"Ion --- Cyclotron --------- i n s t a b i l i t i e s i n magnetic -- ----- fusion ------ plasmas"

Chapter I

Introduction - - - - - - - - - -. - -

A t the 1958 Geneva Conference on the Peaceful Uses of Atomic Energy

[I] , research on fusion power was declasr;i.fied by the United Kingdom, the

United S ta tes and the USSR. Since then the successful functioning of a

self-sustaining controlled thermonuclear fusion reactor delivering

economically competitive e l e c t r i c a l power [23 has been the dream of any

plasma physicist .

Two of the a o r problems t o be tackled in t h i s venture are the

heating of plasma pa r t i c l e s upto the ignit ion and at ta ining the theoret ical

value of the fusion t r i p l e product (density times confinement time times

temperature - t h i s is also known as the Lawsc~n c r i t e r ion ) .

During the last four decades considerable progress has been achieved

towards t h i s goal. In the present experimental and theoret ical scenario

magnetically confined reactor models, par t icular ly the tokamaks, are much

superior t o the i n e r t i a l confinement devices in many aspects.

In the last twenty years, plasma confinement has improved

4 dramatically, by a factor of l0 as measured by the fusion t r i p l e product

2B -3 C31. A recent typical value reached is ni(0)rETi(O) = (8-9)*l0 m skeV in

JFr C41. Record ion temperatures of about 30 keV, which is about twice the

value needed for igni t ion, have been achieved in the tokamaks TETR and JET.

The highest electron temperature of about 12 keV has been obtained in m.

Several other tokanaks a l so operate routinely at nulti-keV temperatures;

fo r example. JT-60, T-l.0, D 111-D, ASDM, e t c . The poss ib i l i t y of high

m -3 density operation i n large tokamaks, t h a t is, with ne grea te r than XI m ,

has been demonstrated.

In JT-60, a current of ZMA has been driven non-inductively by lower

hybrid waves [5]. Recently, a boot-strap current ( t h a t is, the current

generated by the plasma i t s e l f ) upto 80% of the t o t a l current was

estimated a t high plasna pressure in JT-60. Current d r ive f o r about one

hour has been achieved i n the superconducting tokamak TlUAM - lH. There have been s ign i f ican t achievements in the control of plasma

ac t iv i ty . In JET, sawtooth f r ee periods i n excess of 5s have been obtained

w i t h ion cyclotron resonance heating ( ICRH ) [4] .

These r e su l t s , which highlight the pinr~aoles of present achievements

in tokamak research and signpost the way towards a fusion reactor , a r e

founded on a broad, rapidly expanding database provided by a large number

of tokamaks and improved theoret ical understanding.

Studies on mirror devices a r e a l so encouraging. Recent minority slow

wave beach heating experiments i n the Phaedrus-B tandem mirror, using H-He

plasmas s tabi l ized and heated with ICRF power alone, have achieved peak

values of beta, i n the cen t ra l c e l l , of 0.26 [6].

Heating ------ The current c i rculat ing i n any magnetic confinement plasma device such

as tokamak, mirror, s t e l l a r a to r , e t c heats the plasma res i s t ive ly . However

i n t h e present scenario, t h i s ohmic heating regime is limited by t h e

decrease in r e s i s t i v i t y with increasing temperature t o temperatures below

ign i t ion . Auxiliary heating ( a l s o known as supplementary heating ) is

required t o heat a magnetically confined plasma f u r t h e r from d i r e c t

ohmic heating [2,7,8,9]. This can be in t h e form of t h e in jec t ion of a beam

of h a h energy n e u t r a l p a r t i c l e s (NBI) ; electromagnetic waves in d i f f e r e n t

frequency r w e s : e lec t ron cyclotron re:sonance heating (ECRH), lower hybrid

resonance heating (LHRH), magnetic p u m p f i , Alfven resonance heating, ion

cyclotron resonance heating (ICRH), el;<!. A b r i e f review of var ious

supplementary heating methods a r e given below.

1. Neutral beam in jec t ion (NBI): ------- ---- --------- ---

In t h e present scenario, n e u t r a l beam heating method and ICRH

method are employed together in leading tokamaks and a b r i e f repor t of t h e

ICRH method is given later. Neutral beam heating method was developed in

the e a r l y 1970s, which in f a c t has seen its bigges t successes before high

frequency heating: the in jec t ion of f a s t n e u t r a l hydrogen atoms [I@].

The p r i n c i p l e of t h i s concept is straight-forward and was suggested

in the e a r l y 19Ws [11,121. The technique c o n s i s t s of i n j e c t i n g a be= of

high energy n e u t r a l p a r t i c l e s i n t o the plasma where they become ionized,

confined by the magnetic f i e l d s and slowed down by binary c o l l i s i o n s with

the background pl-, which is consequ~?n!nt:ly heated. The processes involved

are c l a s s i c a l and w e l l understood [3].

The n e u t r a l beam is at tenuated in t h e plasma by e lec t ron impact

ioniza t ion, charge exchange and ioniza t ion by c o l l i s i o n s with ions (

including i r p u r i t i e s ); a measure of the attenuation being given by the

nean f r ee path A , which, in the relevant ~tange of beam energy between 20

and 270 keV per nucleon can be approximatd as

17 h = 5 . 5 * l0 ( 1Zf/Af )/ne

where Ef/Af is the energy of the beam part.icles in keV per nucleon and ne

is the electron n W e r density.

Although neutral beam inject ion has a lso been used on mirror

experiments C131, the purpose there was primarily t o f i l l the nagnetic

t r ap with f a s t ions ra ther than heat an exis t ing t a rge t pl-. Within

the scope of t h i s review we w i l l therefore r e s t r i c t the discussion t o

neutral injection into toroidal devices: tok8naks and s t e l l a r a t o r s , where

the emphasis l i e s on neutral beam heating and the s ide e f f ec t s l i ke

p a r t i c l e and momentum input are of secor~drlry importance.

Tangential injection ( where the angle of incidence, a, of the beam

with respect t o the direct ion of the toroidal magnetic f i e l d is small )

helps t o increase the path length through the plasma and the absorption of

the beam and is a l so best f o r current dr ive (current driv2: In tokamaks,

there a r e two types of current d r ive - the inductive (o r ohmic) and the

non-inductive, of which the NBI belongs t o the non-inductive type. The

o h i c current dr ive r e l i e s on inducing im MF around the toroidal plasma by

changing the magnetic f lux which passes through its centre . However, it is

c l ea r t ha t the magnetic f l u x cannot change monotonically for an indef in i te

period of time and tha t the process is necessarily pulsed in nature, though

in a reactor the loop voltage required is small and the pulses could be

qui te long, perhaps of the order of an hour. From an engineering point of

view it would be mch simpler t o operate a reactor in a continuous mode,

and it is t h i s which h a s motivated research in to various schemes fo r

producing non-inductive current dr ive. Non-inductive current dr ive can

f a c i l i t a t e operation, especially at high plasma current o r in a compact

high f i e l d tokamak. Inductive current dr ive can be replaced, a t l ea s t

par t ia l ly , during the steady state current phase or , preferably, during the

current r i s e phase. Ultimately, complete non-inductive current dr ive of fe rs

the potent ia l of eliminating the transformer.). There are , however,

problems of access between toroidal f i e l d c o i l s and, at high plasma

density, absorption occurs in the outer regions. These problems are

overcome by perpendicular inject ion, which is a lso technologically l e s s

demanding, since access can be between t.he toroidal f i e l d co i l s . However,

perpendicular injection is inef f ic ien t for current dr ive, and new loss

processes are introduced.

