Comparison of H-mode plasma simulations using toroidal...

Original Article

Comparison of H-mode plasma simulations using toroidal velocity modelsdepending on plasma current density and ion temperature in presence of an ITB

Boonyarit Chatthong* and Thawatchai Onjun

School of Manufacturing Systems and Mechanical Engineering,Sirindhorn International Institute of Technology, Thammasat University, Khlong Luang, Pathum Thani, 12121 Thailand.

Received 14 June 2013; Accepted 19 February 2014

Abstract

Two different approaches for predicting plasma toroidal velocity ( v ) are developed and used in self-consistentsimulations of H-mode plasmas with the presence of ITB using BALDUR integrated predictive modelling code. In the firstapproach, the toroidal velocity depends on the plasma current density; while in the second approach the toroidal velocity isdirectly proportional to the ion temperature. The profile of v is used to calculate the ExB flow shear which is a main mechan-ism for plasma transport suppression, leading to the ITB formation. In all simulations, the core transport model is a combina-tion of NCLASS neoclassical transport and semi-empirical Mixed Bohm/gyro-Bohm model that includes the ITB effects.The boundary condition is set at top of the pedestal and is estimated using a pedestal model based on a combination ofmagnetic and flow shear stabilization pedestal width scaling and an infinite-n ballooning pressure gradient. Two toroidalvelocity models are used to simulate the time evolution of plasma temperature and density profiles of 10 JET discharges.The root mean square error (RMSE) is used to compare simulation results of those 10 JET discharges with experimental data.It is found that RMSE of Ti, Te, ne are 28.1%, 31.8%, and 15.0% for the first toroidal velocity model and 25.5%, 30.2%, and15.1% for the second toroidal velocity model, respectively. Furthermore, this suite of codes is used to predict the ITERperformance under standard type I ELMy H-mode. It is found that the simulation yields formation of a narrow ITB near r/a =0.7 in the simulation using the current density dependent model and a wide ITB from r/a = 0.5 to 0.8 in the simulation usingthe ion temperature dependent model. The average of central ion temperature, total fusion power output and alpha powerare predicted to be 36 keV, 159 MW and 492 MW for the current density dependent model and 49 keV, 218 MW and 786 MWfor the ion temperature dependent model, respectively.

Keywords: ITB, H-mode, toroidal velocity, BALDUR, JET, ITER

Songklanakarin J. Sci. Technol.36 (3), 375-387, May - Jun. 2014

1. Introduction

Currently, Magnetic Confinement Fusion (MFC) basedon tokamak concept is the most advanced experimentalmachine in term of nuclear fusion energy production and isin the process to extend for nuclear fusion reactor. Productionof significant fusion reactions inside a tokamak requires high

plasma temperature and density, as well as a sufficient energyconfinement time. One of the milestones in fusion researchwas marked by the discovery of high confinement mode (H-mode), which results from the formation of an Edge TransportBarrier (ETB) (Wagner et al., 1982). Since the high confine-ment mode (H-mode) plasmas in tokamaks generally providehigh temperature and excellent energy confinement time,burning fusion experiment such as ITER is designed tooperate in the H-mode regime. It is widely accepted thatthe performance of an H-mode discharge can be furtherimproved with the formation of a transport barrier inside theplasma, called an Internal Transport Barrier (ITB) (Connor

* Corresponding author.Email address: [email protected]

http://www.sjst.psu.ac.th

B. Chatthong & T. Onjun / Songklanakarin J. Sci. Technol. 36 (3), 375-387, 2014376

et al., 2004). The presence of both ETB and ITB in the plasmacauses major improvement in core temperature, pressure,confinement time, and hence, fusion power production.

Simulation is one of the tools that can be used tostudy and learn about the plasma behavior. Due to the reli-ability and the speed of today’s computer, the simulationcodes can be integrated and complicated enough for theresults to be trustworthy. A number of studies have beendone on both simulating the existing tokamaks and predict-ing the future machine, like ITER (Bateman et al., 2003;Budny et al., 2008; Chatthong et al., 2010; Chatthong et al.,2011; Halpern et al., 2008; Onjun et al., 2005; Pianroj et al.,2012; Roach et al., 2008). There are various integrated pre-dictive modeling codes such as CRONOS (Artaud et al.,2010), JETTO (Cenacchi et al., 1988), ASTRA (Pereverzevet al., 2002), and BALDUR (Singer et al., 1988), aiming toself-consistently predict plasma performance. They are runwith a variety of transport models like MMM95 (Hannum etal., 2001), GLF23 (Kinsey et al., 2002), and Mixed B/gB (Talaet al., 2002). Those works yielded a different range of resultsbecause, partly, different assumptions were used, such asinitial conditions of heating power and plasma density,impurity condition, or even different transport models.In addition, many simulations are carried out to study ITERplasma. In Onjun et al. (2009), ITER with combined effects ofboth ITB and ETB was simulated to predict the performanceof ITB H-mode plasma. Also the behaviors of impurity inITER were studied and analyzed (Pianroj et al., 2010) and theimpact of pellet injection on ITB in ITER H-mode plasma(Leekhaphan et al., 2011) and on ITER plasma without ITB(Klaywitthaphat et al., 2012; Wisitsorasak et al., 2011) werestudied via simulation method as well. Recently, the effect ofsymmetry breaking via the application of non-axisymmetricfield leading to an offset NTV toroidal rotation has beeninvestigated in ITB ITER-like plasma using BALDUR code(Chatthong et al., 2013).

There are several mechanisms involved in the forma-tion of ITB. It is widely accepted that an ExB flow shear playsa significant role in this phenomenon. According to (Burrell1997), ExB induces de-correlation of turbulent convectivecells resulting in less transport of plasma heat and particlesfrom its core. Thus, in the region with strong flow shear thetransport is reduced to neoclassical level and the barrier isformed which is shown as plasmas having relatively highgradient temperature or density. Even though anothermechanism like zonal flow (Diamond et al., 2005) can alsointrinsically generate the electric field shear, its role isomitted in this work. In the future work, it is interesting toincorporate the contribution of shear effects both from thezonal flow and the flow shear. It is found that the reductionof transport is associated with shear effects, especially thevelocity shear and magnetic shear (Burrell, 1997). Theoreti-cally, the calculation of ExB is derived from the forcebalanced equation which requires information such as iondensity, pressure gradient, poloidal velocity (v) and toroidalvelocity ( v ). There have been studies of momentum and

velocity transport in poloidal direction (Eriksson et al., 2007,Rogister et al., 2002; Rozhansky et al., 2002; Tala et al., 2007)but not much has been done on toroidal direction. Therehave been some theoretical works on toroidal velocity pre-diction like those in Callen et al. (2009), and Stacey (2004),but for simplicity, simple models are used in this work. Anempirical model based on local ion temperature for predictingtoroidal rotation was proposed (Chatthong et al., 2010),it was then used to simulate ITER performance (Chatthonget al., 2011). There is a doubt in the empirical model mainlybecause it was developed solely based on JET experimentaldata so its general validity especially its projection to thebigger machine like ITER is uncertain. In this paper, a newcurrent density dependent toroidal velocity calculation isproposed and derived based on electromagnetism theory ofcharge flow, which could potentially remove the projectionvalidity problem.

