edge current density (due to thehigher electrical conductivity and the bootstrap effect)provides better stability against current driven modes

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ASDEX TEAM

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[50] STROTH U FAHRBACH HU HERRMANN WMAYER HM Nucl Fusion 29 (1989) 761

[51] KALLENBACH A MAYER HM FUSSMANN Get al Improvement of angular momentum confinement withdensity peaking on ASDEX submitted to Nucl Fusion

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[53] GRUBER O in Plasma Physics (Proc Int ConfLausanne 1984) Vol 1 CEC Brussels (1985) 67

[54] SOLDNER FX MULLER ER WAGNER F et alPhys Rev Lett 61 (1988) 1105

[55] KAYE SM GOLDSTON RJ Nucl Fusion 25 (1985)65


THE H-MODE OF ASDEX

[56] NIEDERMEYER H WAGNER F BECKER G et alin Plasma Physics and Controlled Nuclear Fusion Research1986 (Proc 11th Int Conf Kyoto 1986) Vol 1 IAEAVienna (1987) 125

[57] KEILHACKER M BISHOP CM CORDEY JGMUIR DG WATKINS ML in Controlled Fusion andPlasma Physics (Proc 14th Eur Conf Madrid 1987)Vol 11D Part III European Physical Society (1987) 1339

[58] WAGNER F GRUBER O GEHRE 0 LACKNER K MULLER ER STAEBLER A in Con-trolled Fusion and Plasma Heating (Proc 15th Eur ConfDubrovnik 1988) Vol 12B Part I European PhysicalSociety (1988) 207

[59] GOLDSTON R Plasma Phys Controll Fusion 26 (1984)87

[60] KAYE SM GOLDSTON R Nucl Fusion 25 (1985) 65[61] TANGA A BARTLETT D BURES M et al in Con-

trolled Fusion and Plasma Heating (Proc 15th Eur ConfDubrovnik 1988) Vol 12B Part I European PhysicalSociety (1988) 235

[62] BURRELL KH ALLEN SL BRAMSON G et alin Plasma Physics and Controlled Nuclear Fusion Research1988 (Proc 12th Int Conf Nice 1988) Vol 1 IAEAVienna (1989) 193

[63] FONCK RJ BEIERSDORFER P BELL M et alin Heating in Toroidal Plasmas (Proc 4th Int Symp Rome1984) Vol 1 ENEA Rome (1984) 37

[64] GRUBER O BECKER G GIERKE G von et alin Plasma Physics and Controlled Nuclear Fusion Resarch1986 (Proc 11th Int Conf Kyoto 1986) Vol 1 IAEAVienna (1987) 357

[65] GIERKE G von KEILHACKER M BARTIROMO Ret al in Controlled Fusion and Plasma Physics (Proc 12thEur Conf Budapest 1985) Vol 9F Part I EuropeanPhysical Society (1985) 331

[66] NIEDERMEYER H BECKER G BOMBA B et alPlasma Phys Controll Fusion 30 (1988) 1443

[67] STEINMETZ K NOTERDAEME J-M WAGNER Fet al Phys Rev Lett 58 (1987) 124

[68] OGAWA Y HOFMEISTER F NOTERDAEME J-Met al in Controlled Fusion and Plasma Physics (Proc 16thEur Conf Venice 1989) Vol 13B Part III EuropeanPhysical Society (1989) 1085

[69] STEINMETZ K SOLDNER FX ECKHARTT Det al in Plasma Physics and Controlled Nuclear FusionResearch 1986 (Proc 11th Int Conf Kyoto 1986) Vol 1IAEA Vienna (1987)461

[70] LEUTERER F SOLDNER FX ECKHARTT Det al Plasma Phys Controll Fusion 27 (1985) 1399

[71] KAUFMANN M BUCHL K FUSSMANN G et alNucl Fusion 28 (1988) 827

[72] WAGNER F KEILHACKER M ASDEX and NITeams J Nucl Mater 121 (1984) 193WAGNER F In Basic Physical Processes of ToroidalFusion Plasmas (Proc Course and Workshop Varenna1985) Vol 1 CEC Luxembourg (1985) 65

[73] EUBANK H GOLDSTON RJ ARUNASALAM Vet al in Plasma Physics and Controlled Nuclear FusionResearch 1978 (Proc 7th Int Conf Innsbruck 1978)Vol 1 IAEA Vienna (1979) 167

[74] DODEL G HOLZHAUER E in Controlled Fusion andPlasma Heating (Proc 15th Eur Conf Dubrovnik 1988)Vol 12B Part I European Physical Society (1988) 43

[75] DODEL G HOLZHAUER E Annual Report 1987Max-Planck-Institut fur Plasmaphysik Garching (1987)

[76] CROWLEY T MAZZUCATO E Nucl Fusion 25(1985) 507

[77] RUDYJ A BENGTSON RD CARLSON A et alin Controlled Fusion and Plasma Physics (Proc 16th EurConf Venice 1989) Vol 13B Part I European PhysicalSociety (1989) 27

[78] HOLLENSTEIN C KELLER R POCHELON Aet al Broadband Magnetic and Density Fluctuations in theTCA Tokamak Rep CRPP LRP 306 Centre de recherchesen physique des plasmas Lausanne (1986)

[79] McGUIRE K ARUNASALAM V BELL MG et alCoherent and Turbulent Fluctuations in TFTR RepPPPL-2435 Princeton Plasma Physics LaboratoryPrinceton NJ (1987)

[80] GIANNONE L Experimental Observations of BroadbandMagnetic Fluctuations in ASDEX Rep IPP-III138 Max-Planck-Institut fur Plasmaphysik Garching (1988)

[81] KIM YJ GENTLE KW RITZ CP RHODES TLBENGTSON RD Nucl Fusion 29 (1989) 99

[82] DODEL G HOLZHAUER E MASSIG J in Con-trolled Fusion and Plasma Physics (Proc 14th Eur ConfMadrid 1987) Vol 11D Part I European Physical Society(1987) 249

[83] KWON OJ DIAMOND PH WAGNER F et alNucl Fusion 28 (1988) 1931

[84] LEE JK Nucl Fusion 26 (1986) 955[85] McGUIRE K BEIERSDORFER P BELL M et al

in Plasma Physics and Controlled Nuclear Fusion Research1984 (Proc 10th Int Conf London 1984) Vol 1 IAEAVienna (1985) 117

[86] KEILHACKER M GIERKE G von MULLER ERet al Plasma Phys Controll Fusion 28 (1986) 29

[87] GRASSIE K BECKER G GRUBER O et al inTurbulence and Anomalous Transport in Magnetized Plasmas(Proc Int Workshop Cargese 1986) Editions de PhysiqueOrsay (1987) 279

[88] GRASSIE K GRUBER O KLUBER O et al in Con-trolled Fusion and Plasma Physics (Proc 14th Eur ConfMadrid 1987) Vol 11D Part I European Physical Society(1987) 226

[89] JAKOBY A Non-Linear Resistive MHD-Code in Cylindri-cal Geometry Rep IPP-6269 Max-Planck-Institut furPlasmaphysik Garching (1987)

[90] CONNOR JW HASTIE RJ TAYLOR JB PhysRev Lett 40 (1987) 396

[91] CHOE WH FREIDBERG JP Phys Fluids 29 (1986)1766

[92] NEUHAUSER J SCHNEIDER W WUNDERLICH RNucl Fusion 26 (1986) 1679

[93] CONNOR JW HASTIE RJ MARTIN TJ PlasmaPhys Controll Fusion 27 (1985) 1509

[94] CORREA-RESTREPO D Z Naturforsch A 37 (1982)848

[95] ZEHRFELD HP GRASSIE K Nucl Fusion 28 (1988)891


ASDEX TEAM

[96] GRASSIE K ZEHRFELD HP Nucl Fusion 28 (1988)

899[97] CONNOR JW HASTIE RJ MARTIN TJ

SYKES A TURNER MF in Plasma Physics and Con-trolled Nuclear Fusion Research 1982 (Proc 9th Int Conf

Baltimore 1982) Vol 3 IAEA Vienna (1983) 403[98] DRAKE JF ANTONSEN TM Phys Fluids 28 (1985)

544[99] HENDER TC CARRERAS BR COOPER WA

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in Plasma Physics and Controlled Nuclear Fusion Research

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Vienna (1989) 97[101] MANICKAM J ARUNASALAM V BARNES CW

etal ibid p 395[102] SCHISSEL R in Controlled Fusion and Plasma Physics

(Proc 16th Eur Conf Venice 1989) Vol 13B Part I

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Phys Rev Lett 58 (1987) 1004[105] GEHRE O GRUBER O MURMANN HD et al

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(1987) 1401[107] LOHR J STALLARD BW PRATER R et al Phys

Rev Lett 60 (1988) 2630[108] OHKAWA T CHU MS HINTON FL LIU CS

LEE YC Phys Rev Lett 51 (1983) 2101[109] HOSHINO K YAMAMOTO T KAWASHIMA H

YAMANCHI T UESUGI Y J Phys Soc Jpn 56

(1987) 1750[110] SUGIHARA M SAITO S HITOKI S et al J Nucl

Mater 128amp129 (1984) 114[ I l l ] SINGER CE REDI MH BOYD DA et al Nucl

Fusion 25 (1985) 1555[112] SHIMADA M Bull Am Phys Soc 32 (1987) 1898[113] BISHOP C M KIRBY P CONNOR JW

HASTIE RJ TAYLOR JB Nucl Fusion 24 (1984)1579

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[115] BISHOP C M in Theory of Fusion Plasmas (Proc Work-shop Lausanne 1988) Editrice Compositori Bologna (1988)123

[116] HAHM TS DIAMOND PH Phys Fluids 30 (1987)133

[117] BURRELL KH ALLEN SL BRAMSON G et al inPlasma Physics and Controlled Nucler Fusion Research 1988(Proc 12th Int Conf Nice 1988) Vol 1 IAEA Vienna(1989) 193

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[123] BURRELL KH Physics of enhanced confinementH-mode discharges in DIII-D presented at Workshop onEnhanced Confinement Regimes Nice 1988

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(Manuscript received 21 August 1988Final manuscript received 21 July 1989)


SPECIAL TOPIC

THE H-MODE OF ASDEX

ASDEX TeamMax-Planck-Institut fur PlasmaphysikEuratom-IPP AssociationGarching bei MiinchenFederal Republic of Germany

ABSTRACT The paper is a review of investigations of the H-mode on ASDEX performed since its discoveryin 1982 The topics discussed are (1) the development of the plasma profiles with steep gradients in the edge regionand flat profiles in the bulk plasma (2) the MHD properties resulting from the profile changes including an extensivestability analysis (3) the impurity development with special emphasis on the MHD aspects and on neoclassical impuritytransport effects in quiescent H-phases and (4) the properties of the edge plasma including the evidence of three-dimensional distortions at the edge The part on confinement includes scaling studies and the results of transport analysisThe power threshold of the H-mode is found to depend weakly on the density but there is probably no dependenceon the toroidal field or the current For the operational range of the H-mode new results for the limiter H-mode onASDEX and the development of the H-mode under beam current drive conditions are included A number of experi-ments are described which demonstrate the crucial role of the edge electron temperature in the L-H transition Newresults of magnetic and density fluctuation studies at the plasma edge within the edge transport barrier are presentedFinally the findings on ASDEX are compared with results obtained on other machines and are used to test variousH-mode theories