Another parameter important in NBI is the direct ion of injection

re la t ive t o the direct ion of the plasma current. In co-injection ( in the

same direct ion as the current ) the f a s t ions generated a r e well confined.

In counter-injection ( in the direct ion opposite t o the current ), some of

t h e f a s t ions produced in the outer regions a re promptly l o s t [3].

The f a s t ions created as the neutral beam is attenuated, lose t h e i r

energy by co l l i s ions w i t h the plasma, heating electrons and ions at a r a t e

which depends on the energy of the beam pa r t i c l e s re la t ive t o the electron

temperature. A t a c r i t i c a l energy, Ecrit = 14.8 Te (where Te is the

electron temperature) f o r a proton beam in a hydrogen plasma, electrons and

ions a re equally heated. For Ef < Ecrit. the ions a re heated predominantly;

t h i s occurs usually in the centre of high temperature plasras and with

deuterium injection. For Ef > Ecrit, electron heating is predominant; t h i s

condition is only ra re ly sa t i s f i ed in large tokamaks, except i n the outer,

colder regions.

During thermalization of the neutral beam ions, momentum is a lso

transferred t o the pl-, leading t o rotat ion. This can be a problem at

high powers in large devices where momer~tum is slowly transferred t o the

environment (e.g. in TFTR ). It can be controlled by p a r t i a l balancing of

injection.

2. Electron cyclotron resonance heating (ECWj: -------- --------- --------- ------ This heating n e t M is based on the absorption of radiofrequency

waves of ordinary o r extraordinary polarization and with frequency near the

electron gyrofrequency:

= 28 B (where 1) is the magnetic f i e l d )

or higher harmonics. Usually such a wave d i r ec t ly heats the resonant

electrons in the region of Doppler resonance, where w - nu = kMv,, . where ce

w is the wave frequency and k,, is the wave number pa ra l l e l t o the magnetic

f i e ld . In the case of propagation nearly perpendicular t o the magnetic

f i e ld , the resonance is broadened by the r e l a t i v i s t i c dependence of the

electron mass on its energy. In the case of oblique incidence, the

resonance is broadened by the Doppler s h i f t of the wave frequency due t o

pa r t i c l e motion along the magnetic f i e l d . The damping of the extraordinary

wave is higher fo r oblique propagation.

Although the potent ia l advantage of using electron cyclotron

resonance heating in fusion plasnas, due t o the expected g o d coupling t o

the plasma and localization of absorption of electron cyclotron waves has

been recognized f o r a lmg time, l i t t l e progress w a s made with t h i s method

in the e a r l i e r scenario of controlled fusion research because of t h e lack

of sui table power sources f o r the frequency range in question (30-150 GHz).

Only in the late seventies has the s i tua t ion changed, as microwave sources

(gyrotrons) in the lower half of t h i s frequency range becane available.

This has stimulated both experirmental work and more detai led s tudies of

potent ia l applications of ECRH [141.

The physical picture of what happens during ECIW start-up assist

is visualized as follows : I n the beginning of plasma generation;

2 when the tenuous plasma linit [ ( o ) 5 v /c] , (where o is the d c t P electron plasma frequency , o the electron cyclotron frequency,

C vt

the thermal veloci ty of the electron and c the speed of l i gh t ) applies

t o the dynamics of the X - d e , the absorption is proportional t o the

electron density and the interaction is localized around o = wc. A s the

density increases, the high density regime of the X - male is reached. Then

the absorption a t the resonant layer o =: oc decreases and a t some s tage the

waves start t o propagate towards the upper hybrid layer. This process is

part icular ly important in small devices, but tends t o become

un-important in reactor-size tokamaks. A t the upper hybrid layer the waves

convert l inear ly in to e l ec t ros t a t i c Bernstein - l i k e modes. Nonlinear

ef fec ts , in par t icular a parametric decay near the upper hybrid e .g . i n to

ion acoustic and / or lower hybrid waves, and upper hybrid waves of lower

frequency, can also appear. Hence in a l l cases, strong absorption is

expected t o occur in the region between the upper hybrid and the cyclotron

layer. The f i r s t study of ECRH was undertaken the TH-3 tokamak C141.

In conclusion, it must be emphasized tha t developing electron

cyclotron heating t o a viable scheme fo r its potent ia l applications

requires both intensif icat ion of the experimental programe and of the

development of high power gyrotrons of greater eff ic iency in the relevant

frequency range.

3.Louer hybrid resonance heating : ----- ------ --------- ------ Plasnas can be heated e f f i c i en t ly by waves with frequencies near

the geometrical average of the ion and electron gyrofrequencies:

fie = 0.65 B-/A

where A is the atomic number. For these frequencies ( few GHz ), the index

of refraction for the plasma is large, highly anisotropic and depends

strongly on density [31. A s a r e su l t , the plasma r e f l e c t s the wave, thereby

precluding d i r e c t heating. Rather, it is necessary fo r a slow wave t o

tunnel through the edge p l a s m and exc i te a propagating wave inside the

plasna.

The slow wave launchers ( g r i l l s ) used u n t i l now comprise a number

of juxtaposed open waveguides which can be phased re la t ive t o each other

t o make a ra ther narrow and adjustable spectrum in the toroidal direct ion.

The launcher has t o be placed very close t o the plasma ( within the

scrape-off layer and f i t t e d close t o the plasma shape ) since the near

f i e l d decays rapidly ( in 0.7 cm fo r a large device such as JFP fo r a

frequency of 3.4 GHz and a refract ive index of 0.2).

Proper design of the launcher ensures access ib i l i ty t o the plasma

between the edge re f lec t ing layer and a second re f lec t ing layer deeper

inside the plasma. Here, e i the r wave conversion and ion o r electron

Landau damping, o r propagation and nor-linear absorption may occur.

Ion heating has been obtained in a narrow parameter range only.

Electron heating is preferred, and very high cent ra l electron temperatures

(multi-keV) have been achieved a t low dens i t ies . Many experiments have

proved the soundness of the theore t ica l understanding of t h i s heating

scheme, including its l imitat ions arising from the access ib i l i ty condition.

Electron heating a l so leads t o some current generation when a

unidirectional wave is launched around the torus .

In the tokamaks MRE SUPRA and JET [151, with the simultaneous

application of ICRH (4.5 HW) and LHCD (l.Ci MU), the f a s t electron rad ia l

dis t r ibut ion was still hollow and the energy dependence of the suprathermal

t a i l was much f l a t t e r . Apparent "photon tenperatures" upto 800 keV were

observed from X rays as compared t o 150 keV in the pure Lower Hybrid

Current Drive (LHCD) case [16]. This indicates t ha t the f a s t wave was

s ignif icant ly cwpled t o t he f a s t electrons accelerated by the lower hybrid

waves, thus explaining the improved current dr ive efficiency and electron

heating also observed in the combined LHCD + ICRH scenario.