In this work, plasma spatiotemporal profiles includingplasma current, ion and electron temperatures and densitiesare simulated self-consistently using BALDUR integratedpredictive modeling code. The impact of ETB on plasma isexpressed in terms of a pedestal model (Onjun et al., 2002).This region is a raising pedestal at the edge of plasma andthe gradient is assumed to be constant. The pedestal tem-perature is explained using the theory based pedestal widthmodel combined with pressure gradient limits by ballooningmode instability. The pedestal width model is based onmagnetic and flow shear stabilization ( 2

i s ) (Sugiharaet al., 2000). The model is found to be in agreement withexperimental data within around 30% RMSE (Onjun et al.,2002). The model for ITB used in this paper is based onliterature review of ITB (both theoretical work and experi-mental work). It is called semi-empirical Mixed Bohm/gyroBohm (Mixed B/gB) core transport model whichproposes that formation of ITB is caused by the suppressionin anomalous transport due to ExB flow shear and magneticshear (Tala et al., 2001). This model is successfully found tobe in agreement with data from various JET experiments(Parail et al., 1999; Parail, 2002; Tala et al., 2005; Tala et al.,2006; Tala et al., 2001; Tala et al., 2002). In BALDUR, datafor ExB is given to the code. Moreover, ExB can be calculatedfrom toroidal velocity through the force balance equation.In order to predict the future machine like ITER, it isimportant to develop a model estimating toroidal velocity.In addition, to be fully self-consistent, it is essential forBALDUR to be able to calculate, hence, ExB from fundamen-tal physics quantities such as geometrical data of eachtokamak, density, current, magnetic field, temperature, etc.This paper focuses on the development of a current densitydependentmodel for use in simulations of JET and predictionof ITER with combination of ITB and ETB. Theprofiles arealso compared with those predicted by the ion temperaturedependent model.

The paper is organized as follows: an introduction tosimulation methods including the models used is discussedin section 2; the toroidal velocity models are presented in

377B. Chatthong & T. Onjun / Songklanakarin J. Sci. Technol. 36 (3), 375-387, 2014

section 3; results of simulations and discussion are describedin section 4; and a summary is given in section 5.

2. Simulation Methods

2.1 BALDUR

BALDUR integrated predictive modeling code (Singeret al., 1988) is a time-dependent transport modeling codewhich is used to compute many physical quantities intokamaks. The code itself simultaneously solves three diffu-sion equations of number density, energy density and poloidalmagnetic field. It can be used to compute the profiles ofplasma densities and temperatures as well as q profile.BALDUR code self-consistently computes plasma profiles bycombining many physical processes together in the form ofmodular structures, for example, heat and particle transport,plasma heating, particle flux, boundary conditions, andsawtooth oscillations. It was found that results fromBALDUR are in decent agreements with experimental data.For example, BALDUR simulations yielded an agreement ofabout 10% relative root mean square deviation (RMSD) fortemperature and density profiles of H-mode JET and DIII-Dplasmas (Hannum et al., 2001).

2.2 Mixed B/gB model

Mixed B/gB is a semi-empirical anomalous transportmodel. It consists of a combination of Bohm and gyro-Bohmscaling. The Bohm model was first derived for electrontransport for the JET tokamak (Taroni et al., 1994). Then,it was modified to additionally describe ion transport (Erbaet al., 1995) with a Gyro-Bohm term. Usually, the Bohm termdominates over most of the plasma. The gyro-Bohm termcontributes mainly in the deep core of the plasma and insmall tokamaks with low heating power and low magneticfield. The Mixed B/gB model includes ITB effect by havinga cut-off in Bohm term which is a step function of flow shearand magnetic shear. The model can be expressed as of thefollowing (Tala et al., 2002)

e gB B1.0 2.0 , (1)

i gB B0.5 4.0 , (2)

e iH Z

e i

0.3 0.7D D

, (3)

with

6 egB e 2

T5 10 TB

, (4)

0

E BB B

ITG

1.47ωχ χ Θ 0.14 sγ

, (5)

0

e max max-5 2B

e max

T 0.8χ 4x10

Te e e

e

n T TR q

n B

,

(6)

where e (m2/s) is the electron diffusivity, i (m

2/s) is the iondiffusivity, gB (m2/s) is the gyro-Bohm contribution, B (m2/s)is the Bohm contribution, DH (m2/s) is the particle diffusivity,DZ (m

2/s) is the impurity diffusivity, is normalized minorradius, Te (keV) is the local electron temperature, B (T) is thetoroidal magnetic field, s is the magnetic shear, ExB (s-1) isthe shearing rate, ITG (s-1) is the linear growth rate, R (m) isthe major radius, and ne (m

-3) is the local electron density.The linear growth rate ITG is calculated from vth/qR, wherevth (m/s) is the electron thermal velocity.

The ExB shearing rate can be calculated according toHahm-Burrell model (Zhu et al., 2000),

2 /rExB

RB E RBB

, (7)

where B is the poloidal magnetic field, is the poloidalflux, and Er is the radial electric field, which can be calculatedfrom the force balance equation as follows:

1 ir

i

pE v B v BZen r

(8)

where ipr

is the pressure gradient, ni is the ion density, Z is

the ion charge number, e is the elementary charge, and vand v are the poloidal and toroidal velocities, respectively..Note that the poloidal velocity is estimated using NCLASS(Houlberg et al., 1997).