CONTENTS GENERAL INTRODUCTION 1 INTRODUCTION AND OVERVIEW OF THE H-MODE2 CHARACTERISTICS OF H-MODE PLASMAS 21 Equilibrium parameters 22 Main plasma parameters

221 Profile development 222 Bootstrap currents and beam driven currents in the H-mode 23 MHD charac-teristics of the H-mode 231 Behaviour of the m = 1 mode and the sawteeth 232 Localized m pound 2 modes233 Edge localized modes 24 Impurity development in the H-mode 25 Scrape-off layer and divertor plasmaparameters 3 CONFINEMENT IN THE H-MODE 31 Power fluxes in the H-mode 32 Global confinement33 Transport analysis 34 Scaling of the energy confinement time in the H-mode 341 Density dependence

342 Current dependence 343 Power dependence 3431 Power scaling of TE in the quiescent H-mode3432 Effect of ELMs on global confinement 344 Plasma species dependence 345 Toroidal field dependence346 Summary of the TE scaling results 347 Scaling of transport coefficients 4 OPERATIONAL RANGE OFTHE H-MODE 41 Parameter dependence of the H-mode power threshold 42 Study of the H-mode under variousdivertor topologies 43 Limiter H-mode of ASDEX 5 USE OF OTHER HEATING AND REFUELLINGTECHNIQUES FOR H-MODE PLASMAS 51 ICRF heating 511 Hydrogen minority heating 512 Second-harmonic hydrogen heating 52 Lower hybrid heating and beam current drive in the H-mode 53 Pellet refuellingin the H-mode 6 PHYSICS ASPECTS OF THE L-H TRANSITION 61 Role of the edge electron temperature

611 Addition of impurities 612 Development of the electron temperature in limiter discharges 613 Post-beampulse H-phase 614 Comparison of L-H and H-L transitions 615 Sawteeth as H-mode trigger 62 Formationof a transport barrier at the plasma edge 63 Microscopic turbulence in H-phases 631 Density fluctuations

632 Fluctuations of the Ha light emission 633 Magnetic field fluctuations 634 Confinement of runawayelectrons 7 MHD STABILITY ANALYSIS OF H-MODE DISCHARGES 71 Medium m-mode stability72 Resistive MHD simulations of ELMs 73 Ballooning stability calculations 731 Ideal ballooning modes732 Resistive ballooning modes 8 COMPARISON OF H-MODE PROPERTDZS ON ASDEX WITH THOSEFOR OTHER EXPERIMENTS 81 Agreement between the observations on ASDEX and DITJ-D 82 Disagree-ment between the observations on ASDEX and DIII-D 9 DIFFERENT THEORETICAL MODELS FOR THEH-MODE 91 H-regime theories involving SOL physics 92 Models of high shear zone effects 93 Effects of thediscontinuity between open and closed flux surfaces on plasma transport 94 H-mode transport in the plasma interior10 SUMMARY References


ASDEX TEAM




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ASDEX TEAM










h 20

V

ne

o

X

A

qa = 365qQ = 29qa = 26qa=275

--10



THE H-MODE OF ASDEX

AA

sawtooth

r fcmJ








9630

ELMin

ltMio

CM



ASDEX TEAM

90 180 270 360












11 12 13 t (s)



THE H-MODE OF ASDEX

a

2 4 6

dnedr (1012cm-4)









ASDEX TEAM

10

10

2 poundbull

4

1 4804

4745

Lj( b )

13 15 16

t Is]


with ELMs wo ELMs

rRAO

(MW)

(au)



THE H-MODE OF ASDEX

08

04

- - 5

with ELMs 11338

time 11) 1095 s12) 1155 s13) 1215 s14) 1230 s15) 1245 s6I 1260 s

10 20r (cm)

30

s

6

gt

- bull 2

wo ELMs 11447

( b )s

i bull i i f

time- (1)(2)13114)IS]161

1095 s1155 s1215 s1230 s1245 s1260 S

10 20 30rcm)





nFel0)nel0) =

io-2-

bullo

5 io3J

10110 120 130

t(s)



ASDEX TEAM











THE H-MODE OF ASDEX







ASDEX TEAM

600-

500-

i00-20-

15-

( b )

-6 -6 -2 0

Ar= r-r (cm)








THE H-MODE OF ASDEX

[cm]

1013

9630OH 105s

- - - L 113H 1164

1012

R-Rs [cm]

-2 8









ASDEX TEAM

o

c

O

15-

10-

os-

o-

4-

2-

n-

raquo 96301

)bull

L

- - ^

0 (DO 0 bdquo

H

Nl

1

i

idegC11

i

ii

i

o o o

Lm

mdash

11 12 13 t [sJ 14







20t



neutralizer plates

infrared camera

HaDQ



THE H-MODE OF ASDEX

J

L

VUilillililUH V

1bullE 25u

2 20

S 15cat

Z 10c

s ^

sect 0

raquo 9393

10 12 U

t (si


cm = 30 MW






175 165 170 175 165

Rlcml

170 175



ASDEX TEAM

1520243 (L 2=0) 20241 (H Z=+1 Cm)

| ri

0

40

gt

20

4

On 2

40

-40

165 170 175 165

R (cm)170 175








THE H-MODE OF ASDEX

90 91 92







30


Z mdash



ASDEX TEAM






N I A

10 11

t (s)





THE H-MODE OF ASDEX

E

Ul

Ul

80-

70-

60-

50-

40-

30-

20-

10-

0 bull

D 1

bull

itlw deg


A A

A

2 3 U

n e [10

p

0

oo

1 8

0

bull OX +

5

cm3]

D+

a

5

A

hrP

PN

6

oD

H-type

= 370 kA= 300 kA

gt 2 MW

7 8











ASDEX TEAM







dNdt = - N T P (2)


= N0TD (3)



6028 laquo 5991

oe



THE H-MODE OF ASDEX


Phase

OH

L

H

dNdt

(s-1)

0

0

2 x 1021

(s-1)

1O21

6 x 1O21

0

V(s-1)

0

8 x 1O20

8 x 102 0

2

2

2

(s

X

X

X

Rb

-)

1O21

102 1

1O21

TP

(s)

OO5

001

015


dN N

dt + rp deg +












ASDEX TEAM

17005r=2a3

11O H V NI (

115 12 125

X

[m2s]

1-

1-

(

bull

17005

b)

s

IS 11 S2 = 115 s3S 1195 s4U205s551215s

bullXe(a)

0 05 r a 1









3-T

[keV]2-

1-

mdash

(a )

r o )N

t

XCH+X

17005123s

05 ra 1

1

3-

2-

1 -

L (1 15S)

H(1215s)

( b )

OH(ils)

- lt

05 ra 1





THE H-MODE OF ASDEX

10








180 190 200

R (cm)

210



ASDEX TEAM

A- L1227s

0 20 A0r (cm)














THE H-MODE OF ASDEX

02 03Io IMA)

04













yj

UJ

60-

40-

-

20-

0-

o

0

L-

^

O

Mode

H

o

bull fraquo

- Mode

w o

ot



ASDEX TEAM






100

80-

60-

40-

20-

WOELMS (D-D+)

Hdeg-D +

-x-N


Po




I -prad (p) p dp dr


(1)



2)




THE H-MODE OF ASDEX

U13-

_ 010-

ujH

005-

0-

11513

xE(35cmh

XElSOcmly^

PNI=177MW

I

1I v

110 120 130015

010 j ^3 _

HIP

005

11447Tcl35cm)

PW1=348MW

105 110 115 120 125

t(s)


















ASDEX TEAM

111

Qgt 0

n

2 8

PN1= 12 MW

I I I

Id

32 MW

I2 4 6 8


10












100-

50-



0 2 I 6 8 10

ne (1013 cm3)



THE H-MODE OF ASDEX

60-

20-

02 MA

0 1 2 3

PNI CMW]




















50-

Emdash 30H

10-

H-TYPE

_ g 1 1 bull

L-TYPE

IP= 295-315 kA

mdashr~15

1 1 1 1 1 120 25

B [ T ]



ASDEX TEAM




Xe(r) (cm2-s-) =

D(r) = 04









THE H-MODE OF ASDEX

0 100 200 300 400 500


( c )

10 20B (T)

30






08 10 12 14 16 18



ASDEX TEAM

3-o L - Mode

H - Mode

B (T)









150

10CH

2Q

bull bull

16 18 20 22 24

B (T)


25

20-

~ 15 bull

a

lt

10

5

0-

L

r

H-type

8

W L-type )pound

= 200 kA

300 kA

380 kA

PN CMW]





THE H-MODE OF ASDEX

Imdash_gtlaquo

LUP

70-

60-

50-

30-

20-

10-

0-

bullbull

4 V


3 1 2 3

V 1

ao

irftv

ON

6ooP0 Q 0


bull

[101

tP aaa a

a a

^

Sraquoodego deg00 g

bulldeg Pbull 0 Ip

DN

PN

5 6

3cm3)

H-type

o

N

= 370 kAc 300 k A

gt2 MW

7


sCL

o

2 4 6

fie (1013crrv3)


PN| (MW)







ASDEX TEAM

without insertsDV-I

with inserts

Pumping panels

DV-II Limiter

I Ti-sublimator








THE H-MODE OF ASDEX








ASDEX TEAM

1 2 3 4 5

ne (1013crrv3)







10



THE H-MODE OF ASDEX





FOR H-MODE PLASMAS

51 ICRF heating




(cm)

MoV ctldiv)

(QU)





ASDEX TEAM
















THE H-MODE OF ASDEX

Ic

cQJ

4-

2-

r

JO

JQ

11 12

o

c

cQJ

curr

d

[asm

a

01

d

Vol

t

a oo

u)

JO

3co

d

da

rb

u)

co

d

dcccot_

4-

2-

bull

AU

-

m

o-

o-

0-

Jp

UiX u l

FB )

Fe X

bull L (6124)

- H (6125)

lasma

I

1

If Main plasmaij

Oivertor

i bull bull i 1

t

r u

S 2-co

Zn

S o

-2-

2-

1-

bull 1 -

11 12 11 12

Us)







ASDEX TEAM

o 0

mo

^ 6

1 2 -

8672

8671

-J

10 11 12 13 14 15

t (sJ






6-

EV

CO

gt-8-c

o Hbull L


ARL [cm]



THE H-MODE OF ASDEX

8-

E L


N

2

IMW]









E



ASDEX TEAM









t Is]



THE H-MODE OF ASDEX

10 11










ASDEX TEAM

2 0

Plasma

A2 1

H mdash25 cm

10 ms


Te (keV)

t (s)






1-

units

)

p

0

001-y

r0I y

Single-Nu

s

SX-lntensityNS

- bull

1 Plasma

-5 -10 -20

r-re (cm)

