J. Plasma Fusion Res. SERIES, Yol.2 (199D 125-128

Plasma Transport Modeling for Tokamak andHelical Systems
YAMAZAKI Kozo, NAKAJIMA Noriyoshi,MURAKAMI Sadayoshi and YOKOyAMA Masayuki
National Institute for Fusion science, 322-6 oroshi-cho, Toki-shi, Gifu 509-s292, Japan(Received: 3 June 1999 / Accepted: 22 July 1999)

Abstract
The plasma transport code TOTAL (Toroidal Transport Analysis Linkage) is developed to clarify
physics properties of both tokamak and helical plasmas. This is composed of one-dimensional transport

code with magnetic ripple effects and three-dimensional equilibrium code with bootstrap currents.
Ballooning-mode marginal-stable spherical tokamak configurations have been studied and their high beta
values are found to be consistent with the normalized beta scaling. However, the engineering beta definedby maximum toroidal field on the plasma surface is found as small as the standard tokamak. The L:uge
Helical Device (LHD) plasmas are also studied using this code, and the bootstrap cunent is found to
make the radial axis-shift smaller, which leads to the decrease in the neoclassical ripple transport loss andthe increase in the attainable plasma temperature.

Keywords:
plasma transport simulation, Large Helical Device, spherical tokamak, bootstrap current, NBI heating
deposition

1. Introduction

operation from the end of March in 1998 [2j, and tospherical tokamak configurations with ballooning mode
stable profiles [3].

Toroidal confinement system has a great advantage
for producing higher plasma performance in tokamak
systems, and sustaining longer plasma operation inhelical systems. Both confinement properties are quite
similar with each other, and it is important to develop a

2. Model of Transport Simulation
In order to describe two-dimensional (for tokamak)

plasma transport modeling code applicable to tokamak,and three-dimensional (for helical system) equilibria, thehelical and hybrid systems for optimizing toroidal

VMEC code with bootstrap currents [4] are adopted inaddition to two-dimensional equilibrium code
APOLLO[3], and the helical and toroidal ripple

confinement systems.

A new simulation code TOTAL (ToroidalTransport Analysis Linkage) is developed for thispurpose using the previous code HSTR []. Thisconsists of a three-dimensional equilibrium code withohmic and bootstrap currents and a one-dimensionaltransport code with neoclassical and anomaloustransport losses. This code is applied to the Large
Helical Device (LHD) which had started plasma
C o r e sp o ndi n g aut ho r' s e - mai I : y amazaki @ nifs. ac.

transport losses are studied by taking radial electric field

effects into account self-consistently. Especially themulti-helicity field effects on neoclassical ripple
transport are included in this code as shown in Ref. [1].

Recently, we have revised the previous code toinclude impurity transport, bootstrap current and so on.
@1999 by The Japan Society of Plasma
Science and Nuclear Fusion Researchjpt25

Yamazaki K. et al., Plasma Transport Modeling for Tokamak and Helical Systems

toroidal field fits well with 4 times of normalized
toroidal beta value, 4fu, defined with toroidal plasma

The interface to the experimental data has been also
added in a new code named as "TOTAL" (ToroidalTransport Analysis Linkage). This is applicable to thecurrent 10, averaged plasma pressure <p>, plasma minor
radius ao and central toroidal field 8,. However, the total
beta value p is as low as 157o. Moreover, the reactor-simulation prediction and experimental data analysis forboth helical and tokamak systems. The flow chart of thisanalysis code is shown in Fig. l. The equilibrium isrelevant engineering beta value f"n, defined withaveraged square pressure and maximum surface toroidal
magnetic field is almost independent of aspect ratio. It is

iteratively solved with plasma radial profiles obtainedby transport equations or experimental measurements.
The details of transport equations adopted here areconcluded that the low aspect ratio configuration has nobenefit in increasing the engineering beta value whenthe maximum field strength is limited by thedescribed in the previous literature Il].

engineering design of the toroidal coil conductors'

3. Simulation Results
3.1 Tokamak simulation for beta limits

3.2 Helical plasmas without and withbootstrap current

Ballooning mode stable high-beta configurations in

spherical tokamak are obtained by using a part ofTOTAL code as shown in Fig. 2. This is the typicalThe initial plasma was produced in the LHD (LargeHelical Device) experiment on March 31, 1998, with 1.5
T magnetic field strength and typically 100 kW ECH

configuration with central and surface q-values of 1.0
and 3.0, aspect ratio of 1.5, plasma elongation andtriangularity of 1.5 and 0.5, respectively. In this case theballooning-mode marginal-stable toroidal beta value is
22.57o. Here, several beta definitions are used;heating power. The typical and preliminary simulation
results have been reported in Ref [5].
Recently we have developed our code to include
bootstrap current (BSC) self-consistently in the TOTAL
code. Figure 3 shows the BSC effects on the magnetic

B, = 2 lto<P>R/B.2,
4 FN = 4lp(MA)llar(m)8,(T)) (vo),p = 0t&+ UB)-L,

configurations at the central beta value of 3.35Vo. The
rotational transform near plasma center increases
dramatically and the radial axis-shift is relaxed. The
magnetic well is not stronger than the BSC-freeF"ng = 2 po<p2>tt2lfB^u^(R = Rp - a))''Here, poloidal beta value Byis defined by