2.3 Pedestal model

For BALDUR calculation, the boundary conditionsare set at the top of the pedestal, which is where the edgetransport barrier (ETB) is observed. The pedestal region islocated at the steep gradient right near the edge of theplasma. It is assumed that the pressure gradient ( /p r )within this region is constant so the pedestal temperature(Tped) can be calculated as follows (Onjun et al., 2002):

12ped

ped

pTkn r

(9)

where nped (m-3) is pedestal density, k is the Boltzmann’s

constant, and is the pedestal width. So in order to calculatepedestal temperature one must obtain pedestal density,pedestal width and pedestal gradient. The pedestal density,nped, is obtained by an empirical model which is based on thefact that nped is a fraction of line average density, nl, that canbe taken from experimental data, as shown:


0.71ped ln n . (10)This empirical pedestal density model agrees with the

data from the International Tokamak Physics Activity (ITPA)pedestal database with 12% RMSE (Bateman et al., 2003).

The pedestal pressure gradient scaling is limited bythe ballooning mode instability (Connor 1998). It is based onthe assumption that there exists a maximum normalizedpressure gradient with critical pressure gradient, c

2

02

2, ,cc

Rq psB r

. (11)

Here, is triangularity, is elongation, 0 is perme-ability of free space, R is the tokamak major radius, q issafety factor, and B is vacuum toroidal magnetic field. Thetriangularity and elongation are the plasma parameters thatdefine its cross section shape; detailed definition of thesevariables can be seen in Wesson et al. (2004). Note that thiscritical pressure gradient may implicitly depend on themagnetic shear, the triangularity and the elongation becausethese parameters can affect the safety factor and pressuregradient in the pedestal region. Rewriting this relation andsubstituting pressure gradient into equation (10) gives

2

202 2c

pedped

BT

kn Rq

(12)

The pedestal width scaling model is based on mag-netic and flow shear stabilization ( 2

i s ) (Sugihara et al.,2000). There is an assumption that the transport barrier isformed in the region where the turbulence growth rate isbalanced by a stabilizing ErxB shearing rate. The scalingwidth is derived to be

2 3 21 1 4.57 10 H ped

T

A TC s C x s

B

, (13)

where C1 is the constant of proportionality and AH is theaverage hydrogenic mass. After combining this scaling withthe previous pressure gradient scaling, the scaling of Tped isas follows

2 2232 4

1 4 2160

4.57 104 1.6022 10

cHped

ped

B AxT C sq R nx

.

(14)

This result is used in BALDUR code to calculate thepedestal temperature, which is the boundary condition ofthe transport model, and to eventually compute plasmaprofiles. The constant C1 was chosen to minimize the RMSDwith 533 experimental data points from four large tokamaksobtained from ITPA pedestal database. The constant wasfound to be 2.42 (Onjun et al., 2002).

3. Models for Predicting Toroidal Velocity

3.1 Current density dependent approach

This model is based on the current density flow ofcharge, in which, for simplicity, it is assumed to be in term ofdrift velocity of plasma flow.

,i e eff

Jv

en Z

, (15)

where J represents the current density flow in toroidaldirection which can be calculated in BALDUR via Ampere’slaw, ni,e is ion and electron density, and Zeff is effective charge.Figure 1 shows normalized minor radius (r/a) comparisonprofile of experimental v of JET discharge 40847 withcurrent density in toroidal direction from the diagnosticsimulation (simulation using toroidal velocity from experi-ment to construct the current profile) at the diagnostic time.It can be seen that the profiles are similar in which the valuesare high near the centre and low near the edge with relativelyflat profiles at the regions close to both boundaries.

3.2 Ion temperature dependent approach

This model describes that the toroidal velocity islinearly proportional to the local ion temperature (Ti), theexact form is as follows:

4[ / ] 1.43 10 iv m s T keV . (16)It was developed and used to simulate JET data

(Chatthong et al., 2010). Then later it was used to predictITER performance (Chatthong et al., 2011), which illustratedthat during plasma quasi-steady state the anomaloustransport was suppressed over a wide region. The problemis that this model is empirically built based solely from datafrom JET tokamak. So the projection problem is rather

Figure 1. Profile plot of toroidal velocity v (solid) together withtoroidal current density J (dashed) as a function of r/afor JET 40847 discharge at the diagnostic time.


questionable. Moreover, the set of experimental data usedin the model development is mainly NBI (neutral beam injec-tion)-heated plasma. In other words, the plasma is rotatedtoroidally by the external torque caused by NBI heating. Thisraises an important issue because ITER will be much larger(840 m3 plasma volume compared to 100 m3 of JET) so thatthe torque from NBI should not be enough to rotate ittoroidally.

4. Results and Discussion

4.1 JET simulations

In this work, 10 JET optimized shear H-mode dis-charges with ITB formation (40542, 40847, 46123, 46664,51599, 51976, 52009, 53521, 53532, and 53537) are chosenfrom the International Profile Database (Boucher et al., 2000).Table 1 shows the summary of parameters from all 10 dis-charges used for the simulations where R is major radius,a is minor radius, Ip is plasma current, B is toroidal mag-netic field, is plasma elongation, is plasma triangularityand nl is line average density.

4.1.1 Comparison

In this part, the predicted toroidal velocityfrom twomodels are compared. Examples ofprofile are shown in Figure2. Each demonstratesas a function of r/a, the closed circlesrepresent experimental data, the solid line with trianglemarkers represents simulation result of ion temperaturedependent model, and the solid line represents simulationresult of current density dependent model. Note that diagnos-tic time for each discharge is selected based on ITB and H-mode considerations. From this figure, it can be observedthat the simulation results tend to over-predict the experi-ments. This is almost always the case for all 10 JET discharges.Furthermore, the general profile shape of the current densitydependent model is rather unsmooth near the edge of theplasma where thevalues abruptly spike up and then decreaseto zero right at the edge. This strange behaviour is a result of

numerical procedure according to how BALDUR computesthe current density. BALDUR assumes that the current iszero at the edge, the value at the next grid is high to conserveoverall current flow.

Quantitatively, the root mean square error (RMSE)values between simulation results and experimental data arecomputed for comparison according to:

2

_ exp _ mod1

ln lnRMSE % 100

1

i i

N

i

v v

N

,

(17)

Figure 2. Comparison of toroidal velocity v between experimen-tal values (dots) and simulation results using ion tempera-ture Ti dependent (solid-triangle) and current density Jdependent (solid) models for JET discharges 40542 (top)and 40847 (bottom) during their diagnostic time.

Table 1. Summary of plasma parameters for 10 JET optimized shear discharges during their diagnostic time.