-30



THE H-MODE OF ASDEX











view A-Aentrance

A - windows

0degodegodegexit

windows



ASDEX TEAM

24942


18


S SCATTERED SIGNAL

SIGNAL

LINE DENSITY

23463

H

116 118t (S)

120 122






E 2u



23445



THE H-MODE OF ASDEX

-50 -25

T (us)







I W 21895H laquo 21696

Miriiov activity

-4-

10 14 Ms) 18

f= 30 kHz

(= 82 kHz

fe222kHz

f 1 MHz

18



ASDEX TEAM









l=380kA B=236T q=30

f-30kHz

U82kHz

(=222 kHz

f 606 kHz

14 10

Time (s)14



THE H-MODE OF ASDEX

24896


(MA

)

Euo

ic

wcD

xij5e

04-

02-

o-

08-

u^

J

6

9JLT

) 02

m =

5 J

04

mdash ^ j ^ p _ _ _

06 08

t(s)

1

-8(A

)u

o

bull0

10


r-8

a

mpoundurgtO

0)IC

A-

3-

-

1-

n -u

5982 J

mdashJ J

itiik

W^^V^A

idisruptive

I p = 300 kA

Bt = 22 T 2e

10 ii 12 13

t Is]

U









ASDEX TEAM






R2 div + Mo

JJOO = mdash (1R2)1

Mo

+ 4TT2

dldV

= 0







yco

101

10-2

106 10-5104 10-3

B =1

X V 0 + x0J









THE H-MODE OF ASDEX

0A-Z[m]

02-

00-

-02-

-04-

(a)


12 14 16 18 20 R[m]

BeBe

00015

0001

00005

0

-00005

-0001

(b)

50 100 150 200 250 300 350





0-5

= Mo Since







ASDEX TEAM

















THE H-MODE OF ASDEX

6

6-

4-

2-

bull H - Mode

L - Mode

100 101 102 103 104

ra







t = 0



ASDEX TEAM

0 02 01 06 r Q 10 0 02 0A 06 r 0 10







3PC2(0))u = 0




THE H-MODE OF ASDEX

05-









ASDEX TEAM

107

71


- 0002 0005 0010 Re7












THE H-MODE OF ASDEX

R o ( 7 gt

G005 bull bull

00


ra = 0867

03



is the solid line



10

06-

02 bull

00

00

Toroidal

current IIp

1mdash1mdash1

^

025 05 075

Volume VVp


10 I 14 16 I8 20

10

06

02

00

V PPO

bull bull bull bull

Plasn


1a pressure pPO

025 05 075

Volume VVp

0075Pressure Volume

I Window


085 09 095 10 VVp

10






ASDEX TEAM






10

10-2


^ ^ 1 1

5 x 1 0 -4 105 15 1 0 5










THE H-MODE OF ASDEX













ASDEX TEAM













THE H-MODE OF ASDEX













ASDEX TEAM

16











THE H-MODE OF ASDEX












ASDEX TEAM

E

I1 ( b )

bull mdash mdash

10 15 20

t(s)






(b)2 (cm)

4-

2--

o--

-2-

-4-bull

0 bull VB-drift

0 lt bull

O 0 0 bull 10 bull

0

bullVB-drift

PN (MW)



THE H-MODE OF ASDEX

( b )

2-










ASDEX TEAM









THE H-MODE OF ASDEX









ASDEX TEAM




10 SUMMARY









THE H-MODE OF ASDEX









ASDEX TEAM












THE H-MODE OF ASDEX










REFERENCES












ASDEX TEAM































































THE H-MODE OF ASDEX










































ASDEX TEAM




































(1987) 65







ASDEX TEAM




40



t ( s )






THE H-MODE OF ASDEX










ASDEX TEAM














THE H-MODE OF ASDEX

30

lt 20

ugt

~ 10

0

2

bulla i

0

(a) ~^

t 4804bull 4803

(b) A

1

Nl

j

i

13 U 15 16

t ts) t Isl










ASDEX TEAM

3

11 12 t ( s )



transition






2-




THE H-MODE OF ASDEX










110



ASDEX TEAM

lt200-

~ 100-

H phase1262 s

lp= 320 kA

100kA

50 kA

40











Te (keV)

M-5

bull10

-05

-0

Te(keV)e

15-

10-

05-

o-


6046

(a )

j

y(

VNl

A

A

A09 10 11 12 13

Ms)

HCL

d

Eob

vIC

dd

2-

1-

o-4-

2-

-

0-

raquo 5982

^_

i 111 1

1 ML mi l

10 12 14 10 12 14

t(s) Ms)



THE H-MODE OF ASDEX

PN| = 75MW

K 86C

PNI=15 MW

laquo 8603

(a

(b )









04

5 03 H0)

I 02-

^ 01 -

Eu

m

raquo St

i V

tf bull 88U L I ^



ASDEX TEAM

112













THE H-MODE OF ASDEX

1292 1294













ASDEX TEAM










h 20

V

ne

o

X

A

qa = 365qQ = 29qa = 26qa=275

--10



THE H-MODE OF ASDEX

AA

sawtooth

r fcmJ








9630

ELMin

ltMio

CM



ASDEX TEAM

90 180 270 360












11 12 13 t (s)



THE H-MODE OF ASDEX

a

2 4 6

dnedr (1012cm-4)









ASDEX TEAM

10

10

2 poundbull

4

1 4804

4745

Lj( b )

13 15 16

t Is]


with ELMs wo ELMs

rRAO

(MW)

(au)



THE H-MODE OF ASDEX

08

04

- - 5

with ELMs 11338

time 11) 1095 s12) 1155 s13) 1215 s14) 1230 s15) 1245 s6I 1260 s

10 20r (cm)

30

s

6

gt

- bull 2

wo ELMs 11447

( b )s

i bull i i f

time- (1)(2)13114)IS]161

1095 s1155 s1215 s1230 s1245 s1260 S

10 20 30rcm)





nFel0)nel0) =

io-2-

bullo

5 io3J

10110 120 130

t(s)



ASDEX TEAM











THE H-MODE OF ASDEX







ASDEX TEAM

600-

500-

i00-20-

15-

( b )

-6 -6 -2 0

Ar= r-r (cm)








THE H-MODE OF ASDEX

[cm]

1013

9630OH 105s

- - - L 113H 1164

1012

R-Rs [cm]

-2 8









ASDEX TEAM

o

c

O

15-

10-

os-

o-

4-

2-

n-

raquo 96301

)bull

L

- - ^

0 (DO 0 bdquo

H

Nl

1

i

idegC11

i

ii

i

o o o

Lm

mdash

11 12 13 t [sJ 14







20t



neutralizer plates

infrared camera

HaDQ



THE H-MODE OF ASDEX

J

L

VUilillililUH V

1bullE 25u

2 20

S 15cat

Z 10c

s ^

sect 0

raquo 9393

10 12 U

t (si


cm = 30 MW






175 165 170 175 165

Rlcml

170 175



ASDEX TEAM

1520243 (L 2=0) 20241 (H Z=+1 Cm)

| ri

0

40

gt

20

4

On 2

40

-40

165 170 175 165

R (cm)170 175








THE H-MODE OF ASDEX

90 91 92







30


Z mdash



ASDEX TEAM






N I A

10 11

t (s)





THE H-MODE OF ASDEX

E

Ul

Ul

80-

70-

60-

50-

40-

30-

20-

10-

0 bull

D 1

bull

itlw deg


A A

A

2 3 U

n e [10

p

0

oo

1 8

0

bull OX +

5

cm3]

D+

a

5

A

hrP

PN

6

oD

H-type

= 370 kA= 300 kA

gt 2 MW

7 8











ASDEX TEAM







dNdt = - N T P (2)


= N0TD (3)



6028 laquo 5991

oe



THE H-MODE OF ASDEX


Phase

OH

L

H

dNdt

(s-1)

0

0

2 x 1021

(s-1)

1O21

6 x 1O21

0

V(s-1)

0

8 x 1O20

8 x 102 0

2

2

2

(s

X

X

X

Rb

-)

1O21

102 1

1O21

TP

(s)

OO5

001

015


dN N

dt + rp deg +












ASDEX TEAM

17005r=2a3

11O H V NI (

115 12 125

X

[m2s]

1-

1-

(

bull

17005

b)

s

IS 11 S2 = 115 s3S 1195 s4U205s551215s

bullXe(a)

0 05 r a 1









3-T

[keV]2-

1-

mdash

(a )

r o )N

t

XCH+X

17005123s

05 ra 1

1

3-

2-

1 -

L (1 15S)

H(1215s)

( b )

OH(ils)

- lt

05 ra 1





THE H-MODE OF ASDEX

10








180 190 200

R (cm)

210



ASDEX TEAM

A- L1227s

0 20 A0r (cm)














THE H-MODE OF ASDEX

02 03Io IMA)

04













yj

UJ

60-

40-

-

20-

0-

o

0

L-

^

O

Mode

H

o

bull fraquo

- Mode

w o

ot



ASDEX TEAM






100

80-

60-

40-

20-

WOELMS (D-D+)

Hdeg-D +

-x-N


Po




I -prad (p) p dp dr


(1)



2)




THE H-MODE OF ASDEX

U13-

_ 010-

ujH

005-

0-

11513

xE(35cmh

XElSOcmly^

PNI=177MW

I

1I v

110 120 130015

010 j ^3 _

HIP

005

11447Tcl35cm)

PW1=348MW

105 110 115 120 125

t(s)


















ASDEX TEAM

111

Qgt 0

n

2 8

PN1= 12 MW

I I I

Id

32 MW

I2 4 6 8


10












100-

50-



0 2 I 6 8 10

ne (1013 cm3)



THE H-MODE OF ASDEX

60-

20-

02 MA

0 1 2 3

PNI CMW]




















50-

Emdash 30H

10-

H-TYPE

_ g 1 1 bull

L-TYPE

IP= 295-315 kA

mdashr~15

1 1 1 1 1 120 25

B [ T ]



ASDEX TEAM




Xe(r) (cm2-s-) =

D(r) = 04









THE H-MODE OF ASDEX

0 100 200 300 400 500


( c )

10 20B (T)

30






08 10 12 14 16 18



ASDEX TEAM

3-o L - Mode

H - Mode

B (T)









150

10CH

2Q

bull bull

16 18 20 22 24

B (T)


25

20-

~ 15 bull

a

lt

10

5

0-

L

r

H-type

8

W L-type )pound

= 200 kA

300 kA

380 kA

PN CMW]





THE H-MODE OF ASDEX

Imdash_gtlaquo

LUP

70-

60-

50-

30-

20-

10-

0-

bullbull

4 V


3 1 2 3

V 1

ao

irftv

ON

6ooP0 Q 0


bull

[101

tP aaa a

a a

^

Sraquoodego deg00 g

bulldeg Pbull 0 Ip

DN

PN

5 6

3cm3)

H-type

o

N

= 370 kAc 300 k A

gt2 MW

7


sCL

o

2 4 6

fie (1013crrv3)


PN| (MW)