4 . Low frequency heating : --- --------- ------- a ) Magnetic pumping : -------- ------

The theory of plasma heating by low frequency f i e l d s w a s

independently in i t ia ted by Budker [I71 in 1951, by Spitzer and Witten El81

i n 1953, and by Schluter [I91 in 1957. These authors showed t h a t an

osc i l la t ing e l e c t r i c f i e l d perpendicular t o a confining nagnetostatic f i e l d

can be used t o heat a plasma v i a t h e gyro-relaxation e f f ec t , i . e . the

exchange of energy between perpendicular and para l l e l degrees of freedom of

the plasma pa r t i c l e s due t o co l l i s ions . Since the osc i l la tory e l e c t r i c

f i e ld w a s assumed t o be produced by a change of confining magnetic f i e l d in

time, t h i s heating method was cal led 'magnetic pumping'. The theory of

gyro-relaxation heating w a s fur ther developed in [20-221, which include

the e f fec ts of ion viscosi ty , electron and ion heat conductivit ies and the

generation of sound waves:

When the pa r t i c l e co l l i s ion frequencies a re much smaller than the

frequency of the osc i l la t ing f i e l d , gyro-relaxation heating is not

e f f i c i en t . Another mechanism of energy t ransfer fo r t h i s case w a s

considered by Berger e t -- a1 -- C231 i n 1958, who showed tha t s ign i f icant

heating can be achieved when the t r a n s i t time fo r pa r t i c l e s across a

pumping section of the plasma is comparable t o the period of the

osc i l la t ing f i e l d . The energy t ransfer is caused by a force pa ra l l e l t o the

magnetostatic f i e l d which a r i s e s from the interaction between the pumping

f i e ld and the magnetic moment of the pa r t i c l e . The scheme based on t h i s

co l l i s ion less mechanism w a s denoted ' t r ans i t time heating'.

In general, the pumping magnetic f i e l d exci tes compressional motion

i n the plasna. This motion, in pa r t i cu l t r the variation of the electron

pressure, in turn produces an e l e c t r i c f i e l d pa ra l l e l t o the magnetostatic

f i e ld . Thus, an additional force a c t s on the plasma par t ic les . A s a resu l t ,

the pa r t i c l e s nay gain kinet ic energy v ia Landau damping which is

associated with t h i s force. The importance of t h i s mechanism was pointed

out by Stepanov [24] i n 1963. Considering electromagnetic waves t rave l l ing

along the magnetostatic f i e ld , he showed tha t Landau damping considerably

enhances the heating r a t e . Moreover, he concluded t h a t in the case of

strongly non-isothermal plasmas, heating becomes especially e f fec t ive i f

the phase velocity of the pumping wave is close t o the veloci ty of the ion

acoustic wave. Further improvements of the modelling of transit t i n e

heating by compressional magnetic perturbations were made by a number of

authors [21,25-273.

A l l of these s tudies concentrated on the heating of ions by magnetic

perturbations with frequencies that a re muoh smaller than the frequency of

the f a s t w e t o - a c o u s t i c wave. The poss ib i l i ty of electron heating by

making use of the f a s t magneto-acoustic wave w a s f i r s t discussed by

Dolgopolov and Stepanov [28] in 1965, and l a t e r by Canobbio [291 and by

Lashmore-Davies and Hay [a].

In 1971, Samain and Koechlin [31,32] suggested the use of a tors ional

perturbation rather than a compressional magnetic perturbation fo r t r a n s i t

t i n e heating of ions. They argued that for large aspect r a t i o tokanaks t h i s

scheme is more e f f i c i en t than compressional msgnetic pumping while using a

lower working frequency. The theory of tors ional m e t i c pump& w a s

fur ther developed in [33,34].

The co l l i s ion le s s heating schemes mentioned so f a r a r e a l l based on

the Cerenkov resonance involving only the p a r t i c l e veloci ty component

pa ra l l e l t o the magnetostatic f i e l d . A scheme based on the Cerenkov

resonance involving a l so perpendicular velocity conponents w a s proposed by

Canobbio 135,361 in 1976. This scheme called toro ida l d r i f t magnetic

pumping, requires a punping f i e l d tha t exci tes tors ional perturbations in

toroidal geometry. The heating eff ic iency of t h i s scheme w a s shown t o be

higher than t h a t of tors ional magnetic punping.

In a11 papers referred t o , the amplitude of the electromagnetic f i e l d

w a s assumed t o be su f f i c i en t ly small so tha t l inear theory is applicable.

The use of stronger f i e l d s , however, nay lead t o a non-linear d i s tor t ion of

the p a r t i c l e d i s t r ibu t ion function. In t h i s case, it would be necessary t o

develop a theory t h a t takes t h i s e f f e c t in to account. Two such theories

have been developed so f a r . The f i r s t one, based on the quasi-linear

approximation, w a s put forward by Dolgopolov and Sizonenko [37] in 1967.

The other theory which uses a single-wave approximation, was advanced by

Canobbio [29,33,381 in the early 1970s. I t follows from both theories t ha t ,

fo r the same f i e l d amplitude, the non-linear energy absorption is smaller

than the energy absorption calculated from the l inear theory.

The eff ic iency of plasma heating by electromagnetic waves strongly

depends on the way in which the energy is transferred from an antenna t o

the plasma. A s ea r ly as 1960, Franck - Kamenetskij [39,40] pointed out

t h a t the energy transfer can be facilitated if an eigenmcde of

electromagnetic oscillations in a bounded plasma system is excited.

Specifically, he suggested using an eigenmode of t he fast magneto-acoustic

wave. Hence, this methd of plasma heating was denoted 'magneto-acoustic

resonance'. It should be borne in mind that t h i s m e t h d is rather generic,

since it can be used in conjunction with any dissipative mechanism. The

magneto-acoust ic resonance involving col llisional dissipation was studied in

a number of papers by the Fribourg group [41-46] in t h e late 1960s and

early 1970s, and the Australian group [47-503 in the late 1970s. Using a

two f l u i d plasma model involving both collisional and collisionless damping

mechanisms in a phenomenological maruler, t he magneto-acoustic resonance was

investigated in a series of papers by the Brussels group [51-591 in the

1970s. Finally, a kinetic theory of magneto-acoustic resonance was put

forward in [60,61] in 198Q.

b) Alfven resonce heating : ------ ----....-- ------- Thedevelopment of theore t i ca l work related to Alfven resonance

hea t ing had begun as early as 1965-1966 in the pioneering work by

Dolgopolov and Stepmov [28,62]. Considering a simple model, they showed

that collisional or Landau damping of the fast magneto-acoustic wave in an

inhmogeneous plasm can be strongly enhanced if the condition for the

spatial Alfven resonance is satisfied. The resulting absorbed power was

estimated to be of the same order of magnitude as the circulating power.

T h u s , they predicted one of the most typical characteristics of Alfven

resonance heating .