JET Time (s) R (m) a (m) Ip (MA) B (T) nl (1019 m-3)

40542 47 2.93 0.94 3.22 3.49 1.64 0.35 2.4140847 46 2.92 0.96 2.85 3.50 1.56 0.20 2.3346123 46.5 2.89 0.98 2.50 2.54 1.52 0.17 2.2446664 45.7 2.92 0.94 2.95 3.50 1.71 0.20 2.2751599 46 2.89 0.96 2.21 2.64 1.66 0.23 1.9051976 46.3 2.92 0.95 2.40 3.49 1.69 0.26 2.4552009 21.6 3.01 0.88 2.49 2.70 1.72 0.47 7.3053521 49 2.89 0.97 2.00 3.54 1.63 0.21 2.9953532 46.5 2.89 0.96 2.22 2.64 1.67 0.23 2.5253537 46.5 2.90 0.96 2.22 2.64 1.67 0.23 2.15


where _ expv is the experimental value, _ modv is the valuecalculated from the models, and N is total number of datapoints. The summary results are shown in Figure 3. TheRMSE ranges from 16.99% to 200.5% for the current densitydependent model, whereas it ranges from 18.58% to 55.50%for the ion temperature dependent model. The best agree-ment is found in the current density dependent prediction ofdischarge 51976, while the worst agreement is ironicallyfound in the prediction using the same model of discharge46664. The average RMSE of all 10 discharges is found to be73.02% with the standard deviation of 60.81% for the currentdensity dependent model, and found to be 37.09% with thestandard deviation of 13.04% for the ion temperature depen-dent model. The average values imply that the prediction byion temperature dependent model is better. However, if oneobserves discharge by discharge and also from the highstandard deviation, one can see that it is possible that thiscurrent density dependent model can only capture a limitedregime of the plasma. So for the applicable discharges, it canpredict the profile rather adequately. While in some otherdischarges additional physics or models are needed.

4.1.2 Simulation profiles

For simulations of each JET discharge, the time-evolution profiles of ion temperature (Ti), electron tempera-ture (Te), and electron density (ne) are calculated andpredicted by BALDUR. Figure 4 illustrates example profilesof JET discharges 40847 and 52009; note that the dots re-present experimental data, the dashed line represents simula-tion results using current density dependent model, and thesolid line represents simulation results using ion tempera-ture dependent model. First of all, the figure shows that thesimulation results over-predict both the temperatures andthe density at the edge while they tend to under-predict thevalues at plasma center. In other words, the pedestal modelyields higher predicted values and the Mixed B/gB modelyields lower predicted values than the experimental data.Furthermore, it can be observed that when comparing toexperimental data the general features of this dischargeprofiles are retained. However, when observing the generalfeatures of the profile plots for all 10 JET discharges the briefsummary can be discussed as follows. Firstly, the simulationresults of Ti, Te, and ne are in agreement within one order ofmagnitude with experimental measurements. Secondly, thegeneral trend of the profile such as the inclination is similarin some results and different in others. This can be due to thelimited availability of some experimental parameters andincompleteness of the model. And lastly, ne profiles areusually in better agreement with experimental data than theothers. This is because in BALDUR, the boundary conditionfor density equation is empirically determined from lineaverage density (nl) according to equation (10). On thecontrary, the pedestal temperature (Tped) is theoretically calcu-lated according to equation (14) so the prediction accuracyshould be less than that of empirical approach. This also can

be seen in Figure 4, in which the temperatures for both ionand electron at the edge are predicted much higher than thatof the experiment, while the densities are predicted roughlycloser to the experimental values.

Figure 3. RMSE deviations of 10 JET discharges and their averagefor toroidal velocity v using current density J depen-dent (solid bars) and ion temperature Ti dependent(striped bars) models.

Figure 4. JET 40847 (left) and 52009 (right) time-evolution profilesof ion temperature Ti (top), electron temperature Te(middle), and electron density ne (bottom): experimentaldata (dots) simulation results using current density Jdependent (dashed) and ion temperature dependent(solid) models at the center (dark) and edge (gray) of theplasma.


Quantitatively, the three physical quantities profilesare compared with experimental data using the followingnormalized RMS comparison:

0

2

exp mod

1 exp

1RMS(%) 100i iN

i

x xN x

, (18)

where x represents interested physical quantities (Te, Ti, andne) and x0 represents experimental data at the centre of theplasma. Note that in these comparisons, data of all grid posi-tions in the plasma are included and of the entire durationthat the discharge remains in H-mode. These results areshown as bar plots in Figure 5. For Ti comparison, the maxi-mum of 41.48% is found in discharge 53532 of current densitydependent model and the minimum of 18.14% is found indischarge 53521 of ion temperature dependent model. Theaverages of all discharges are 28.13±7.71% standard devia-tion for the current density dependent model, and 25.47±7.10% standard deviation for the ion temperature dependentmodel. For Te comparison, the maximum of 63.74% is foundin discharge 53532 of current density dependent model andthe minimum of 14.88% is found in discharge 40847 of thesame model. The averages of all discharges are 31.78±14.51%standard deviation for the current density dependent model,and 30.19±13.64% standard deviation for the ion tempera-ture dependent model. For ne comparison, the maximum of21.54% is found in discharge 52009 of ion temperature de-pendent model and the minimum of 9.66% is found indischarge 46664 of the same model. The averages of all dis-charges are 15.00±3.23% standard deviation for the currentdensity dependent model, and 15.15±3.50% standarddeviation for the ion temperature dependent model. Onaverage, it cannot be concluded which model is betterbecause they are within the standard deviation of each other.This conclusion is different from the toroidal velocity predic-tion where it can be clearly seen that the ion temperaturedependent model predicts better. This shows that thesimulations profiles are not so much sensitive to the toroidalvelocity profile. Nevertheless, if one observes the perform-ance of each discharge simulation individually, one can findthat on some discharge like 46664 the difference is signifi-cant in which the empirical model performs better.

4.1.3 ITB Formation

One physical phenomenon that is important to explorein this work is the ability of this suite of code to simulate ITBformation. This v model is developed to explain the velocityin toroidal direction which is used to calculate the shearingrate ExB, the cause of ITB formation. ITB formation can befound in either ion or electron channel, or both channels atthe same time depending on heating method. Since the mainheating in JET is either NBI (neutral beam injection) or ICRF(ion cyclotron resonance frequency) or both, ITB formationsare found mainly in ion temperature profile so the work onITB identification will be in Ti profile plots. ITB is defined as

a local region of steep temperature gradient. So, the gradientwill be used in order to identify ITB location and time of itsoccurrence.