ASDEX TEAM

without insertsDV-I

with inserts

Pumping panels

DV-II Limiter

I Ti-sublimator








THE H-MODE OF ASDEX








ASDEX TEAM

1 2 3 4 5

ne (1013crrv3)







10



THE H-MODE OF ASDEX





FOR H-MODE PLASMAS

51 ICRF heating




(cm)

MoV ctldiv)

(QU)





ASDEX TEAM
















THE H-MODE OF ASDEX

Ic

cQJ

4-

2-

r

JO

JQ

11 12

o

c

cQJ

curr

d

[asm

a

01

d

Vol

t

a oo

u)

JO

3co

d

da

rb

u)

co

d

dcccot_

4-

2-

bull

AU

-

m

o-

o-

0-

Jp

UiX u l

FB )

Fe X

bull L (6124)

- H (6125)

lasma

I

1

If Main plasmaij

Oivertor

i bull bull i 1

t

r u

S 2-co

Zn

S o

-2-

2-

1-

bull 1 -

11 12 11 12

Us)







ASDEX TEAM

o 0

mo

^ 6

1 2 -

8672

8671

-J

10 11 12 13 14 15

t (sJ






6-

EV

CO

gt-8-c

o Hbull L


ARL [cm]



THE H-MODE OF ASDEX

8-

E L


N

2

IMW]









E



ASDEX TEAM









t Is]



THE H-MODE OF ASDEX

10 11










ASDEX TEAM

2 0

Plasma

A2 1

H mdash25 cm

10 ms


Te (keV)

t (s)






1-

units

)

p

0

001-y

r0I y

Single-Nu

s

SX-lntensityNS

- bull

1 Plasma

-5 -10 -20

r-re (cm)

-30



THE H-MODE OF ASDEX











view A-Aentrance

A - windows

0degodegodegexit

windows



ASDEX TEAM

24942


18


S SCATTERED SIGNAL

SIGNAL

LINE DENSITY

23463

H

116 118t (S)

120 122






E 2u



23445



THE H-MODE OF ASDEX

-50 -25

T (us)







I W 21895H laquo 21696

Miriiov activity

-4-

10 14 Ms) 18

f= 30 kHz

(= 82 kHz

fe222kHz

f 1 MHz

18



ASDEX TEAM









l=380kA B=236T q=30

f-30kHz

U82kHz

(=222 kHz

f 606 kHz

14 10

Time (s)14



THE H-MODE OF ASDEX

24896


(MA

)

Euo

ic

wcD

xij5e

04-

02-

o-

08-

u^

J

6

9JLT

) 02

m =

5 J

04

mdash ^ j ^ p _ _ _

06 08

t(s)

1

-8(A

)u

o

bull0

10


r-8

a

mpoundurgtO

0)IC

A-

3-

-

1-

n -u

5982 J

mdashJ J

itiik

W^^V^A

idisruptive

I p = 300 kA

Bt = 22 T 2e

10 ii 12 13

t Is]

U









ASDEX TEAM






R2 div + Mo

JJOO = mdash (1R2)1

Mo

+ 4TT2

dldV

= 0







yco

101

10-2

106 10-5104 10-3

B =1

X V 0 + x0J









THE H-MODE OF ASDEX

0A-Z[m]

02-

00-

-02-

-04-

(a)


12 14 16 18 20 R[m]

BeBe

00015

0001

00005

0

-00005

-0001

(b)

50 100 150 200 250 300 350





0-5

= Mo Since







ASDEX TEAM

















THE H-MODE OF ASDEX

6

6-

4-

2-

bull H - Mode

L - Mode

100 101 102 103 104

ra







t = 0



ASDEX TEAM

0 02 01 06 r Q 10 0 02 0A 06 r 0 10







3PC2(0))u = 0




THE H-MODE OF ASDEX

05-









ASDEX TEAM

107

71


- 0002 0005 0010 Re7












THE H-MODE OF ASDEX

R o ( 7 gt

G005 bull bull

00


ra = 0867

03



is the solid line



10

06-

02 bull

00

00

Toroidal

current IIp

1mdash1mdash1

^

025 05 075

Volume VVp


10 I 14 16 I8 20

10

06

02

00

V PPO

bull bull bull bull

Plasn


1a pressure pPO

025 05 075

Volume VVp

0075Pressure Volume

I Window


085 09 095 10 VVp

10






ASDEX TEAM






10

10-2


^ ^ 1 1

5 x 1 0 -4 105 15 1 0 5










THE H-MODE OF ASDEX













ASDEX TEAM













THE H-MODE OF ASDEX













ASDEX TEAM

16











THE H-MODE OF ASDEX












ASDEX TEAM

E

I1 ( b )

bull mdash mdash

10 15 20

t(s)






(b)2 (cm)

4-

2--

o--

-2-

-4-bull

0 bull VB-drift

0 lt bull

O 0 0 bull 10 bull

0

bullVB-drift

PN (MW)



THE H-MODE OF ASDEX

( b )

2-










ASDEX TEAM









THE H-MODE OF ASDEX









ASDEX TEAM




10 SUMMARY









THE H-MODE OF ASDEX









ASDEX TEAM












THE H-MODE OF ASDEX










REFERENCES












ASDEX TEAM































































THE H-MODE OF ASDEX










































ASDEX TEAM




































(1987) 65







THE H-MODE OF ASDEX










ASDEX TEAM














THE H-MODE OF ASDEX

30

lt 20

ugt

~ 10

0

2

bulla i

0

(a) ~^

t 4804bull 4803

(b) A

1

Nl

j

i

13 U 15 16

t ts) t Isl










ASDEX TEAM

3

11 12 t ( s )



transition






2-




THE H-MODE OF ASDEX










110



ASDEX TEAM

lt200-

~ 100-

H phase1262 s

lp= 320 kA

100kA

50 kA

40











Te (keV)

M-5

bull10

-05

-0

Te(keV)e

15-

10-

05-

o-


6046

(a )

j

y(

VNl

A

A

A09 10 11 12 13

Ms)

HCL

d

Eob

vIC

dd

2-

1-

o-4-

2-

-

0-

raquo 5982

^_

i 111 1

1 ML mi l

10 12 14 10 12 14

t(s) Ms)



THE H-MODE OF ASDEX

PN| = 75MW

K 86C

PNI=15 MW

laquo 8603

(a

(b )









04

5 03 H0)

I 02-

^ 01 -

Eu

m

raquo St

i V

tf bull 88U L I ^



ASDEX TEAM

112













THE H-MODE OF ASDEX

1292 1294













ASDEX TEAM










h 20

V

ne

o

X

A

qa = 365qQ = 29qa = 26qa=275

--10



THE H-MODE OF ASDEX

AA

sawtooth

r fcmJ








9630

ELMin

ltMio

CM



ASDEX TEAM

90 180 270 360












11 12 13 t (s)



THE H-MODE OF ASDEX

a

2 4 6

dnedr (1012cm-4)









ASDEX TEAM

10

10

2 poundbull

4

1 4804

4745

Lj( b )

13 15 16

t Is]


with ELMs wo ELMs

rRAO

(MW)

(au)



THE H-MODE OF ASDEX

08

04

- - 5

with ELMs 11338

time 11) 1095 s12) 1155 s13) 1215 s14) 1230 s15) 1245 s6I 1260 s

10 20r (cm)

30

s

6

gt

- bull 2

wo ELMs 11447

( b )s

i bull i i f

time- (1)(2)13114)IS]161

1095 s1155 s1215 s1230 s1245 s1260 S

10 20 30rcm)





nFel0)nel0) =

io-2-

bullo

5 io3J

10110 120 130

t(s)



ASDEX TEAM











THE H-MODE OF ASDEX







ASDEX TEAM

600-

500-

i00-20-

15-

( b )

-6 -6 -2 0

Ar= r-r (cm)








THE H-MODE OF ASDEX

[cm]

1013

9630OH 105s

- - - L 113H 1164

1012

R-Rs [cm]

-2 8









ASDEX TEAM

o

c

O

15-

10-

os-

o-

4-

2-

n-

raquo 96301

)bull

L

- - ^

0 (DO 0 bdquo

H

Nl

1

i

idegC11

i

ii

i

o o o

Lm

mdash

11 12 13 t [sJ 14







20t



neutralizer plates

infrared camera

HaDQ



THE H-MODE OF ASDEX

J

L

VUilillililUH V

1bullE 25u

2 20

S 15cat

Z 10c

s ^

sect 0

raquo 9393

10 12 U

t (si


cm = 30 MW






175 165 170 175 165

Rlcml

170 175



ASDEX TEAM

1520243 (L 2=0) 20241 (H Z=+1 Cm)

| ri

0

40

gt

20

4

On 2

40

-40

165 170 175 165

R (cm)170 175








THE H-MODE OF ASDEX

90 91 92







30


Z mdash



ASDEX TEAM






N I A

10 11

t (s)





THE H-MODE OF ASDEX

E

Ul

Ul

80-

70-

60-

50-

40-

30-

20-

10-

0 bull

D 1

bull

itlw deg


A A

A

2 3 U

n e [10

p

0

oo

1 8

0

bull OX +

5

cm3]

D+

a

5

A

hrP

PN

6

oD

H-type

= 370 kA= 300 kA

gt 2 MW

7 8











ASDEX TEAM







dNdt = - N T P (2)


= N0TD (3)



6028 laquo 5991

oe



THE H-MODE OF ASDEX


Phase

OH

L

H

dNdt

(s-1)

0

0

2 x 1021

(s-1)

1O21

6 x 1O21

0

V(s-1)

0

8 x 1O20

8 x 102 0

2

2

2

(s

X

X

X

Rb

-)

1O21

102 1

1O21

TP

(s)

OO5

001

015


dN N

dt + rp deg +












ASDEX TEAM

17005r=2a3

11O H V NI (

115 12 125

X

[m2s]

1-

1-

(

bull

17005

b)

s

IS 11 S2 = 115 s3S 1195 s4U205s551215s

bullXe(a)

0 05 r a 1









3-T

[keV]2-

1-

mdash

(a )

r o )N

t

XCH+X

17005123s

05 ra 1

1

3-

2-

1 -

L (1 15S)

H(1215s)

( b )

OH(ils)

- lt

05 ra 1





THE H-MODE OF ASDEX

10








180 190 200

R (cm)

210



ASDEX TEAM

A- L1227s

0 20 A0r (cm)














THE H-MODE OF ASDEX

02 03Io IMA)

04













yj

UJ

60-

40-

-

20-

0-

o

0

L-

^

O

Mode

H

o

bull fraquo

- Mode

w o

ot



ASDEX TEAM






100

80-

60-

40-

20-

WOELMS (D-D+)

Hdeg-D +

-x-N


Po




I -prad (p) p dp dr


(1)



2)




THE H-MODE OF ASDEX

U13-

_ 010-

ujH

005-

0-

11513

xE(35cmh

XElSOcmly^

PNI=177MW

I

1I v

110 120 130015

010 j ^3 _

HIP

005

11447Tcl35cm)

PW1=348MW

105 110 115 120 125

t(s)


















ASDEX TEAM

111

Qgt 0

n

2 8

PN1= 12 MW

I I I

Id

32 MW

I2 4 6 8


10












100-

50-



0 2 I 6 8 10

ne (1013 cm3)