Alfven resonance heating as a scheme for heating tokamak plasmas was

first proposed by Tataranis and Grossmum [63] in 1973 and independently

by Hasegawa and Chen [64,65] in 1974. An important result of t he latter

authors, obtained w i t h an ideal magnetohydrtriynamic (MHD) model in slab

geometry, was the finding t h a t the absorbed power is strongly enhanced if

t h e surface W e ( t h e first radial eigen m d e of t h e fast w e t o - a c o u s t i c

wave) is excited in the p lasm, (discussed further in [BE]). In 1976,

Hasegaua and Chen [67,68] using a simple kinetic model in slab geometry,

showed that in a hot plasma t he f a s t magneto-acoustic wave is mode

converted tokinetic Alfven wave in t he neigtlbourhood of the spatial Alfven

resonance (discussed also in [69]). The mount of absorbed power was

found t o be the same as that obtained from calculations. Moreover,

these authors considered non-linear heat ing processes due t o parametric

decay instabilities excited by the converted kinetic Alfven wave

(discussed also in [703). The effects of resistive dissipation an energy

ahsorption at the spatial Alfven resonancewere investigatedby Kappraff

e t -- a1 -- [71,72] in 1975. They demonstrated that t he results found in ideal

MHD theory are unaltered for plasma res is t iv i t ies of t he order typical of

tokamaks.

The first numerical calculations based on MHD equa t ions in cylindrical

geometry were carried out by Tataronis and Grosslnann [73] in 1976. The

authors confirmed the importance of the exci ta t ion of the surface m d e . A

sinrple analytical &el for resonance absorption of the surface mode in

cyl indrical geometry has been given in [74] . More detailed numerical

computations [75,76] using an HHLl cyl indrical code revealed tha t the

presence of an equilibrium plasma current can dramatically improve the

coupling t o the innermost resonant surfaces. The phenomenon w a s l a t e r

ident i f ied [77] as being due t o the e f f ec t s of magnetic f i e l d curvature.

The f i r s t extensive cyl indrical kirietic calculatiorls which took into

account the e f f e c t s of f i n i t e ion Larmor radius and pa ra l l e l electron

dynamics (Landau damping) were carried out in 1982. Rose g at C781

confirmed the importance of an equilibrium plasma current. Moreover, these

r e su l t s indicated the exci ta t ion of the quasi e l ec t ros t a t i c surface

wave nodes near the pl- periphery.

The poss ib i l i t y of using magneto-acoustic cavity modes (higher radial

eigen modes of the f a s t magneto-acoustic wave) for plasma heating in large

tokamaks w a s discussed f o r the f i r s t time in 1978 C793, in the context of

an H-Ul nude1 in s l ab geometry. Including in the i r analysis the

t r a n s i t time pumping mechanism, the authors concluded tha t t h i s mechanism

can compete with Alfven resonance absorption fo r high rad ia l mode numbers.

Furthermore it was show tha t these modes have typical ly a much higher

cavity Q value than the surface mode. The theory of plasma heating by

cavity modes w a s fur ther advanced in [80-841.

5 . Ion cyclotron resonance heating (ICRH): --- --------- --------- ------- Heating i n the ion cyclotron range of frequencies (ICRF) is probably

the most common scheme a t present, being used on a considerable number of

tokamaks, mirrors and s t e l l a r a t o r s .

T h i s scheme fo r fusion plasmas, was f i r s t demonstrated in a

non-axisymmetric device, the B-65 race back s t e l l a r a to r in 1958 [85,861.

Eventhough f a i r l y extensive ICRF heating experiments were conducted in t h i s

device and its successors (B-66 mirror [87] and model C s t e l l a r a t o r

[88-001 the most successful heating experiments have been performed in

tokamaks since the tokamak concept w a s introduced in the late 1960s.

Eventhough ICRH has been used in s t e l l a r a t o r s s ince 1958, many aspects

of it are not well understood ye t [9]. Only a few ICRH experiments have

been conducted in non-axisymmetric systems ( i . e . s t e l l a r a to r s ) and the

development of the theory and technology in them is jus t beginning. Hence

in the following review of ICRH, works only in tokamaks and mirrors a re

considered.

The ICRH has been regarded as one of the important heating methods of

magnetized plasmas capable of heating ions d i r ec t ly [91]. This type of

heating of a plasma with two (or more) species of ions has part icular

applications in fusion [921. This mechanism may a lso be in operation in

the %e r i ch so la r wind during some strong so lar f l a r e s [93].

Ion cyclotron resonance heating of fusion plasmas is considered a s one

of the a t t r ac t ive candidates for heating plasmas confined in a torus ( a

tokaJnak) [92,94,951 or a s t e l l a r a t o r [96-981 and in a mirror [99] ( a

ying-yang mirror, tandem mirror or multiple mirror) [lEW,l01]. Some of the

a t t r ac t ive features of ion cyclotron heating are:

a ) The low frequency of t h i s scheme means t h a t high power technology is

available for the wave generator, and a l so of being capable of being

launched from couparatively simple antenna s t ructures within the plasma

vacuum vessel.

b) I t would heat the p l a s l a ions d i rec t ly , e i the r heating the bulk

dis t r ibut ion o r producing energetic t a i l s which a re more reactive and

C ) Ion cyclotron heating might be an a l te rna t ive t o the expensive neutral

beam injection in te rns of g o d penetration t o the centre of the plasma.

Recently NBI is combined with ICRH in leading tokamaks JET, T M M R and

JT-60 t o ge t be t te r resu l t s .

Another possible application is in radio frequency plugging [ l 0 - l 0 3 ]

of mirror plasmas. Ion cyclotron heating is an essent ia l pa r t of the

operation of isotope separation; an ion species with ion cyclotron

frequency matched t o the pump frequency is preferent ia l ly heated and may

be picked out by d is t inc t ion CUB] . One scheme of radio frequency plugging

of a mirror u t i l i z e s ion cyclotron resonance heating t o increase the r a t i o

of the perpendicular t o the pa ra l l e l ion temperature; thus, advantage could

be taken of the increased, favourable d is t r ibu t ion of magnetic moments of

the ions in the magnetic t rap . Another way of radio frequency plugging is

t o setup a ponderonotive potent ia l by using s l igh t ly off-resonant ion

cyclotron waves in the plasma Cl02,l03]; ions would be repelled by the

effect ive potent ia l w a l l . Such a scheme might a l so be employed t o

preferent ia l ly pick out or confine par t icu lar types of ions fo r impurity

removal in diver tors fo r tokamaks or other devices.

Among the applications mentioned here, some re ly on the f a s t Alfven o r

magnetosonic branch (compressional wave), while others resor t t o the slow

branch (shear wave). The slow branch may a l so be called the Alfven - ion

cyclotron branch. The f i r s t group includes f a s t Alfven wave heating of

tokaiuak plasmas [92,94,95], isotope separation [W], and the radio

frequency plugging experiments a t Nagoya Cl021, t o name only a few

applications. In the second group, f o r example, a r e the heating of tandem

mirrors [99] and the plugging scheme u t i l i z i n g the enhanced magnetic

moment [l01].