Figure 6 illustrates the contour plot of ion tempera-ture gradient spatiotemporal profiles with darker arearepresenting relative higher temperature gradient area,showing examples for JET discharges 46664 and 53532. Onlyion temperature profiles are shown here because BALDURsimulations yield similar qualitative behaviour for ion andelectron profiles. Moreover, there is no ITB formation in theparticle channels from these experiments. In this sense, thefigure can be used to trace the location and the time evolu-tion of the ITB. The top panels are experimental data, the

Figure 5. RMS deviations of 10 JET discharges and their averagesfor ion temperature Ti, electron temperature Te, andelectron density ne simulation results using currentdensity J dependent (dark) and ion temperature Tidependent (gray) models.


middle panels are the simulation results from current densitydependent model and the bottom panels are simulationresults from ion temperature dependent model. In discharge46664, ITB forms around the time of 45.5 seconds near theposition r/a = 0.4. It appears that the empirical model predictsalmost the exact time of formation with a location slightly

shifted toward r/a = 0.5. On the contrary, the current densitydependent model predicts a wider ITB from r/a = 0.4 to 0.8with formation time as early as 45 seconds. In discharge53532, ITB forms around the time of 46 seconds near theposition r/a = 0.4. Similar to the previous discharge, theempirical model predicts ITB formation better for both itstime and location. Current density dependent model predictssofter ITB but for wider region. As a summary, from thisqualitative observation, the empirical model predicts forma-tion of ITB better. These results are as expected because,as mentioned earlier, the empirical model was derived fromthese discharges so they should fit the experimental resultsbetter. However, it is more interesting to see how it projectsinto a larger machine like ITER.

4.2 ITER predictions

ITER is an international collaboration with the maingoal of demonstrating scientific and engineering feasibilityof nuclear fusion machine (Aymar et al., 2002). In this work,a standard type I ELMy H-mode ITER is chosen. Its designparameters are shown in Table 2, where RF represents radiofrequency heating scheme and NBI represents neutral beaminjection heating scheme, and the details of the operationscenario can be found in Onjun et al. (2009).

4.2.1 ITER performance and ITB effect

Figure 7 illustrates simulations of ITER for ion tem-perature (Ti), electron temperature (Te), deuterium density(nD), tritium density (nT), beryllium density (nBe), and heliumdensity (nHe) as a function of normalized minor radius r/a atthe time of 2,700 seconds. Note that at this time, the plasmahas reached quasi-steady state condition as observed fromFigure 8 that the plasma becomes relatively steady after 200seconds. In both figures, the solid line is for simulation using

Figure 6. Contour plots of ion temperature gradient iT profile ofJET discharge 40542: experimental results (top) andsimulation results using current density J dependent(middle) and ion temperature Ti dependent (bottom)models.

Figure 7. Comparison of ITER performance (for ion temperature Ti, electron temperature Te, deuterium density nD, tritium density nT,beryllium density nBe, and helium density nHe) between simulations with ITB (both current density and ion temperature dependentmodels) and without ITB effect during steady state (t = 2700 s).


current density dependent model, the solid line with bullet isfor simulation using ion temperature dependent model, andthe dashed line is for simulation without ITB. It can be seenin Figure 7 that both temperatures are high near the centerand lower toward the edge (from 3 to 10 times reduction),while the densities of all species remain roughly the samethroughout the plasma (around 2 times or less reduction)except helium density in ITB simulation which accumulatesmore toward the plasma center (at most 4 times reduction).

The temperature profiles indicate the existence of ITBformations which is shown by significant improvements ofplasma temperature over those results without ITB. It can beseen that when ITB effects are included in the simulation,the central temperature for both ion and electron increasesignificantly, from 12 keV to 38 keV (current density depen-dent) and 49 keV (ion temperature dependent), and from 13keV to 33 keV (current density dependent) and 39 keV (iontemperature dependent), respectively. Yet, the temperaturesnear the edge of plasma remain approximately the same. Thisimplies that ITB formations indeed result in better plasmaconfinement for the plasma temperature, hence energy. Thisalso shows that the empirical model predicts higher valuesfor ITER by around 20% for ion and 15% for electrontemperatures at plasma center.

The bottom right panel shows that helium impurityaccumulates more in the plasma core for simulations withITB included, also in the ion temperature dependent modelmore than in the current density dependent model. Thisagrees with the trend in central temperatures which results inhigher fusion reaction. Additionally, it means that ITB forma-tions also prevent transport of impurity species especiallyhelium. Beryllium is an impurity from the first wall outside ofthe plasma, the concentration is slightly higher in plasmawith the ion temperature dependent model run as expectedbecause there are more beryllium trapped in the core. How-ever, the current density dependent model appears to showsimilar beryllium accumulation to that of simulation withoutITB. The situation is similar for helium species, except thatthe concentration in the run with ITB effect is much higherthan the run without ITB effect. As stated earlier, transportbarriers improve plasma energy confinement and powerproduction, which mean the fusion reaction rate is enhancedas well. This is confirmed by Figure 8 in the bottom panelwhich shows the time-evolution profile of alpha power.During quasi-steady state, the alpha powers of ITB simula-tions are almost 10 times higher than that without ITBformation. These alpha particles are not neutral so they aretrapped by the magnetic field inside the tokamak. The energyis used to reheat the plasma, transferred back to deuteriumand tritium by way of collision. More alpha power meansmore alpha particles produced from fusion reaction so higherhelium density is observed. This result is further confirmedby deuterium and tritium density plots in Figure 7. Since bothspecies are starting particles of the fusion reaction, a higherreaction rate implies more fuel burnt and hence less densityaccumulated for both. As observed from the figure, ITB simu-lation shows lower tritium and slightly lower deuteriumconcentrations.

In summary, to see what is happening at the center ofthe plasma, the central ion temperature is plotted as functionsof time (Figure 8) along with total fusion power output andalpha power of the plasma. As expected, they are higher insimulations with ITB formation. Initially, during current ramp-up phase the profiles increase steeply and reach maximumaround 100 seconds before dropping down because of thehigh radiation power to reach quasi-steady state. During thislatter state, the average values of central ion temperature are36 and 49 keV, of the total power outputs of the plasma are492 and 800 MW, and of the alpha powers are 159 and 218MW for the current density dependent and ion temperaturedependent models, respectively. Note that the ion tempera-ture dependent model provides more steady plasma profileswhile the results from current density dependent model aremuch rather fluctuated.

It is interesting to observe how ITB forms in ITERusing the two toroidal rotation models. Figure 9 illustratesthe contour plots of the ion temperature gradient profiles.The top panel shows that the current density dependentmodel predicts ITB to be locally located around r/a = 0.7with some slight fluctuations. Once formed, its location is

Table 2. Engineering design parameters for ITER.