THE H-MODE OF ASDEX

60-

20-

02 MA

0 1 2 3

PNI CMW]




















50-

Emdash 30H

10-

H-TYPE

_ g 1 1 bull

L-TYPE

IP= 295-315 kA

mdashr~15

1 1 1 1 1 120 25

B [ T ]



ASDEX TEAM




Xe(r) (cm2-s-) =

D(r) = 04









THE H-MODE OF ASDEX

0 100 200 300 400 500


( c )

10 20B (T)

30






08 10 12 14 16 18



ASDEX TEAM

3-o L - Mode

H - Mode

B (T)









150

10CH

2Q

bull bull

16 18 20 22 24

B (T)


25

20-

~ 15 bull

a

lt

10

5

0-

L

r

H-type

8

W L-type )pound

= 200 kA

300 kA

380 kA

PN CMW]





THE H-MODE OF ASDEX

Imdash_gtlaquo

LUP

70-

60-

50-

30-

20-

10-

0-

bullbull

4 V


3 1 2 3

V 1

ao

irftv

ON

6ooP0 Q 0


bull

[101

tP aaa a

a a

^

Sraquoodego deg00 g

bulldeg Pbull 0 Ip

DN

PN

5 6

3cm3)

H-type

o

N

= 370 kAc 300 k A

gt2 MW

7


sCL

o

2 4 6

fie (1013crrv3)


PN| (MW)







ASDEX TEAM

without insertsDV-I

with inserts

Pumping panels

DV-II Limiter

I Ti-sublimator








THE H-MODE OF ASDEX








ASDEX TEAM

1 2 3 4 5

ne (1013crrv3)







10



THE H-MODE OF ASDEX





FOR H-MODE PLASMAS

51 ICRF heating




(cm)

MoV ctldiv)

(QU)





ASDEX TEAM
















THE H-MODE OF ASDEX

Ic

cQJ

4-

2-

r

JO

JQ

11 12

o

c

cQJ

curr

d

[asm

a

01

d

Vol

t

a oo

u)

JO

3co

d

da

rb

u)

co

d

dcccot_

4-

2-

bull

AU

-

m

o-

o-

0-

Jp

UiX u l

FB )

Fe X

bull L (6124)

- H (6125)

lasma

I

1

If Main plasmaij

Oivertor

i bull bull i 1

t

r u

S 2-co

Zn

S o

-2-

2-

1-

bull 1 -

11 12 11 12

Us)







ASDEX TEAM

o 0

mo

^ 6

1 2 -

8672

8671

-J

10 11 12 13 14 15

t (sJ






6-

EV

CO

gt-8-c

o Hbull L


ARL [cm]



THE H-MODE OF ASDEX

8-

E L


N

2

IMW]









E



ASDEX TEAM









t Is]



THE H-MODE OF ASDEX

10 11










ASDEX TEAM

2 0

Plasma

A2 1

H mdash25 cm

10 ms


Te (keV)

t (s)






1-

units

)

p

0

001-y

r0I y

Single-Nu

s

SX-lntensityNS

- bull

1 Plasma

-5 -10 -20

r-re (cm)

-30



THE H-MODE OF ASDEX











view A-Aentrance

A - windows

0degodegodegexit

windows



ASDEX TEAM

24942


18


S SCATTERED SIGNAL

SIGNAL

LINE DENSITY

23463

H

116 118t (S)

120 122






E 2u



23445



THE H-MODE OF ASDEX

-50 -25

T (us)







I W 21895H laquo 21696

Miriiov activity

-4-

10 14 Ms) 18

f= 30 kHz

(= 82 kHz

fe222kHz

f 1 MHz

18



ASDEX TEAM









l=380kA B=236T q=30

f-30kHz

U82kHz

(=222 kHz

f 606 kHz

14 10

Time (s)14



THE H-MODE OF ASDEX

24896


(MA

)

Euo

ic

wcD

xij5e

04-

02-

o-

08-

u^

J

6

9JLT

) 02

m =

5 J

04

mdash ^ j ^ p _ _ _

06 08

t(s)

1

-8(A

)u

o

bull0

10


r-8

a

mpoundurgtO

0)IC

A-

3-

-

1-

n -u

5982 J

mdashJ J

itiik

W^^V^A

idisruptive

I p = 300 kA

Bt = 22 T 2e

10 ii 12 13

t Is]

U









ASDEX TEAM






R2 div + Mo

JJOO = mdash (1R2)1

Mo

+ 4TT2

dldV

= 0







yco

101

10-2

106 10-5104 10-3

B =1

X V 0 + x0J









THE H-MODE OF ASDEX

0A-Z[m]

02-

00-

-02-

-04-

(a)


12 14 16 18 20 R[m]

BeBe

00015

0001

00005

0

-00005

-0001

(b)

50 100 150 200 250 300 350





0-5

= Mo Since







ASDEX TEAM

















THE H-MODE OF ASDEX

6

6-

4-

2-

bull H - Mode

L - Mode

100 101 102 103 104

ra







t = 0



ASDEX TEAM

0 02 01 06 r Q 10 0 02 0A 06 r 0 10







3PC2(0))u = 0




THE H-MODE OF ASDEX

05-









ASDEX TEAM

107

71


- 0002 0005 0010 Re7












THE H-MODE OF ASDEX

R o ( 7 gt

G005 bull bull

00


ra = 0867

03



is the solid line



10

06-

02 bull

00

00

Toroidal

current IIp

1mdash1mdash1

^

025 05 075

Volume VVp


10 I 14 16 I8 20

10

06

02

00

V PPO

bull bull bull bull

Plasn


1a pressure pPO

025 05 075

Volume VVp

0075Pressure Volume

I Window


085 09 095 10 VVp

10






ASDEX TEAM






10

10-2


^ ^ 1 1

5 x 1 0 -4 105 15 1 0 5










THE H-MODE OF ASDEX













ASDEX TEAM













THE H-MODE OF ASDEX













ASDEX TEAM

16











THE H-MODE OF ASDEX












ASDEX TEAM

E

I1 ( b )

bull mdash mdash

10 15 20

t(s)






(b)2 (cm)

4-

2--

o--

-2-

-4-bull

0 bull VB-drift

0 lt bull

O 0 0 bull 10 bull

0

bullVB-drift

PN (MW)



THE H-MODE OF ASDEX

( b )

2-










ASDEX TEAM









THE H-MODE OF ASDEX









ASDEX TEAM




10 SUMMARY









THE H-MODE OF ASDEX









ASDEX TEAM












THE H-MODE OF ASDEX










REFERENCES












ASDEX TEAM































































THE H-MODE OF ASDEX










































ASDEX TEAM




































(1987) 65







ASDEX TEAM














THE H-MODE OF ASDEX

30

lt 20

ugt

~ 10

0

2

bulla i

0

(a) ~^

t 4804bull 4803

(b) A

1

Nl

j

i

13 U 15 16

t ts) t Isl










ASDEX TEAM

3

11 12 t ( s )



transition






2-




THE H-MODE OF ASDEX










110



ASDEX TEAM

lt200-

~ 100-

H phase1262 s

lp= 320 kA

100kA

50 kA

40











Te (keV)

M-5

bull10

-05

-0

Te(keV)e

15-

10-

05-

o-


6046

(a )

j

y(

VNl

A

A

A09 10 11 12 13

Ms)

HCL

d

Eob

vIC

dd

2-

1-

o-4-

2-

-

0-

raquo 5982

^_

i 111 1

1 ML mi l

10 12 14 10 12 14

t(s) Ms)



THE H-MODE OF ASDEX

PN| = 75MW

K 86C

PNI=15 MW

laquo 8603

(a

(b )









04

5 03 H0)

I 02-

^ 01 -

Eu

m

raquo St

i V

tf bull 88U L I ^



ASDEX TEAM

112













THE H-MODE OF ASDEX

1292 1294













ASDEX TEAM










h 20

V

ne

o

X

A

qa = 365qQ = 29qa = 26qa=275

--10



THE H-MODE OF ASDEX

AA

sawtooth

r fcmJ








9630

ELMin

ltMio

CM



ASDEX TEAM

90 180 270 360












11 12 13 t (s)



THE H-MODE OF ASDEX

a

2 4 6

dnedr (1012cm-4)









ASDEX TEAM

10

10

2 poundbull

4

1 4804

4745

Lj( b )

13 15 16

t Is]


with ELMs wo ELMs

rRAO

(MW)

(au)



THE H-MODE OF ASDEX

08

04

- - 5

with ELMs 11338

time 11) 1095 s12) 1155 s13) 1215 s14) 1230 s15) 1245 s6I 1260 s

10 20r (cm)

30

s

6

gt

- bull 2

wo ELMs 11447

( b )s

i bull i i f

time- (1)(2)13114)IS]161

1095 s1155 s1215 s1230 s1245 s1260 S

10 20 30rcm)





nFel0)nel0) =

io-2-

bullo

5 io3J

10110 120 130

t(s)



ASDEX TEAM











THE H-MODE OF ASDEX







ASDEX TEAM

600-

500-

i00-20-

15-

( b )

-6 -6 -2 0

Ar= r-r (cm)








THE H-MODE OF ASDEX

[cm]

1013

9630OH 105s

- - - L 113H 1164

1012

R-Rs [cm]

-2 8









ASDEX TEAM

o

c

O

15-

10-

os-

o-

4-

2-

n-

raquo 96301

)bull

L

- - ^

0 (DO 0 bdquo

H

Nl

1

i

idegC11

i

ii

i

o o o

Lm

mdash

11 12 13 t [sJ 14







20t



neutralizer plates

infrared camera

HaDQ



THE H-MODE OF ASDEX

J

L

VUilillililUH V

1bullE 25u

2 20

S 15cat

Z 10c

s ^

sect 0

raquo 9393

10 12 U

t (si


cm = 30 MW






175 165 170 175 165

Rlcml

170 175



ASDEX TEAM

1520243 (L 2=0) 20241 (H Z=+1 Cm)

| ri

0

40

gt

20

4

On 2

40

-40

165 170 175 165

R (cm)170 175








THE H-MODE OF ASDEX

90 91 92







30


Z mdash



ASDEX TEAM






N I A

10 11

t (s)





THE H-MODE OF ASDEX

E

Ul

Ul

80-

70-

60-

50-

40-

30-

20-

10-

0 bull

D 1

bull

itlw deg


A A

A

2 3 U

n e [10

p

0

oo

1 8

0

bull OX +

5

cm3]

D+

a

5

A

hrP

PN

6

oD

H-type

= 370 kA= 300 kA

gt 2 MW

7 8











ASDEX TEAM







dNdt = - N T P (2)


= N0TD (3)



6028 laquo 5991

oe



THE H-MODE OF ASDEX


Phase

OH

L

H

dNdt

(s-1)

0

0

2 x 1021

(s-1)

1O21

6 x 1O21

0

V(s-1)

0

8 x 1O20

8 x 102 0

2

2

2

(s

X

X

X

Rb

-)

1O21

102 1

1O21

TP

(s)