Ion cyclotron waves --- - ------- ----- Theoretical considerations indicate t h a t [I], in moderately dense

plasmas, there can occur na tura l o sc i l l a t i ons a t frequencies s l i g h t l y lower

than the ion cyclotron frequency in a given magnetic f i e l d Cl041. These

osc i l l a t ions , cal led ion cyclotron waves, are the shor t wavelength, low

density limit of transverse hydromagnetic waves (a l so cal led

magnetosonic waves) [l05.l06]. I f an external f i e l d of the proper frequency

is applied t o the plasma, the individual ions move in c i r c l e s around the

l ines of force, j u s t as a t low dens i t ies . But the phases and amplitudes of

the ion ve loc i t ies now vary sinusoidally both i n space and time, because

the notions of the p l a s m p a r t i c l e s a r e coupled electromagnetically t o one

another. The resu l t ing osc i l l a t i ons ( or waves ) ths represent a

cooperative organized motion of the plasma as a whole.

The ion flow is divergent, as in the s ing le p a r t i c l e pic ture , and t h i s

would be expected t o produce a large space charge and accompanying r ad i a l

e l e c t r i c f i e l d s . However, since, a s a r e su l t of the wave motion, the ion

flow pattern in the ax ia l di rect ion is pericdic as shown in the f igure ,

the electrons a r e able t o flow along the l i nes of force and neutral ize the

space charge.

Thus, i f a t some ins tan t the ions a t a given point have an inward

motion, then a t a distance of half a Debye wavelength away they w i l l be

moving outward with the same amplitude. The ion density w i l l thus vary in

the ax ia l di rect ion and so e lectrons can flow along the l i nes of force from

a region where the ion density is low t o one where it is high. There is

experimental evidence, that the flow of t h i s neutral iz ing electron current

produces ohmic heating of t he plasma [IJ

A much more important heating mode is expected t o a r i s e from the

damping of the ion cyclotron waves , called ion cyclotron resonance

heating (ICRH) 11,U371; a more detai led discussion of it is given below.

However, the essence of the mechanism is as follows: When the waves may be

allowed t o propagate into a region of slowly decreasing magnetic f i e l d , the

decreasing f i e ld , w i l l cause the wavelength t o become shorter and shorter

and the frequency w i l l approach the local ion cyclotron frequency [3],

given by

fci = 15 B Z/A (MHz)

Any ions entering the plasma wave w i l l then be subjected t o an e l e c t r i c

f i e l d o sc i l l a t i ng a t the resonant frequency, and so they w i l l pick up

energy from the f i e l d . A s a r e su l t , the plasma wave amplitude w i l l damp

out; there is thus a decrease in the wave energy accompanied by an increase

in the pa r t i c l e energy. This energy is perpendicular t o the f i e l d l ines ,

but it soon becanes randm in direct ion, i . e . it is themalized. It is t o

be noted that the heating by cyclotron damping is not a d i r e c t process,

but involves the internediate action of the ion cyclotron waves.

clotron absorption mechanism !a! ------- -------:-- ------I-- We shall f i r s t consider the values of the following plasma parameters,

typical of moderate plasma performance in a machine l i ke SET Cl091, fo r a

g o d discussion based on the present scenario: The ion and electron

co l l i s ion frequencies are v = MHz, v i = 1PWkHz. The machine s i z e is e

characterised by % = 3x1, a = 1.5m (% is the major radius and a is P P

the minor or poloidal radius of the tokamak). In view of these numbers, a

few coments a re in order. F i r s t , the time fo r a cyclotron gyration is

extremely short: l0ps fo r an electron, 40ns fo r an ion. During t h i s s ing le

gyration, the electron t rave ls 0.- i n the toroidal direct ion and the ion

2cm. I t takes ips fo r an electron t o complete a toroidal turn around the

machine; 40ps fo r an ion. During t h i s turn, an electron has performed

Z3.W cyclotron gyrations, and ion 1PWG1. This means that gyromotion is an

extremely f a s t process w i t h respect t o t r a n s i t times across any macroscopic

area. Equivalently, the gyroradii of electrons ( 0 . 0 5 1 ~ ~ ) and of ions (3mm)

are small as compared t o plasma s i ze . The plasma is nearly non-collisional:

the electron mean f r ee path is 3km and t h a t for the ions 5km; or ,

respectively, 150 and 250 toroidal revolutions. The parameters of the RF

are: Frequency, f = 50MNz, Power is WW/antenna s t rap , Voltage is 20kV a t

the antenna, Antenna current, I lkA, typical RF e l e c t r i c f i e l d is ZkV/n A =

and typical B I magnetic induction is l0-%.

The above numbers show t h a t t he RF only causes a small perturbation of

the p a r t i c l e t ra jec tory . F i r s t , the RF magnetic f i e l d is much smaller than

the s t a t i c one: B = 10-% and B0 = 3. Second, the RF e l e c t r i c f i e l d =

20 kV/m is also much smaller than the dB f i e l d associated with the ion ' s

(and even more e lec t ron ' s ) thermal motion. Third, we s h a l l show below tha t

the perturbation of the pa ra l l e l motion is also small. L e t u s now m i t e t he

equation of motion of a p a r t i c l e in the RF f i e l d , decomposing the motion

in to an unperturbed (thermal) p a r t labelled 0 and a perturbed pa r t v-> v0 +

The unperturbed p a r t of t h i s equation

describes the unperturbed cyclotron motion. I t is convenient t o solve it

using complex variables t o describe the perpendicular motion, ug = vgx +

where wc = ZeB$m has the same s ign as the charge (Ze) of the p a r t i c l e

under consideration. Hence w e see t h a t cyclotron motion of ions is

left-handed and tha t of electrons right-handed.

(1) - (2) leaves us with the perturbed pa r t of the equation of motion.

dv m - - = Z e ( E t v A B + v A B O + v A B ) d t 0 (4)

In the r . h . s . parenthesis the last term is c lear ly negl ible with respect t o

the 3rd one. Dropping it w e a r e l e f t with an equation which is l i n e a r i n

the perturbed q u a n t i t i e s . Now comparing the order of magnitude of the f i r s t

t h r e e terms, we see t h a t f o r e l e c t r o n s , t h e second term w i l l be dominant

term. However f o r ions it is neg l ig ib le with respect t o the two o the r

terms. Note t h a t w e have a l s o proved the asse r t ion t h a t the per turbat ion

due t o the RF in t h e p a r a l l e l d i r e c t i o n is a l s o small . Let u s r ewr i t e t h e

f i n a l equations of the perturbed motion:

Although these equations look l i n e a r , they a r e no t . Indeed, t h e e l e c t r i c

f i e l d depends (in genera l ) non-linearly on the p a r t i c l e pos i t ion r through

We split again t h e motion i n t o a thermal and a perturbed p a r t r-->rO + r

and def ine t h e cowlex perpendicular pos i t ion p = px + ip The problem now Y '

becones f u l l y l i n e a r i f in E( r ) , we replace r by rO, i .e. i f we evaluate

the RF f i e l d at the unperturbed p a r t i c l e pos i t ion:

z O ( t ) = zg(0) + vgZ(0)t ( 7 . b )

Evaluating E(rO) w i l l c l e a r l y b r ing t h e harmonics of the cyclotron motion

i n t o the equations. This surprising result follows from the f a c t t h e

cyclotron motion is the zeroth order motion and t h a t t h e f u l l

non-linearit ies in the zeroth order motion have been retained. The problem

is linearized in the RF perturbations.