Parameters unit Values

R m 6.2a m 2.0Ip MA 15.0B T 5.3 - 1.7 - 0.33

RF MW 7.0NBI MW 33.0nl m-3 1.0x1020

Figure 8. Time-evolution plots of central ion temperature Ti (top),total fusion power output Wtot (middle), and alpha powerPá (bottom) for simulations with ITB (both current den-sity J and ion temperature Ti dependent models) andwithout ITB effect during steady state (t = 2700 s).


moving in and out around the position. It also appears tocollapse and reform. However, the period of collapsing andreformation is not regular or deterministic; future investiga-tion is required. On the contrary, the ITB region fromempirical model appears to be much wider, from r/a = 0.5 to0.8. This agrees with what could be observed in the toppanels of Figure 7, in which the strong gradient from thecurrent density dependent model can be easily identified atr/a = 0.7 but not so for the ion temperature dependent modelbecause it covers a wider region. This also explains why theempirical model yields higher temperature profiles, as it hasa wider region of ITB, the transport reduction is muchstronger. The toroidal velocity and the flow shear profiles areshown in Figure 10. It can be observed that in the simulationusing current density dependent model, there exists a spikefeature representing strong shear of the profiles at thevicinity of the ITB location. So there is a correlation betweenthe location of the strong shear of toroidal velocity and ExBflow shear profiles with that of temperature gradient or ITB.Moreover, the plasma appears to be rotated much faster,toroidally, in the simulation using empirical model. This willbe physically quite challenging in ITER since NBI, as impliedby the empirical model, should not be able to rotate thebigger machine that fast.

4.2.2 Test for plasma ignition

Plasma reaches an ignition condition if the auxiliaryheating (NBI plus RF heating) is shut down but the plasma isstill able to self-sustain. It is very important to study this issue

for ITER because self-heating leads to possibility of longduration operation for fusion reactor. In this study, BALDURcode is used to simulate the similar ITER performance asbefore but the auxiliary heating is turned off after 2000 s, atwhich point the plasma has reached a quasi-steady state.After that, the plasma is solely heated by ohmic heating andalpha heating.

It is found in Figure 11 that ion temperatures, totalpowers and alpha powers drop as soon as the external heatingis shutdown. Nevertheless, the plasma adjusts to a newquasi-steady state shortly after with lower temperatures andpowers. In simulation without ITB effects included, theoperation continues for about 400 seconds longer beforereaching disruption because alpha heating diminishes assoon as auxiliary heating is off and then ohmic heatingcarries on the operation until the operation stops. Note thatohmic heating is small compared to other heating modes.With ITB effects included, the plasma achieves a new quasi-steady state at central ion temperatures of around 30 and 40keV, total powers of 400 and 650 MW and alpha powers of110 and 180 MW, for current density dependent and iontemperature dependent models, respectively. Note that ITBformations are still maintained even after auxiliary heatingis turned off as shown in Figure 12 but the values of tempera-tures are slightly lower.

5. Conclusions

Self-consistent simulations of ITER with the presenceof both ITB and ETB are carried out using the BALDUR code.

Figure 9. Contour plots of ion temperature gradient iT profile ofITER simulations: simulation results using currentdensity J dependent (top) and ion temperature Tidependent (bottom) models.

Figure 10. Toroidal velocityand flow shear ExB profiles of simula-tions results for current density J dependent (solid)and ion temperature Ti dependent (dashed) modelsduring steady state (t = 2700 s).


Figure 11. Time-evolution plots of central ion temperature Ti (top), total fusion power output Wtot (middle), and alpha power P (bottom)for simulations with ITB (both current density J and ion temperature Ti dependent models) and without ITB effect duringsteady state (t = 2700 s), auxiliary heating is turned off after 2000 s.

Figure 12. ITER performance simulations (for ion temperature Ti, electron temperature Te, deuterium density nD, tritium density nT,beryllium density nBe, and helium density nHe) with ITB (both current density and ion temperature dependent models) andwithout ITB effect at time after auxiliary heating is turned off (t = 2400 s).

The combination of Mixed B/gB transport model togetherwith pedestal model based on magnetic and flow shear stabi-lization pedestal width scaling and an infinite-n ballooningpressure gradient model, and with two toroidal velocitymodels based on ion temperature and current density of theplasma, is used to simulate the time-evolution profiles ofplasma temperature, density, and current for JET optimizedshear discharges and ITER standard type I ELMy H-modeoperation. It is found that the simulations with the iontemperature dependent toroidal velocity model yield betteragreement with JET experimental data. For ITER prediction,the ion temperature dependent model yields more optimisticpredictions but the current density dependent model predictsa rather narrow region of ITB. The presence of ITB is verycrucial for ITER because it results in greater plasma energyconfinement over standard run without ITB effects. Thepresence of ITB causes both ion and electron temperaturesto be higher, especially at the center. However, it only slightly

affects the densities of deuterium, tritium, and beryllium.Helium concentration is higher in ITB simulation because ofa higher fusion reaction rate. Therefore, this is a critical issuefor ITER. In addition, when the auxiliary heating is turned off,it is found that the core temperature, total power and alphapower are decreased slightly. Nevertheless, significantfusion energy still remains. The ignition condition cannot beachieved without the formations of ITB.

Acknowledgments

This work was supported by the Commission onHigher Education (CHE) and the Thailand Research Fund(TRF) under contract No.RSA5580041, the National ResearchUniversity Project of Thailand Office of Higher EducationCommission, and Low Carbon scholarship from BangchakPetroleum PCL. B Chatthong thanks the Royal Thai Scholar-ship for monthly support.


References

Artaud, J. F., Basiuk, V., Imbeaux, F., Schneider, M., Garcia, J.,Giruzzi, G., Huynh, P., Aniel, T., Albajar, F., Ané, J. M.,Bécoulet, A., Bourdelle, C., Casati, A., Colas, L.,Decker, J., Dumont, R., Eriksson, L. G., Garbet, X.,Guirlet, R., Hertout, P., Hoang, G. T., Houlberg, W.,Huysmans, G., Joffrin, E., Kim, S. H., Köchl, F., Lister,J., Litaudon, X., Maget, P., Masset, R., Pégourié, B.,Peysson, Y., Thomas, P., Tsitrone, E., and Turco, F.2010. The CRONOS suite of codes for integratedtokamak modelling. Nuclear Fusion. 50, 043001.

Aymar, R., Barabaschi, P., and Shimomura, Y. 2002. The ITERdesign. Plasma Physics and Controlled Fusion. 44,519.