OO5

001

015


dN N

dt + rp deg +












ASDEX TEAM

17005r=2a3

11O H V NI (

115 12 125

X

[m2s]

1-

1-

(

bull

17005

b)

s

IS 11 S2 = 115 s3S 1195 s4U205s551215s

bullXe(a)

0 05 r a 1









3-T

[keV]2-

1-

mdash

(a )

r o )N

t

XCH+X

17005123s

05 ra 1

1

3-

2-

1 -

L (1 15S)

H(1215s)

( b )

OH(ils)

- lt

05 ra 1





THE H-MODE OF ASDEX

10








180 190 200

R (cm)

210



ASDEX TEAM

A- L1227s

0 20 A0r (cm)














THE H-MODE OF ASDEX

02 03Io IMA)

04













yj

UJ

60-

40-

-

20-

0-

o

0

L-

^

O

Mode

H

o

bull fraquo

- Mode

w o

ot



ASDEX TEAM






100

80-

60-

40-

20-

WOELMS (D-D+)

Hdeg-D +

-x-N


Po




I -prad (p) p dp dr


(1)



2)




THE H-MODE OF ASDEX

U13-

_ 010-

ujH

005-

0-

11513

xE(35cmh

XElSOcmly^

PNI=177MW

I

1I v

110 120 130015

010 j ^3 _

HIP

005

11447Tcl35cm)

PW1=348MW

105 110 115 120 125

t(s)


















ASDEX TEAM

111

Qgt 0

n

2 8

PN1= 12 MW

I I I

Id

32 MW

I2 4 6 8


10












100-

50-



0 2 I 6 8 10

ne (1013 cm3)



THE H-MODE OF ASDEX

60-

20-

02 MA

0 1 2 3

PNI CMW]




















50-

Emdash 30H

10-

H-TYPE

_ g 1 1 bull

L-TYPE

IP= 295-315 kA

mdashr~15

1 1 1 1 1 120 25

B [ T ]



ASDEX TEAM




Xe(r) (cm2-s-) =

D(r) = 04









THE H-MODE OF ASDEX

0 100 200 300 400 500


( c )

10 20B (T)

30






08 10 12 14 16 18



ASDEX TEAM

3-o L - Mode

H - Mode

B (T)









150

10CH

2Q

bull bull

16 18 20 22 24

B (T)


25

20-

~ 15 bull

a

lt

10

5

0-

L

r

H-type

8

W L-type )pound

= 200 kA

300 kA

380 kA

PN CMW]





THE H-MODE OF ASDEX

Imdash_gtlaquo

LUP

70-

60-

50-

30-

20-

10-

0-

bullbull

4 V


3 1 2 3

V 1

ao

irftv

ON

6ooP0 Q 0


bull

[101

tP aaa a

a a

^

Sraquoodego deg00 g

bulldeg Pbull 0 Ip

DN

PN

5 6

3cm3)

H-type

o

N

= 370 kAc 300 k A

gt2 MW

7


sCL

o

2 4 6

fie (1013crrv3)


PN| (MW)







ASDEX TEAM

without insertsDV-I

with inserts

Pumping panels

DV-II Limiter

I Ti-sublimator








THE H-MODE OF ASDEX








ASDEX TEAM

1 2 3 4 5

ne (1013crrv3)







10



THE H-MODE OF ASDEX





FOR H-MODE PLASMAS

51 ICRF heating




(cm)

MoV ctldiv)

(QU)





ASDEX TEAM
















THE H-MODE OF ASDEX

Ic

cQJ

4-

2-

r

JO

JQ

11 12

o

c

cQJ

curr

d

[asm

a

01

d

Vol

t

a oo

u)

JO

3co

d

da

rb

u)

co

d

dcccot_

4-

2-

bull

AU

-

m

o-

o-

0-

Jp

UiX u l

FB )

Fe X

bull L (6124)

- H (6125)

lasma

I

1

If Main plasmaij

Oivertor

i bull bull i 1

t

r u

S 2-co

Zn

S o

-2-

2-

1-

bull 1 -

11 12 11 12

Us)







ASDEX TEAM

o 0

mo

^ 6

1 2 -

8672

8671

-J

10 11 12 13 14 15

t (sJ






6-

EV

CO

gt-8-c

o Hbull L


ARL [cm]



THE H-MODE OF ASDEX

8-

E L


N

2

IMW]









E



ASDEX TEAM









t Is]



THE H-MODE OF ASDEX

10 11










ASDEX TEAM

2 0

Plasma

A2 1

H mdash25 cm

10 ms


Te (keV)

t (s)






1-

units

)

p

0

001-y

r0I y

Single-Nu

s

SX-lntensityNS

- bull

1 Plasma

-5 -10 -20

r-re (cm)

-30



THE H-MODE OF ASDEX











view A-Aentrance

A - windows

0degodegodegexit

windows



ASDEX TEAM

24942


18


S SCATTERED SIGNAL

SIGNAL

LINE DENSITY

23463

H

116 118t (S)

120 122






E 2u



23445



THE H-MODE OF ASDEX

-50 -25

T (us)







I W 21895H laquo 21696

Miriiov activity

-4-

10 14 Ms) 18

f= 30 kHz

(= 82 kHz

fe222kHz

f 1 MHz

18



ASDEX TEAM









l=380kA B=236T q=30

f-30kHz

U82kHz

(=222 kHz

f 606 kHz

14 10

Time (s)14



THE H-MODE OF ASDEX

24896


(MA

)

Euo

ic

wcD

xij5e

04-

02-

o-

08-

u^

J

6

9JLT

) 02

m =

5 J

04

mdash ^ j ^ p _ _ _

06 08

t(s)

1

-8(A

)u

o

bull0

10


r-8

a

mpoundurgtO

0)IC

A-

3-

-

1-

n -u

5982 J

mdashJ J

itiik

W^^V^A

idisruptive

I p = 300 kA

Bt = 22 T 2e

10 ii 12 13

t Is]

U









ASDEX TEAM






R2 div + Mo

JJOO = mdash (1R2)1

Mo

+ 4TT2

dldV

= 0







yco

101

10-2

106 10-5104 10-3

B =1

X V 0 + x0J









THE H-MODE OF ASDEX

0A-Z[m]

02-

00-

-02-

-04-

(a)


12 14 16 18 20 R[m]

BeBe

00015

0001

00005

0

-00005

-0001

(b)

50 100 150 200 250 300 350





0-5

= Mo Since







ASDEX TEAM

















THE H-MODE OF ASDEX

6

6-

4-

2-

bull H - Mode

L - Mode

100 101 102 103 104

ra







t = 0



ASDEX TEAM

0 02 01 06 r Q 10 0 02 0A 06 r 0 10







3PC2(0))u = 0




THE H-MODE OF ASDEX

05-









ASDEX TEAM

107

71


- 0002 0005 0010 Re7












THE H-MODE OF ASDEX

R o ( 7 gt

G005 bull bull

00


ra = 0867

03



is the solid line



10

06-

02 bull

00

00

Toroidal

current IIp

1mdash1mdash1

^

025 05 075

Volume VVp


10 I 14 16 I8 20

10

06

02

00

V PPO

bull bull bull bull

Plasn


1a pressure pPO

025 05 075

Volume VVp

0075Pressure Volume

I Window


085 09 095 10 VVp

10






ASDEX TEAM






10

10-2


^ ^ 1 1

5 x 1 0 -4 105 15 1 0 5










THE H-MODE OF ASDEX













ASDEX TEAM













THE H-MODE OF ASDEX













ASDEX TEAM

16











THE H-MODE OF ASDEX












ASDEX TEAM

E

I1 ( b )

bull mdash mdash

10 15 20

t(s)






(b)2 (cm)

4-

2--

o--

-2-

-4-bull

0 bull VB-drift

0 lt bull

O 0 0 bull 10 bull

0

bullVB-drift

PN (MW)



THE H-MODE OF ASDEX

( b )

2-










ASDEX TEAM









THE H-MODE OF ASDEX









ASDEX TEAM




10 SUMMARY









THE H-MODE OF ASDEX









ASDEX TEAM












THE H-MODE OF ASDEX










REFERENCES












ASDEX TEAM































































THE H-MODE OF ASDEX










































ASDEX TEAM




































(1987) 65







THE H-MODE OF ASDEX

30

lt 20

ugt

~ 10

0

2

bulla i

0

(a) ~^

t 4804bull 4803

(b) A

1

Nl

j

i

13 U 15 16

t ts) t Isl










ASDEX TEAM

3

11 12 t ( s )



transition






2-




THE H-MODE OF ASDEX










110



ASDEX TEAM

lt200-

~ 100-

H phase1262 s

lp= 320 kA

100kA

50 kA

40











Te (keV)

M-5

bull10

-05

-0

Te(keV)e

15-

10-

05-

o-


6046

(a )

j

y(

VNl

A

A

A09 10 11 12 13

Ms)

HCL

d

Eob

vIC

dd

2-

1-

o-4-

2-

-

0-

raquo 5982

^_

i 111 1

1 ML mi l

10 12 14 10 12 14

t(s) Ms)



THE H-MODE OF ASDEX

PN| = 75MW

K 86C

PNI=15 MW

laquo 8603

(a

(b )









04

5 03 H0)

I 02-

^ 01 -

Eu

m

raquo St

i V

tf bull 88U L I ^



ASDEX TEAM

112













THE H-MODE OF ASDEX

1292 1294













ASDEX TEAM










h 20

V

ne

o

X

A

qa = 365qQ = 29qa = 26qa=275

--10



THE H-MODE OF ASDEX

AA

sawtooth

r fcmJ








9630

ELMin

ltMio

CM



ASDEX TEAM

90 180 270 360












11 12 13 t (s)



THE H-MODE OF ASDEX

a

2 4 6

dnedr (1012cm-4)









ASDEX TEAM

10

10

2 poundbull

4

1 4804

4745

Lj( b )

13 15 16

t Is]


with ELMs wo ELMs

rRAO

(MW)

(au)



THE H-MODE OF ASDEX

08

04

- - 5

with ELMs 11338

time 11) 1095 s12) 1155 s13) 1215 s14) 1230 s15) 1245 s6I 1260 s

10 20r (cm)

30

s

6

gt

- bull 2

wo ELMs 11447

( b )s

i bull i i f

time- (1)(2)13114)IS]161

1095 s1155 s1215 s1230 s1245 s1260 S

10 20 30rcm)





nFel0)nel0) =

io-2-

bullo

5 io3J

10110 120 130

t(s)



ASDEX TEAM











THE H-MODE OF ASDEX







ASDEX TEAM

600-

500-

i00-20-

15-

( b )

-6 -6 -2 0

Ar= r-r (cm)








THE H-MODE OF ASDEX

[cm]

1013

9630OH 105s

- - - L 113H 1164

1012

R-Rs [cm]