The next s t ep towards a solution of the equations of motion (5)

consis ts of expanding the RF f i e l d in Taylor s e r i e s around the guiding

centre motion of the pa r t i c l e s . In ( 7 . a ) the terms in the

bracket on the r . h . s . is the perpendicular component of the p a r t i c l e ' s

guiding centre rG ( the pa ra l l e l component is in Eq.(7.b)). In t h i s

approximation where we consider the unperturbed magnetic f i e l d as uniform,

it is a constant. The second term in Eq.(7.a) decribes the cyclotron

gyration around the guiding centre. The excursion away from the guiding

centre is by one Larmor radius rL = %(@)/ac. We have seen that t h i s is a

f a i r l y small quantity. Thus l e t us perform the Taylor s e r i e s expansion:

where the der ivat ives of E a re evaluated a t the guiding centre posit ion. We

s h a l l recast the double sunmration over n and m as a summation over n'=m-n

in order t o have an expansion i n cyclotron harmonics. In doing so, it is

important t o note t h a t the n ' term of the series which

involves derivatives of the e l e c t r i c f i e l d E (m'n), of order a t l ea s t 1 n ' 1 , is very important for the understanding of the cyclotron harmonic resonance

process as w i l l be made clear in the following. We thus rewrite Es.(8) as

..

where E (" ') represents a f u l l s e r i e s containing higher derivatives of E and

powers of rL. In the par t icular , but widely used, case where E or exp(ik,x),

t h e E("*) coeff ic ients come in the form of Bessel functions; fo r e-le

taking x = -r sin(wct): L OL -ioct

em(ik,x) or exp -i(k,rL) Sin(Wct) (m)

Equation (5) being l inear , w e can study separately the perturbation

induced by each of the terms in Eq.(9). The simplest case is t h a t of

para l le l motion in Eq.(S.b) which ue eas i ly solve f o r the n-th harmonic

contribution and assum& E u exp(iklz) where z is given by &.(7.b): a

i(k,,vBz- w - nwc)t

(11) n=-a

Note that fo r an ion from the bulk of the Maxvellian, kgvgZ is much

smaller than oc. The resonances a r e obtained when the denominator in

Eq.(ll) vanishes. i . e .

* Landau damping: o/kn = VBZ

* Fundamental cyclotron resonance: o = oc

* Second harmonic cyclotron heating: w = 2uc

* e t c . . .

It is t o be noted that uhi le the Landau resonance can take place inside a

uniform e l e c t r i c f i e l d (in the perpendicular direct ion) , the fundamental

resonance requires a gradient of the f i e l d (n= l ) and the second harmonic

requires a parabolic var ia t ion (n=2). For ions, the Landau resonance takes

place a t frequencies much lower than uci SO that electron Landau damping is

a relevant mechanism in the ICRF. Aside from t h i s , the discussion of the

resonance problem fo r pa ra l l e l e l e c t r i c f i e l d s is not very relevant t o

ICRF, because t h i s f i e l d component is usually qui te s m a l l a t these low

frequencies. On the other hand, these mechanisms play an important ro le in

the electron cyclotron frequency range where they are responsible for

cyclotron damping of ordinary mode. We s h a l l now focus on the more

complicated case of perpendicular e l e c t r i c f i e l d s .

Let rewrite Eq.(5.1) in complex form with u = vx + i v : Y

and assume t h a t t he f i e l d is composed of r ight- (+) and l e f t - - hand

polarised components: cos( ku z-ot) cos( kp z-at )

1 + E-[ s in(k, ,z-at )

so t ha t - i (k l lz -a t ) i (kl l z-ot)

E + iE = E+e X

+ E e Y -

I t is easy t o obtain the solution of F,q.(12):

-i[?(o-kllvz)+(n+l)wc]t d t

I f the argument of the exponential under the integral vanishes,

z~E?) - i w t

u = [ + ---=- t C m (16)

indicating tha t the perpendicular p a r t i c l e velocity w i l l grow l inear ly with

time. Looking i n the Fourier domain, we ge t the corresponding resonant

denominators in the expression f o r the veloci ty:

The main difference with formula (11) is t h a t one f inds in the denominator

(n + l ) oc instead of noc resul t ing from the f r ee perpendicular motion. The

resonance condition depends on whether the excit ing f i e l d is r igh t or le f t

handed. In t h i s review on ICWI we need t o consider only the l e f t handed

component of the f i e l d , where the wave has the same handedness as the ions.

Hence we expect t o find the normal cyclotron resonances here. The resonance

condition is:

( ~ - k , , v ~ , ) - (n+l)wc = 0 (18)

and the d i f f e r en t cases are as follows:

* There is no equivalent t o Landau damping in the perpendicular direct ion

in tha t , fo r a uniform f i e l d n=0 and a p a r t i c l e moving in phase with the

wave u/kll = v,, the denominator of Eq.(17) does not vanish. This is

understandable as a p a r t i c l e ro ta t ing i n a uniform s t a t i c f i e l d w i l l

experience a periodic force in its ro ta t ing frame of reference.

* For w = kllvZ and n = -1 there is a resonance leading t o uniform increase

of the ion 's perpendicular energy i f there is a gradient of the e l e c t r i c

f i e l d . A s t h i s resonance corresponds t o a frequency much below the ion

cyclotron frequency, the guiding-centre theory is applicable and the

2 magnetic moment oc v, / % must be invar iant . This can only be ensured i f

the pa r t i c l e moves i n the pa ra l l e l d i rect ion in the non-uniform wave's

magnetic f i e l d . A s 4 3 % klEL, t h i s requires the existence of an e l e c t r i c

f i e ld gradient, in agreement with the above conclusions. Thus perpendicular

heating w i l l be accompanied by a pa ra l l e l acceleration tha t can be recast

i n the form:

where one recognizes on the r . h . s . the v-grad B force, with P being the

magnetic moment. This process is the so-called Transit Time Magnetic

m i n g ('lVlP). Note that t h i s is a low frequency resonance process f o r

ions and hence not relevant t o ICRF ; however, it can be effect ive for

electron heating a t frequencies around the ion cyclotron frequency. As it

pushes electrons in the pa ra l l e l d i rect ion, t h i s process is the bas i s

(together with electron Landau damping discussed above) of f a s t wave

current dr ive and hence is of prime importance.

* In a uniform e l e c t r i c f i e l d (n = 0) there can be a resonance i f

w = w C + kuvz r w . This is the fundamental cyclotron resonance. Because

C

the Doppler s h i f t kl,vz is siuall, t h i s requires t ha t the operating frequency

be ra ther close t o the cyclotron frequency.

* The second harmonic case corresponds t o w = 2wc + kl,vz. A s n = 1 it

requires a gradient of the e l e c t r i c f i e l d .

* Higher order harmonics corresponds t o w = (n + l)wc + kllvz and require

derivatives of the e l e c t r i c f i e l d of order a t l e a s t n .