Bateman, G., Onjun, T., and Kritz, A. H. 2003. Integrated pre-dictive modelling simulations of burning plasmaexperiment designs. Plasma Physics and ControlledFusion. 45, 1939.

Boucher, D., Connor, J. W., Houlberg, W. A., Turner, M. F.,Bracco, G., Chudnovskiy, A., Cordey, J. G., Greenwald,M. J., Hoang, G. T., Hogeweij, G. M. D., Kaye, S. M.,Kinsey, J. E., Mikkelsen, D. R., Ongena, J., Schissel,D. R., Shirai, H., Stober, J., Stubberfield, P. M., Waltz,R. E., Weiland, J., and The ITER 1D Modelling Work-ing Group. 2000. The International Multi-TokamakProfile Database. Nuclear Fusion. 40, 1955.

Budny, R. V., Andre, R., Bateman, G., Halpern, F., Kessel, C. E.,Kritz, A., and McCune, D. 2008. Predictions of H-mode performance in ITER. Nuclear Fusion. 48,075005.

Burrell, K. H. 1997. Effects of E x B velocity shear and mag-netic shear on turbulence and transport in magneticconfinement devices. Physics of Plasmas. 4, 1499-1518.

Callen, J. D., Cole, A. J., and Hegna, C. C. 2009. Toroidalrotation in tokamak plasmas. Nuclear Fusion. 49,085021.

Cenacchi, G., and Taroni, A. 1988. JETTO: a free boundaryplasma transport code. ENEA Report RT/TIB. 88, 5.

Chatthong, B., Onjun, T., and Singhsomroje, W. 2010. Modelfor toroidal velocity in H-mode plasmas in thepresence of internal transport barriers. Nuclear Fusion.50, 064009.

Chatthong, B., and Onjun, T. 2011. Self-Consistent Simula-tion of Standard H-Mode ITER with the Presence of anInternal Transport Barrier. Thammasat InternationalJournal of Science and Technology. 16, 42-53.

Chatthong, B., and Onjun, T. 2013. Simulations of ITER inthe presence of ITB using the NTV intrinsic toroidalrotation model. Nuclear Fusion. 53, 013007.

Connor, J. W. 1998. A review of models for ELMs. PlasmaPhysics and Controlled Fusion. 40, 191.

Connor, J. W., Fukuda, T., Garbet, X., Gormezano, C.,Mukhovatov, V., Wakatani, M., the ITB DatabaseGroup, and the ITPA Topical Group on Transport and

Internal Barrier Physics. 2004. A review of internaltransport barrier physics for steady-state operation oftokamaks. Nuclear Fusion. 44, R1.

Diamond, P. H., Itoh, S.-I., Itoh, K., and Hahm, T. S. 2005.Zonal flows in plasma—a review. Plasma Physics andControlled Fusion. 47, R35.

Erba, M., Parail, V., Springmann, E., and Taroni, A. 1995. Ex-tension of a Bohm model for L-mode electron heattransport to ion heat transport and to the ohmicregime. Plasma Physics and Controlled Fusion. 37,1249.

Eriksson, A., Nordman, H., Strand, P., Weiland, J., Tala, T.,Asp, E., Corrigan, G., Giroud, C., Greef, M. d., Jenkins,I., Knoops, H. C. M., Mantica, P., Rantamäki, K. M.,Vries, P. C. d., Zastrow, K.-D., and JET EFDA Contri-butors. 2007. Predictive simulations of toroidalmomentum transport at JET. Plasma Physics andControlled Fusion. 49, 1931.

Halpern, F. D., Kritz, A. H., Bateman, G., Pankin, A. Y., Budny,R. V., and McCune, D. C. 2008. Predictive simulationsof ITER including neutral beam driven toroidalrotation. Physics of Plasmas. 15, 062505.

Hannum, D., Bateman, G., Kinsey, J., Kritz, A. H., Onjun, T.,and Pankin, A. 2001. Comparison of high-mode pre-dictive simulations using Mixed Bohm/gyro-Bohmand Multi-Mode (MMM95) transport models. Physicsof Plasmas. 8, 964-974.

Houlberg, W. A., Shaing, K. C., Hirshman, S. P., andZarnstorff, M. C. 1997. Bootstrap current and neo-classical transport in tokamaks of arbitrary collision-ality and aspect ratio. Physics of Plasmas. 4, 3230-3242.

Kinsey, J. E., Staebler, G. M., and Waltz, R. E. 2002. Simula-tions of internal transport barrier formation in tokamakdischarges using the GLF23 transport model. Physicsof Plasmas. 9, 1676-1691.

Klaywitthaphat, P., and Onjun, T. 2012. Simulations of plasmabehavior during pellet injection in ITER. PlasmaPhysics Reports. 38, 496-502.

Leekhaphan, P., and Onjun, T. 2011. Pellet Injection intoH_mode ITER Plasma with the Presence of InternalTransport Barriers. Plasma Physics Reports. 37, 321-327.

Onjun, T., Bateman, G., Kritz, A. H., and Hammett, G. 2002.Models for the pedestal temperature at the edge of H-mode tokamak plasmas. Physics of Plasmas. 9, 5018-5030.

Onjun, T., Kritz, A. H., Bateman, G., and Parail, V. 2005.Magnetohydrodynamic-calibrated edge-localized modemodel in simulations of International ThermonuclearExperimental Reactor. Physics of Plasmas. 12, 082513.

Onjun, T., and Pianroj, Y. 2009. Simulations of ITER withcombined effects of internal and edge transportbarriers. Nuclear Fusion. 49, 075003.

Parail, V. V., Baranov, Y. F., Challis, C. D., Cottrell, G. A., Fischer,B., Gormezano, C., Huysmans, G. T. A., Litaudon, X.,


Sips, A. C. C., Söldner, F. X., Springmann, E. M., Taroni,A., and Ward, D. J. 1999. Predictive modelling of JEToptimized shear discharges. Nuclear Fusion. 39, 429.

Parail, V. V. 2002. Energy and particle transport in plasmaswith transport barriers. Plasma Physics and ControlledFusion. 44, A63.

Pereverzev, G., and Yushmanov, P. N. 2002. ASTRA Auto-mated System for Transport Analysis in a Tokamak.Max-Planck Institut fur Plasmaphysik. IPP 5/98.

Pianroj, Y., Chuchinda, C., Leekhaphan, P., and Onjun, T.2010. Behaviors of Impurity in ITER Plasma withStandard Type I ELMy H-mode and Steady StateScenarios. Plasma Physics Reports. 36, 827.