-2 8









ASDEX TEAM

o

c

O

15-

10-

os-

o-

4-

2-

n-

raquo 96301

)bull

L

- - ^

0 (DO 0 bdquo

H

Nl

1

i

idegC11

i

ii

i

o o o

Lm

mdash

11 12 13 t [sJ 14







20t



neutralizer plates

infrared camera

HaDQ



THE H-MODE OF ASDEX

J

L

VUilillililUH V

1bullE 25u

2 20

S 15cat

Z 10c

s ^

sect 0

raquo 9393

10 12 U

t (si


cm = 30 MW






175 165 170 175 165

Rlcml

170 175



ASDEX TEAM

1520243 (L 2=0) 20241 (H Z=+1 Cm)

| ri

0

40

gt

20

4

On 2

40

-40

165 170 175 165

R (cm)170 175








THE H-MODE OF ASDEX

90 91 92







30


Z mdash



ASDEX TEAM






N I A

10 11

t (s)





THE H-MODE OF ASDEX

E

Ul

Ul

80-

70-

60-

50-

40-

30-

20-

10-

0 bull

D 1

bull

itlw deg


A A

A

2 3 U

n e [10

p

0

oo

1 8

0

bull OX +

5

cm3]

D+

a

5

A

hrP

PN

6

oD

H-type

= 370 kA= 300 kA

gt 2 MW

7 8











ASDEX TEAM







dNdt = - N T P (2)


= N0TD (3)



6028 laquo 5991

oe



THE H-MODE OF ASDEX


Phase

OH

L

H

dNdt

(s-1)

0

0

2 x 1021

(s-1)

1O21

6 x 1O21

0

V(s-1)

0

8 x 1O20

8 x 102 0

2

2

2

(s

X

X

X

Rb

-)

1O21

102 1

1O21

TP

(s)

OO5

001

015


dN N

dt + rp deg +












ASDEX TEAM

17005r=2a3

11O H V NI (

115 12 125

X

[m2s]

1-

1-

(

bull

17005

b)

s

IS 11 S2 = 115 s3S 1195 s4U205s551215s

bullXe(a)

0 05 r a 1









3-T

[keV]2-

1-

mdash

(a )

r o )N

t

XCH+X

17005123s

05 ra 1

1

3-

2-

1 -

L (1 15S)

H(1215s)

( b )

OH(ils)

- lt

05 ra 1





THE H-MODE OF ASDEX

10








180 190 200

R (cm)

210



ASDEX TEAM

A- L1227s

0 20 A0r (cm)














THE H-MODE OF ASDEX

02 03Io IMA)

04













yj

UJ

60-

40-

-

20-

0-

o

0

L-

^

O

Mode

H

o

bull fraquo

- Mode

w o

ot



ASDEX TEAM






100

80-

60-

40-

20-

WOELMS (D-D+)

Hdeg-D +

-x-N


Po




I -prad (p) p dp dr


(1)



2)




THE H-MODE OF ASDEX

U13-

_ 010-

ujH

005-

0-

11513

xE(35cmh

XElSOcmly^

PNI=177MW

I

1I v

110 120 130015

010 j ^3 _

HIP

005

11447Tcl35cm)

PW1=348MW

105 110 115 120 125

t(s)


















ASDEX TEAM

111

Qgt 0

n

2 8

PN1= 12 MW

I I I

Id

32 MW

I2 4 6 8


10












100-

50-



0 2 I 6 8 10

ne (1013 cm3)



THE H-MODE OF ASDEX

60-

20-

02 MA

0 1 2 3

PNI CMW]




















50-

Emdash 30H

10-

H-TYPE

_ g 1 1 bull

L-TYPE

IP= 295-315 kA

mdashr~15

1 1 1 1 1 120 25

B [ T ]



ASDEX TEAM




Xe(r) (cm2-s-) =

D(r) = 04









THE H-MODE OF ASDEX

0 100 200 300 400 500


( c )

10 20B (T)

30






08 10 12 14 16 18



ASDEX TEAM

3-o L - Mode

H - Mode

B (T)









150

10CH

2Q

bull bull

16 18 20 22 24

B (T)


25

20-

~ 15 bull

a

lt

10

5

0-

L

r

H-type

8

W L-type )pound

= 200 kA

300 kA

380 kA

PN CMW]





THE H-MODE OF ASDEX

Imdash_gtlaquo

LUP

70-

60-

50-

30-

20-

10-

0-

bullbull

4 V


3 1 2 3

V 1

ao

irftv

ON

6ooP0 Q 0


bull

[101

tP aaa a

a a

^

Sraquoodego deg00 g

bulldeg Pbull 0 Ip

DN

PN

5 6

3cm3)

H-type

o

N

= 370 kAc 300 k A

gt2 MW

7


sCL

o

2 4 6

fie (1013crrv3)


PN| (MW)







ASDEX TEAM

without insertsDV-I

with inserts

Pumping panels

DV-II Limiter

I Ti-sublimator








THE H-MODE OF ASDEX








ASDEX TEAM

1 2 3 4 5

ne (1013crrv3)







10



THE H-MODE OF ASDEX





FOR H-MODE PLASMAS

51 ICRF heating




(cm)

MoV ctldiv)

(QU)





ASDEX TEAM
















THE H-MODE OF ASDEX

Ic

cQJ

4-

2-

r

JO

JQ

11 12

o

c

cQJ

curr

d

[asm

a

01

d

Vol

t

a oo

u)

JO

3co

d

da

rb

u)

co

d

dcccot_

4-

2-

bull

AU

-

m

o-

o-

0-

Jp

UiX u l

FB )

Fe X

bull L (6124)

- H (6125)

lasma

I

1

If Main plasmaij

Oivertor

i bull bull i 1

t

r u

S 2-co

Zn

S o

-2-

2-

1-

bull 1 -

11 12 11 12

Us)







ASDEX TEAM

o 0

mo

^ 6

1 2 -

8672

8671

-J

10 11 12 13 14 15

t (sJ






6-

EV

CO

gt-8-c

o Hbull L


ARL [cm]



THE H-MODE OF ASDEX

8-

E L


N

2

IMW]









E



ASDEX TEAM









t Is]



THE H-MODE OF ASDEX

10 11










ASDEX TEAM

2 0

Plasma

A2 1

H mdash25 cm

10 ms


Te (keV)

t (s)






1-

units

)

p

0

001-y

r0I y

Single-Nu

s

SX-lntensityNS

- bull

1 Plasma

-5 -10 -20

r-re (cm)

-30



THE H-MODE OF ASDEX











view A-Aentrance

A - windows

0degodegodegexit

windows



ASDEX TEAM

24942


18


S SCATTERED SIGNAL

SIGNAL

LINE DENSITY

23463

H

116 118t (S)

120 122






E 2u



23445



THE H-MODE OF ASDEX

-50 -25

T (us)







I W 21895H laquo 21696

Miriiov activity

-4-

10 14 Ms) 18

f= 30 kHz

(= 82 kHz

fe222kHz

f 1 MHz

18



ASDEX TEAM









l=380kA B=236T q=30

f-30kHz

U82kHz

(=222 kHz

f 606 kHz

14 10

Time (s)14



THE H-MODE OF ASDEX

24896


(MA

)

Euo

ic

wcD

xij5e

04-

02-

o-

08-

u^

J

6

9JLT

) 02

m =

5 J

04

mdash ^ j ^ p _ _ _

06 08

t(s)

1

-8(A

)u

o

bull0

10


r-8

a

mpoundurgtO

0)IC

A-

3-

-

1-

n -u

5982 J

mdashJ J

itiik

W^^V^A

idisruptive

I p = 300 kA

Bt = 22 T 2e

10 ii 12 13

t Is]

U









ASDEX TEAM






R2 div + Mo

JJOO = mdash (1R2)1

Mo

+ 4TT2

dldV

= 0







yco

101

10-2

106 10-5104 10-3

B =1

X V 0 + x0J









THE H-MODE OF ASDEX

0A-Z[m]

02-

00-

-02-

-04-

(a)


12 14 16 18 20 R[m]

BeBe

00015

0001

00005

0

-00005

-0001

(b)

50 100 150 200 250 300 350





0-5

= Mo Since







ASDEX TEAM

















THE H-MODE OF ASDEX

6

6-

4-

2-

bull H - Mode

L - Mode

100 101 102 103 104

ra







t = 0



ASDEX TEAM

0 02 01 06 r Q 10 0 02 0A 06 r 0 10







3PC2(0))u = 0




THE H-MODE OF ASDEX

05-









ASDEX TEAM

107

71


- 0002 0005 0010 Re7












THE H-MODE OF ASDEX

R o ( 7 gt

G005 bull bull

00


ra = 0867

03



is the solid line



10

06-

02 bull

00

00

Toroidal

current IIp

1mdash1mdash1

^

025 05 075

Volume VVp


10 I 14 16 I8 20

10

06

02

00

V PPO

bull bull bull bull

Plasn


1a pressure pPO

025 05 075

Volume VVp

0075Pressure Volume

I Window


085 09 095 10 VVp

10






ASDEX TEAM






10

10-2


^ ^ 1 1

5 x 1 0 -4 105 15 1 0 5










THE H-MODE OF ASDEX













ASDEX TEAM













THE H-MODE OF ASDEX













ASDEX TEAM

16











THE H-MODE OF ASDEX












ASDEX TEAM

E

I1 ( b )

bull mdash mdash

10 15 20

t(s)






(b)2 (cm)

4-

2--

o--

-2-

-4-bull

0 bull VB-drift

0 lt bull

O 0 0 bull 10 bull

0

bullVB-drift

PN (MW)



THE H-MODE OF ASDEX

( b )

2-










ASDEX TEAM









THE H-MODE OF ASDEX









ASDEX TEAM




10 SUMMARY









THE H-MODE OF ASDEX









ASDEX TEAM












THE H-MODE OF ASDEX










REFERENCES












ASDEX TEAM































































THE H-MODE OF ASDEX










































ASDEX TEAM




































(1987) 65







ASDEX TEAM

3

11 12 t ( s )



transition






2-




THE H-MODE OF ASDEX










110



ASDEX TEAM

lt200-

~ 100-

H phase1262 s

lp= 320 kA

100kA

50 kA

40











Te (keV)

M-5

bull10

-05

-0

Te(keV)e

15-

10-

05-

o-


6046

(a )

j

y(

VNl

A

A

A09 10 11 12 13

Ms)

HCL

d

Eob

vIC

dd

2-

1-

o-4-

2-

-

0-

raquo 5982

^_

i 111 1

1 ML mi l

10 12 14 10 12 14

t(s) Ms)



THE H-MODE OF ASDEX

PN| = 75MW

K 86C

PNI=15 MW

laquo 8603

(a

(b )









04

5 03 H0)

I 02-

^ 01 -

Eu

m

raquo St

i V

tf bull 88U L I ^



ASDEX TEAM

112













THE H-MODE OF ASDEX

1292 1294













ASDEX TEAM










h 20

V

ne

o

X

A

qa = 365qQ = 29qa = 26qa=275

--10



THE H-MODE OF ASDEX

AA

sawtooth

r fcmJ








9630

ELMin

ltMio

CM



ASDEX TEAM

90 180 270 360












11 12 13 t (s)



THE H-MODE OF ASDEX

a

2 4 6

dnedr (1012cm-4)