The two-ion hybrid resonance and minority heating: --- --- --- - ---- --------- --- -------- ------ Although absorption in a s ing le species plasma can take place

effect ively a t the second harmonic, it is common in prac t ice f o r there t o

be more than one species present, even i f one of them is an impurity which

is only present in a small concentration, for example hydrogen in a

deuterium plasma [l08]. The presence of more than one species allows an

a l te rna t ive heating scheme which is exploited in many of the experiments

which have taken t o da te . With two ion species a cold plasma resonance

appears a t a frequency between the two ion cyclotron frequencies [l09], and

absorption depends on the existence of t h i s resonance combined with the

e f f ec t s of cyclotron damping. In the present scenario, complications

introduced by thermal e f f ec t s a r e t o be added t o the cold plasma resonance

( the thermal corrections introduce higher order terms in to the dispersion

re la t ion) . I f neither of the ion species has a concentration very much

smaller than the other, then the hybrid resonance is not close t o e i ther of

the cyclotron frequencies and cyclotron damping is weak. Under these

circumstances most of the energy which is not transmitted in the f a s t wave

is n d e converted t o the Bernstein node, from which it nay be absorbed by

Landau damping.

Many experiments have been carr ied out in the minority heating regime,

where one of the species is present in a small concentration [l081. The

r e s u l t s show t h a t there is a strong interaction between the f a s t wave and

the minority species, resul t ing in damping of the wave a d heating of the

minority species. Work on t h i s problem by S t ix in 1975 C921, ignored

mode conversion. But it was l a t e r pointed out t ha t mde conversion t o a

Bernstein mde was again possible and t h a t the absorption involves a

combination of mode conversion and damping CI081.

Calculations in tokamak geometry and antenna coupling: ------------ -- ------- ------ --- ------- --- --- Although the basic physics can be elucidated using the simple s l ab

geometry, detai led calculations aimed a t predicting the behaviour of

par t icu la r machines have t o take account of t he to ro ida l geometry of the

plasma. In addition a r e a l i s t i c calculation needs a detai led consideration

of the geometry of the antenna and how it couples t o the plasma. The s i z e

and shape of the antenna is fundamental in determining the spectrum of

para l l e l wavenumbers which it generates, and t h i s in turn is an inportant

factor in the subsequent propagation of the uave.

Calculation of wave propagation and absorption in a toroidal plasma

presents qui te a formidable problem which has been tackled in various ways

l ike ray-tracing technique 1 f i n i t e difference or f i n i t e element

methods [111,112]. Recently a very general computer code containing most of

the relevant physics has been dweloped by Brambilla and Krucken [113].

The other features which must be considered in a r e a l i s t i c calculation

are the boundary conditions a t the walls and the behaviour of the f i e l d s a t

the antennae which produce the waves. I t is generally a reasonable

approximation in a tokamak t o take the walls t o be perfect ly conducting, so

t h a t the appropriate boundary condition is the vanishing of the tangential

component of the e l e c t r i c f i e l d at the wall. An antenna f o r ion cyclotron

heating generally consis ts of a metal s t ruc ture contained within a Faraday

shield, consisting of narrow conducting s t r i p s . These s t r i p s a re aligned

along the magnetic f i e l d direct ion and are intended t o short out the

e l e c t r i c f i e l d component in t h i s direct ion and ensure t h a t the wave is

launched with the polarisation of the f a s t wave. Any energy launched with

the other polarisation is trapped near the plasma edge, and nay contribute

t o undesirable e f f ec t s such as heating the walls and antenna support

s t ructures and providing heavy metal i r p u r i t i e s .

The simplest treatment of the antenna is simply t o t r e a t it as a

current sheet with a given d is t r ibu t ion of current. A variat ional method

fo r the analys of antenna-plasma coupling has been developed by Theilhaber

and Jacquinot in 19&4 C1141.

For the calculations of wave propagation and absorption in a high power

heating system, the pa r t i c l e d i s t r ibu t ion function may be mdi f i ed from a

Maxwellian one. I f absorption takes place on f a s t ions and accelerates them

t o produce a tail on the d is t r ibu t ion function, there may be inportant

consequences in the reactor regime. Such a t a i l can enhance the reaction

r a t e above w h a t would be obtained from a thermal equilibrium dis t r ibu t ion

with the same energy content. An analysis of the evolution of the

d is t r ibu t ion functions under the influence of ion cyclotron heating

requires a Fokker-Planck ca lmla t ion in which the combined e f f ec t of the

col l is ion term and the wave diffusion term is taken in to account. A more

recent study which continues t h i s type of work, is t h a t of Anderson e t -- a1 --

in 1987 C1151. Their r e su l t is jus t saying tha t the average ex t ra energy of

a pa r t i c l e in the high energy t a i l of the d is t r ibu t ion function is of the

order of the r a t e at which it receives energy from the wave multiplied by

its col l is ion time, an in tu i t ive ly plausible r e su l t .

An example of a numerical study of the Fokker-Planck equation applied

t o ion cyclotron heating as given by Morishita e t -- a1 -- i n 1987 [116], shows

general agreement with the numerical model described in [115]. An

interest ing feature of these calculations is tha t the right-hand c i rcu lar ly

polarized component of the wave is found t o contribute s ign i f icant ly t o the

heating. We have seen e a r l i e r that the dominant wave component fo r ion

cyclotron heating is left-hand c i rcu lar ly polarized and tha t the e f fec t of

the right-hand c i rcu lar ly polarized component is smaller, since it is

multiplied by a power of the r a t i o of the ion Larmour radius t o the

wavelength. However, fo r pa r t i c l e s on the t a i l , the f i n i t e Larmour radius

corrections involving the right-hand component may be large enough t o make

a s ignif icant difference t o the power absorption C1151.

With increasing computational power becoming available we may expect t o

see ever more sophisticated and r e a l i s t i c calculations of the behaviour of

a tokamak heated with waves in the ion cyclotron range of frequencies. This

may be accompanied by fur ther development of simpler approximate methods

which, i f they can be shown t o give r e s u l t s comparable t o those obtained

with more elaborate calculations, o f fe r a considerable saving in

computational resources.

%~r%en_t_s on i o n cyclotron he_a_t-%: ICRF heating has been used on a considerable number of tokamaks, in

both the second harmonic and minority heating regimes. Another poss ib i l i ty ,

i n the same frequency range, is heating by means of ion Bernstein waves

excited by an antenna at the plasma edge. Ion cyclotron heating is probably

the most advanced and thoroughly investigated of a l l the schemes, and is

cer ta inly the one for which the highest power t o da te has been used with up

t o 16 MW in JET [l!Z8].

The technology required is well developed, with sources being

available with output powers of several megawatts in the necessary

frequency range. The connection between the generating sources and the

antenna is generally by means of coaxial transmission l ines , again a

reasonably straightforward and well developed technology.

A list of experiments carried out up t o 1986 together with the i r most

important parameters is given by Steinmetz in 1987 [117]. The various

methods t h a t have been studied from a theoret ical point of view, namely

second harnonic heating, node conversion in a two-species plasma

and minority heating, have a l l been used, and fo r a l l of them energy is

found t o be absorbed, basical ly as predicted by theory, and t o produce an

increase in plasma temperature. High power minority heating is found t o

produce high electron temperatures [118], an e f fec t a t t r ibuted t o the f a c t

t h a t the high energy minority ions lose energy t o the electrons much more

rapidly than t o the majority ion species. This occurs because of the way

in which the cross-section fo r Coulomb col l i s ions f a l l s off with the

re la t ive velocity of the pa r t i c l e s . The minority ions a re accelerated t o

ve loc i t ies well in excess of the majority ion thermal velocity, so t h a t

col l is ions with the majority ions a re not very e f fec t ive in slowing down

the minority ions. Gn the other hand, the minority ion veloci ty is still

well below the electron thermal velocity, so the ion-electron co l l i s ion

frequency is not reduced.