Ft =4<p>vplPoRIp2,
with averaged plasma pressure <p>, plasma volume Vo,
major radius R and plasma current 10. The criticaltoroidal beta value B, defined by the central vacuum

configuration.
Figure 4 shows the simulation results showing BSC
effects. In this simulation the anomalous transport is<Tokamak>

Eqffi-lI ,-o(APoLLo)||

3-D Equilibrium(vMEC)
Bootstrao Current,s:Ttffit,./Free-Boundary
Ballooning Mode

Fig. 1 Flow chart of transport modeling code TOTAL (Toroidal Transport Analysis Linkage).
126

Yamazaki K. et al., Plasma Transport Modeling for Tokamak and Helical Systems

(a)

(a)
t.5

Fr= 22.6"/"

1.5

1.01.04m) 0.5

Z(n) 0.500_0.5a-0.5-1.0-l.0
- t.5

3.0

i(R)

4.0

3.0 4.0

R(m)

R(m)

p(R)
t.5

t.5

t.0t.0iohiota

1.00.5R

0.50(b)0l0505Well

Well() o40(%)-5-J-10-15

-20

-100

Bct* lo{9'" ls.0

0.60 0.2 0.4 0.6 0.8

rla!tlFig. 3 Effects of bootstrap current on LHD equilibria
without and (b) with bootstrap current.

I00,$I

1.5t?.53

separately, such as three-dimensional MHD stability
analysis [6] with CAS3D code, high energy particle
heating simulation [7], plasma rotation and H-mode
prediction [8], and so on, and some database has been

3.5

Aspsc! R{ti$Fig. 2 (a)Typical tokamak configuration marginallystable to ballooning mode in the case of plasma
aspect ratio of 1.5, and (b) dependence of beta
limits on aspect ratio.

developed for the experimental analysis. The details ofeach activities are presented in each literature.
Here, the NBI heating simulation analysis isdescribed in Fig. 5. NBI birth profile was calculated by

HFREYA code with the 3-D Equilibrium VMEC/
assumed with 2 times of LHD scaling prediction, which

hollow than without BSC, and the radial electric field
becomes more negative and the neoclassical ion andelectron transport coefficient are reduced by the BSC
effect. The finally obtained temperature reaches to-ZOVo higher value than that of BSC-free plasma. The
detailed effects of free-boundary configuration andNEWBOZ code. The beam slowing down with particleorbit effects was calculated by the 5-dimensional
Monte-Carlo code MCNBI. For 180keV beam, the orbit
effect is important in the case of less than I Tesla
operation. In the case of higher magnetic field than 1.5
T this effect can be neglected as shown in this figure.
The conventional analysis without orbit effects used in
the TOTAL package is appropriate for higher field.
These effects are stored in the simplified database for

impurity accumulation are now under investigation.

the LHD experimental analysis

4. Other Theoretical Analysis Related toSimulation Modeling

5. Summary and Future Plan

is preliminary supported in the LHD experiment [2].
The plasma density profile with BSC becomes lessWe developed a new code TOTAL consisting of
three-dimensional equilibrium and one-dimensionaltransport code with effects of ambipolar electric field,
ripple transport, bootstrap currents, impurities, andThe TOTAL code is general toroidal linkage code,
but does not cover various kinds of analyses because of

the limitation of computer consumption time. In ourgroup, several important analysis are carried out

experimental data analyzing interfaces. This was appliedr27

Yamazaki K. et al., Plasma Transport Modeling for Tokamak and Helical Systemsrb)

ru trw@ @mrcM@ @@Fig. 4 Transport simulation results for LHD (a) without and (b) with bootstrap current. Radial profiles of plasma density(Ne), electron temperature (Te), ion temperature (Ti), radial electric field (Er) and transport coefficients (Ke, Ki) areshown.

to the spherical tokamak configurations and the LHD
experimental plasma analysis. The engineering beta
against ballooning mode in spherical tokamak wasfound as small as the standard configuration. The
bootstrap current effect in the LHD was found favorableiliI

CoovefiSsrrls,9 t!
ain the neoclassical ripple transport.

q{ 2.5In the near future this code will clarify theit\= I keVE-'' :xtffkEtl:ffi:::::::::." *u4wg

,..

'',

l-i

l'*- torl
l"r'" r sr I
l'-*-'tsrl-----0.7r

ase!
1"9

radial electric field control, higher beta effect, plasmaedge effect and long-pulsed equilibrium relaxation:{!eqqA.ryryg$l#t
6

confinement comparison between tokamak and helicalsystems, focusing on magnetic configuration control,*t,;##"-]
T","l'lt*V,,, j&raryi|'

hTOTtl-Sdd6

i.tfII --i--0.5T I

rrylphenomena.
NE*a"j't'*+r&e

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ddI2l A. Iiyoshi et al., l7th IAEA Fusion Energy

Fig. 5 Power deposition profiles of NBI beam by using(a) the conventional code inside the TOTAL codeand (b) the detailed code with orbit effects.

Conference, Yokohama, Japan, 19-24 October
1998, rAEA-CN-69/OVl/4.
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