ASDEX TEAM

10

10

2 poundbull

4

1 4804

4745

Lj( b )

13 15 16

t Is]


with ELMs wo ELMs

rRAO

(MW)

(au)



THE H-MODE OF ASDEX

08

04

- - 5

with ELMs 11338

time 11) 1095 s12) 1155 s13) 1215 s14) 1230 s15) 1245 s6I 1260 s

10 20r (cm)

30

s

6

gt

- bull 2

wo ELMs 11447

( b )s

i bull i i f

time- (1)(2)13114)IS]161

1095 s1155 s1215 s1230 s1245 s1260 S

10 20 30rcm)





nFel0)nel0) =

io-2-

bullo

5 io3J

10110 120 130

t(s)



ASDEX TEAM











THE H-MODE OF ASDEX







ASDEX TEAM

600-

500-

i00-20-

15-

( b )

-6 -6 -2 0

Ar= r-r (cm)








THE H-MODE OF ASDEX

[cm]

1013

9630OH 105s

- - - L 113H 1164

1012

R-Rs [cm]

-2 8









ASDEX TEAM

o

c

O

15-

10-

os-

o-

4-

2-

n-

raquo 96301

)bull

L

- - ^

0 (DO 0 bdquo

H

Nl

1

i

idegC11

i

ii

i

o o o

Lm

mdash

11 12 13 t [sJ 14







20t



neutralizer plates

infrared camera

HaDQ



THE H-MODE OF ASDEX

J

L

VUilillililUH V

1bullE 25u

2 20

S 15cat

Z 10c

s ^

sect 0

raquo 9393

10 12 U

t (si


cm = 30 MW






175 165 170 175 165

Rlcml

170 175



ASDEX TEAM

1520243 (L 2=0) 20241 (H Z=+1 Cm)

| ri

0

40

gt

20

4

On 2

40

-40

165 170 175 165

R (cm)170 175








THE H-MODE OF ASDEX

90 91 92







30


Z mdash



ASDEX TEAM






N I A

10 11

t (s)





THE H-MODE OF ASDEX

E

Ul

Ul

80-

70-

60-

50-

40-

30-

20-

10-

0 bull

D 1

bull

itlw deg


A A

A

2 3 U

n e [10

p

0

oo

1 8

0

bull OX +

5

cm3]

D+

a

5

A

hrP

PN

6

oD

H-type

= 370 kA= 300 kA

gt 2 MW

7 8











ASDEX TEAM







dNdt = - N T P (2)


= N0TD (3)



6028 laquo 5991

oe



THE H-MODE OF ASDEX


Phase

OH

L

H

dNdt

(s-1)

0

0

2 x 1021

(s-1)

1O21

6 x 1O21

0

V(s-1)

0

8 x 1O20

8 x 102 0

2

2

2

(s

X

X

X

Rb

-)

1O21

102 1

1O21

TP

(s)

OO5

001

015


dN N

dt + rp deg +












ASDEX TEAM

17005r=2a3

11O H V NI (

115 12 125

X

[m2s]

1-

1-

(

bull

17005

b)

s

IS 11 S2 = 115 s3S 1195 s4U205s551215s

bullXe(a)

0 05 r a 1









3-T

[keV]2-

1-

mdash

(a )

r o )N

t

XCH+X

17005123s

05 ra 1

1

3-

2-

1 -

L (1 15S)

H(1215s)

( b )

OH(ils)

- lt

05 ra 1





THE H-MODE OF ASDEX

10








180 190 200

R (cm)

210



ASDEX TEAM

A- L1227s

0 20 A0r (cm)














THE H-MODE OF ASDEX

02 03Io IMA)

04













yj

UJ

60-

40-

-

20-

0-

o

0

L-

^

O

Mode

H

o

bull fraquo

- Mode

w o

ot



ASDEX TEAM






100

80-

60-

40-

20-

WOELMS (D-D+)

Hdeg-D +

-x-N


Po




I -prad (p) p dp dr


(1)



2)




THE H-MODE OF ASDEX

U13-

_ 010-

ujH

005-

0-

11513

xE(35cmh

XElSOcmly^

PNI=177MW

I

1I v

110 120 130015

010 j ^3 _

HIP

005

11447Tcl35cm)

PW1=348MW

105 110 115 120 125

t(s)


















ASDEX TEAM

111

Qgt 0

n

2 8

PN1= 12 MW

I I I

Id

32 MW

I2 4 6 8


10












100-

50-



0 2 I 6 8 10

ne (1013 cm3)



THE H-MODE OF ASDEX

60-

20-

02 MA

0 1 2 3

PNI CMW]




















50-

Emdash 30H

10-

H-TYPE

_ g 1 1 bull

L-TYPE

IP= 295-315 kA

mdashr~15

1 1 1 1 1 120 25

B [ T ]



ASDEX TEAM




Xe(r) (cm2-s-) =

D(r) = 04









THE H-MODE OF ASDEX

0 100 200 300 400 500


( c )

10 20B (T)

30






08 10 12 14 16 18



ASDEX TEAM

3-o L - Mode

H - Mode

B (T)









150

10CH

2Q

bull bull

16 18 20 22 24

B (T)


25

20-

~ 15 bull

a

lt

10

5

0-

L

r

H-type

8

W L-type )pound

= 200 kA

300 kA

380 kA

PN CMW]





THE H-MODE OF ASDEX

Imdash_gtlaquo

LUP

70-

60-

50-

30-

20-

10-

0-

bullbull

4 V


3 1 2 3

V 1

ao

irftv

ON

6ooP0 Q 0


bull

[101

tP aaa a

a a

^

Sraquoodego deg00 g

bulldeg Pbull 0 Ip

DN

PN

5 6

3cm3)

H-type

o

N

= 370 kAc 300 k A

gt2 MW

7


sCL

o

2 4 6

fie (1013crrv3)


PN| (MW)







ASDEX TEAM

without insertsDV-I

with inserts

Pumping panels

DV-II Limiter

I Ti-sublimator








THE H-MODE OF ASDEX








ASDEX TEAM

1 2 3 4 5

ne (1013crrv3)







10



THE H-MODE OF ASDEX





FOR H-MODE PLASMAS

51 ICRF heating




(cm)

MoV ctldiv)

(QU)





ASDEX TEAM
















THE H-MODE OF ASDEX

Ic

cQJ

4-

2-

r

JO

JQ

11 12

o

c

cQJ

curr

d

[asm

a

01

d

Vol

t

a oo

u)

JO

3co

d

da

rb

u)

co

d

dcccot_

4-

2-

bull

AU

-

m

o-

o-

0-

Jp

UiX u l

FB )

Fe X

bull L (6124)

- H (6125)

lasma

I

1

If Main plasmaij

Oivertor

i bull bull i 1

t

r u

S 2-co

Zn

S o

-2-

2-

1-

bull 1 -

11 12 11 12

Us)







ASDEX TEAM

o 0

mo

^ 6

1 2 -

8672

8671

-J

10 11 12 13 14 15

t (sJ






6-

EV

CO

gt-8-c

o Hbull L


ARL [cm]



THE H-MODE OF ASDEX

8-

E L


N

2

IMW]









E



ASDEX TEAM









t Is]



THE H-MODE OF ASDEX

10 11










ASDEX TEAM

2 0

Plasma

A2 1

H mdash25 cm

10 ms


Te (keV)

t (s)






1-

units

)

p

0

001-y

r0I y

Single-Nu

s

SX-lntensityNS

- bull

1 Plasma

-5 -10 -20

r-re (cm)

-30



THE H-MODE OF ASDEX











view A-Aentrance

A - windows

0degodegodegexit

windows



ASDEX TEAM

24942


18


S SCATTERED SIGNAL

SIGNAL

LINE DENSITY

23463

H

116 118t (S)

120 122






E 2u



23445



THE H-MODE OF ASDEX

-50 -25

T (us)







I W 21895H laquo 21696

Miriiov activity

-4-

10 14 Ms) 18

f= 30 kHz

(= 82 kHz

fe222kHz

f 1 MHz

18



ASDEX TEAM









l=380kA B=236T q=30

f-30kHz

U82kHz

(=222 kHz

f 606 kHz

14 10

Time (s)14



THE H-MODE OF ASDEX

24896


(MA

)

Euo

ic

wcD

xij5e

04-

02-

o-

08-

u^

J

6

9JLT

) 02

m =

5 J

04

mdash ^ j ^ p _ _ _

06 08

t(s)

1

-8(A

)u

o

bull0

10


r-8

a

mpoundurgtO

0)IC

A-

3-

-

1-

n -u

5982 J

mdashJ J

itiik

W^^V^A

idisruptive

I p = 300 kA

Bt = 22 T 2e

10 ii 12 13

t Is]

U









ASDEX TEAM






R2 div + Mo

JJOO = mdash (1R2)1

Mo

+ 4TT2

dldV

= 0







yco

101

10-2

106 10-5104 10-3

B =1

X V 0 + x0J









THE H-MODE OF ASDEX

0A-Z[m]

02-

00-

-02-

-04-

(a)


12 14 16 18 20 R[m]

BeBe

00015

0001

00005

0

-00005

-0001

(b)

50 100 150 200 250 300 350





0-5

= Mo Since







ASDEX TEAM

















THE H-MODE OF ASDEX

6

6-

4-

2-

bull H - Mode

L - Mode

100 101 102 103 104

ra







t = 0



ASDEX TEAM

0 02 01 06 r Q 10 0 02 0A 06 r 0 10







3PC2(0))u = 0




THE H-MODE OF ASDEX

05-









ASDEX TEAM

107

71


- 0002 0005 0010 Re7












THE H-MODE OF ASDEX

R o ( 7 gt

G005 bull bull

00


ra = 0867

03



is the solid line



10

06-

02 bull

00

00

Toroidal

current IIp

1mdash1mdash1

^

025 05 075

Volume VVp


10 I 14 16 I8 20

10

06

02

00

V PPO

bull bull bull bull

Plasn


1a pressure pPO

025 05 075

Volume VVp

0075Pressure Volume

I Window


085 09 095 10 VVp

10






ASDEX TEAM






10

10-2


^ ^ 1 1

5 x 1 0 -4 105 15 1 0 5










THE H-MODE OF ASDEX













ASDEX TEAM













THE H-MODE OF ASDEX













ASDEX TEAM

16











THE H-MODE OF ASDEX












ASDEX TEAM

E

I1 ( b )

bull mdash mdash

10 15 20

t(s)






(b)2 (cm)

4-

2--

o--

-2-

-4-bull

0 bull VB-drift

0 lt bull

O 0 0 bull 10 bull

0

bullVB-drift

PN (MW)



THE H-MODE OF ASDEX

( b )

2-










ASDEX TEAM









THE H-MODE OF ASDEX









ASDEX TEAM




10 SUMMARY









THE H-MODE OF ASDEX









ASDEX TEAM












THE H-MODE OF ASDEX










REFERENCES












ASDEX TEAM































































THE H-MODE OF ASDEX










































ASDEX TEAM




































(1987) 65







7KH+ 0RGHRI$6'(;

Documents

Transcript of 7KH+ 0RGHRI$6'(;