Pianroj, Y., Techakunchaiyanunt, J., and Onjun, T. 2012. Modelfor Pedestal Transport Based on Suppression ofAnomalous Transport Using ùExB Flow Shear andMagnetic Shear. Journal of the Physical Society ofJapan. 81, 044502.

Roach, C. M., Walters, M., Budny, R. V., Imbeaux, F., Fredian,T. W., Greenwald, M., Stillerman, J. A., Alexander,D. A., Carlsson, J., Cary, J. R., Ryter, F., Stober, J.,Gohil, P., Greenfield, C., Murakami, M., Bracco, G.,Esposito, B., Romanelli, M., Parail, V., Stubberfield,P., Voitsekhovitch, I., Brickley, C., Field, A. R., Saka-moto, Y., Fujita, T., Fukuda, T., Hayashi, N., Hogeweij,G. M. D., Chudnovskiy, A., Kinerva, N. A., Kessel,C. E., Aniel, T., Hoang, G. T., Ongena, J., Doyle, E. J.,Houlberg, W. A., Polevoi, A. R., ITPA ConfinementDatabase Modelling Topical Group, and ITPATransport Physics Topical Group. 2008. The 2008Public Release of the International Multi-tokamakConfinement Profile Database. Nuclear Fusion. 48,125001.

Rogister, A. L., Rice, J. E., Nicolai, A., Ince-Cushman, A.,Gangadhara, S., and Alcator C-Mod Group. 2002.Theoretical interpretation of the toroidal rotationvelocity observed in Alcator C-Mod Ohmic H-modedischarges. Nuclear Fusion. 42, 1144.

Rozhansky, V., Kaveeva, E., Voskoboynikov, S., Coster, D.,Bonnin, X., and Schneider, R. 2002. Modelling ofelectric fields in tokamak edge plasma and L-H transi-tion. Nuclear Fusion. 42, 1110.

Singer, C. E., Post, D. E., Mikkelsen, D. R., Redi, M. H.,McKenney, A., Silverman, A., Seidl, F. G. P., Rutherford,P. H., Hawryluk, R. J., Langer, W. D., Foote, L., Heifetz,D. B., Houlberg, W. A., Hughes, M. H., Jensen, R. V.,Lister, G., and Ogden, J. 1988. Baldur: A one-dimen-sional plasma transport code. Computer PhysicsCommunications. 49, 275-398.

Stacey, W. M. 2004. A neoclassical model for toroidal rota-tion and the radial electric field in the edge pedestal.Physics of Plasmas. 11, 3096-3099.

Sugihara, M., Igitkhanov, Y., Janeschitz, G., Hubbard, A. E.,Kamada, Y., Lingertat, J., Osborne, T. H., and Suttrop,W. 2000. A model for H mode pedestal width scalingusing the International Pedestal Database. Nuclear

Fusion. 40, 1743.Tala, T., Laborde, L., Mazon, D., Moreau, D., Corrigan, G.,

Crisanti, F., Garbet, X., Heading, D., Joffrin, E.,Litaudon, X., Parail, V., Salmi, A., and contributors tothe EFDA-JET workprogramme. 2005. Predictivetransport simulations of real-time profile control inJET advanced tokamak plasmas. Nuclear Fusion. 45,1027.

Tala, T., Imbeaux, F., Parail, V. V., Bourdelle, C., Corrigan, G.,Garbet, X., Heading, D. J., Litaudon, X., Strand, P. I.,Weiland, J., and JET-EFDA contributors. 2006. Fullypredictive time-dependent transport simulations ofITB plasmas in JET, JT-60U and DIII-D. NuclearFusion. 46, 548.

Tala, T., Crombé, K., Vries, P. C. d., Ferreira, J., Mantica, P.,Peeters, A. G., Andrew, Y., Budny, R., Corrigan, G.,Eriksson, A., Garbet, X., Giroud, C., Hua, M.-D.,Nordman, H., Naulin, V., Nave, M. F. F., Parail, V.,Rantamäki, K., Scott, B. D., Strand, P., Tardini, G.,Thyagaraja, A., Weiland, J., Zastrow, K.-D., and JET-EFDA Contributors. 2007. Toroidal and poloidalmomentum transport studies in tokamaks. PlasmaPhysics and Controlled Fusion. 49, B291.

Tala, T. J. J., Heikkinen, J. A., Parail, V. V., Baranov, Y. F., andKarttunen, S. J. 2001. ITB formation in terms of E×Bflow shear and magnetic shear s on JET. PlasmaPhysics and Controlled Fusion. 43, 507.

Tala, T. J. J., Parail, V. V., Becoulet, A., Corrigan, G., Heading,D. J., Mantsinen, M. J., Strand, P. I., and contributorsto the EFDA-JET Workprogramme. 2002. Comparisonof theory-based and semi-empirical transport model-ling in JET plasmas with ITBs. Plasma Physics andControlled Fusion. 44, A495.

Taroni, A., Erba, M., Springmann, E., and Tibone, F. 1994.Global and local energy confinement properties ofsimple transport coefficients of the Bohm type. PlasmaPhysics and Controlled Fusion. 36, 1629.

Wagner, F., Becker, G., Behringer, K., Campbell, D., Eberhagen,A., Engelhardt, W., Fussmann, G., Gehre, O.,Gernhardt, J., Gierke, G. v., Haas, G., Huang, M., Karger,F., Keilhacker, M., Klüber, O., Kornherr, M., Lackner,K., Lisitano, G., Lister, G. G., Mayer, H. M., Meisel,D., Müller, E. R., Murmann, H., Niedermeyer, H.,Poschenrieder, W., Rapp, H., and Röhr, H. 1982.Regime of Improved Confinement and High Beta inNeutral-Beam-Heated Divertor Discharges of theASDEX Tokamak. Physical Review Letters. 49, 1408.

Wesson, J., and Campbell, D. J. 2004. Tokamaks, ClarendonPress ; Oxford University Press, New York, U.S.A.

Wisitsorasak, A., and Onjun, T. 2011. Impacts of PelletsInjected from the Low Field Side on Plasma in ITER.Plasma Physics Reports. 37, 1-18.

Zhu, P., Bateman, G., Kritz, A. H., and Horton, W. 2000. Pre-dictive transport simulations of internal transportbarriers using the Multi-Mode model. Physics ofPlasmas. 7, 2898-2908.

Comparison of H-mode plasma simulations using toroidal...

Documents

Transcript of Comparison of H-mode plasma simulations using toroidal...