Early experiments on heating in the ion cyclotron range of frequencies

were limited in effectiveness by an influx of heavy metal impurities from

the region of the antenna, possibly related t o the acceleration of ions in

the high radiofrequency f i e l d s close t o the antenna and the increased

sputtering produced by the interaction of these ions with the wall [119].

Such heavy metal impurities cause a d r a s t i c increase in plasna radiation

losses and nay even lead t o disruption of the plasma discharge. However

such e f f ec t s have been mitigated in recent experiments by the use of more

sui table materials for the antenna and the shielding of adiacent surfaces

with carbon o r boron wherever possible. Impurity influx does remain an area

of concern nevertheless; however; fur ther s tudies on the interact ions

between the plasma, the antenna and the wall a re being carried out in order

t o understand, in more d e t a i l , the conditions under which the m u r i t y

influx does not cause severe problems. The recent experiments in JJiT with

beryllium-coated walls have achieved a very low impurity level [1Q81.

Early experiments with ICW heating p lus NBI heating were performed

in PLT [120]. The ICRF heating was in the hydrogen minority regime

(fundamental resonance), and hydrogen or deuterium beams were employed.

Combined hydrogen NBI heating and second-harmonic ICRF heating w a s

investigated in JFT-2M [I211 and in ASDEI C1221. Enhancement of the beam

induced high energy t a i l was not observed in these experiments. Beam

acceleration by second harmonic ICW heating was observed in JFT C1231.

However, the RF power absorbed by the bean ions (deuterons) was small and

no synergetic e f fec t was observed because the minority proton heating

regime was employed.

Recently, in JT-60 tokamak, an experiment with combined hydrogen NBI

heating and pure Mrogen second-harmonic ICRF heating was performed. In

t h i s experiment, s ignif icant beam acceleration w a s observed, and t h i s

acceleration was studied systematically. Under optimized conditions

regard- beam acceleration, a strong synergetic e f f ec t was observed during

combined heating, namely an incremental energy confinement time tha t was

t h ree times higher than t h a t in t h e case of NBI heat ing alone o r ICRF

heat ing alone [124,125]. Although t h e ICRF power was small compared with

t h e NBI power in that experiment, t h e dens i ty of t h e high energy ions

reached up t o 40?l!a% of that of t h e t o t a l ions when ICRF heat ing w a s

applied. Thus, a s i g n i f i c a n t enhancement of t h e s to red energy wi th beam

accelera t ion w a s observed. The confinement of high energy ions was found t o

be much b e t t e r than t h a t of t h e bulk p lasna . Hence wi th regard t o plasma

confinement, the results of t h i s experiment suggested t h a t it is important

t o i n j e c t more ICRF power and t o i n v e s t i g a t e t h e behaviour of t h e high

energy ions which dominate t h e t o t a l ion populat ion.

In a review of r ecen t advances in heating and c u r r e n t d r i v e on TMTOR

tokmak by A.M.Messiaen et -- a1 -- [126], a d e t a i l e d a n a l y s i s of t h e synerge t i c

e f f e c t s of combined co-inject ion NBI and ICRH with respect t o heat ing and

confinement, and t h e generat ion of non-inductively dr iven cur ren t s were

presented. ICRH has been added t o n e u t r a l beam i n j e c t i o n (D'->D+) in a D(H)

plasma f o r two s c e n a r i i : RF heating ( a ) at w = w = 2wcD f o r which t h e cH

wave damping by H minority is preponderant, and ( b ) at w = 30 where t h e cD

wave damping by t h e ion beam is one of t h e dominant e f f e c t s .

( a ) A t w = w = 2 w cH cD' it has been shown that t h e r e is a synerge t i c e f f e c t

on confinement and heat ing when ICRH is added t o co-inject ion leading t o a

l a rge r incremental confinement time f o r ICRH and p a r t i c u l a r l y t o t h r e e

tines la rge r heat ing ef f ic iency of t h e ions . I t r e s u l t s t h a t t h e hot ion

mode together with t h e inproved confinement regime remains in presence of

combined heat ing. When ICRH is added t o balanced i n j e c t i o n a larger heat ing

efficiency for the ions is a lso observed but the ICRH energy incremental

confinement time is lower. With one co-injection of 1.8 MW it has been

possible t o dr ive half the plasma current non-ohmically f o r s ta t ionary

conditions (>2s) and fo r any value of the t o t a l plasna current. This value

is fur ther increased (up t o 70%) by the addition of ICRH.

The synergetic e f fec t can be explained in the following tray: ( 1 ) For a

large par t it is due t o electron heating of the ta rge t plasma resul t ing

from the application of ICRH which leads t o an increase of the beam slowing

down time and a r i s e of its c r i t i c a l energy. The electron temperature

increase is mainly due t o minority heating causing an energetic minority

t a i l t o be formed. This produces an increase of beam driven current and of

the beam power fract ion coupled t o the ions. This last ef fec t explains the

apparent increase of the ion heatizg eff ic iency due t o ICRH which mainly

heats the electrons and compensates the decrease of beam power coupled t o

the electrons. (2) It a l so r e su l t s from the d i r e c t RF power coupling t o the

beam. Theoretically it is shown t h a t a non-negligible par t of the RF power

can be absorbed by the bean and t h a t t h i s leads t o a deformation of the

beam dis t r ibu t ion function which mostly increases its contribution towards

larger vl. This explains the fur ther reduction in beam co l l i s iona l i t y and

shows t h a t the beam contributes t o the development of a highly energetic

perpendicular tail. (3) Finally, the synergetic e f fec t is due t o the

decrease of the plasma toroidal rotat ion resul t ing from the addition of RF

which increases the veloci ty of the beam re l a t ive t o the plasma. This

e f fec t leads t o a larger effect ive r a t i o vb/vc and neutron reac t iv i ty .

(b ) A t = 30 no H minority dm@& is present and there is more d i r e c t cD'

interaction of the wave with the beam. A highly energetic tail is produced

which strongly enhances the beam ta rge t neutron yield proportionally t o t he

t o t a l NBI+RF power. A s compared with the w = 20 case, t h i s enhancement is CD

much larger although the bulk energy and temperature increases a r e lower.

This smaller heating efficiency is at t r ibuted t o the lower plasma

absorptivity and the loss of confinement of very energetic par t ic les .

Presence of NBI heating a t suf f ic ien t ly large power level is mandatory t o

have suf f ic ien t ly large absorptivity and even t o avoid disruption caused by

the RF.

Conclusion ---------- In t h i s chapter we have presented a br ief review of the various

mechanisms fo r supplementam heating in magnetically confined fusion

plasma, with par t icu lar a t tent ion t o Ion Cyclotron Resonance Heating

(ICRH). A brief report on the present s t a t u s of experimental scenario has also been presented.

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Fusion 35 A15-A34