J. Plasma Fusion Res. SERIES, Vol.5 (2002) 28-35

High Performance Operational Limits ofTokamak and Helical Systems
YAMAZAKI Kozo and KIKUCHI Mitsurul
lNational Institutefor Fusion Science, Toki 509-5292, Japan

2Japan Atomic Energy Research Instiute, Naka 311-0193, Japan(Received: 22 Jantary 2002 I Accepted'. 26 April 2002)

Abstract
The plasma operational boundaries of tokamak and helical systems are surveyed and compared witheach other. Global confinement scaling laws are similar and gyro-Bohm like, however, local transport
process is different due to sawtooth oscillations in tokamaks and ripple transport loss in helical systems.

As for stability limits, achievable tokamak beta is explained by ideal or resistive MHD theories. On theother hand, beta values obtained so far in helical system are beyond ideal Mercier mode limits. Density
limits in tokamak are often related to the coupling between radiation collapse and disruptive MHD
instabilities, but the slow radiation collapse is dominant in the helical system. The pulse length of bothtokamak and helical systems is on the order of hours in small machines, and the longer-pulsed goodconfinement plasma operations compatible with radiative divertors are anticipated in both systems in the
future.

Keywords:
tokamak, helical system, plasma confinement, stability limit, density limit, steady-state operation

Wagner [2] by using L-mode tokamak database andmedium-sized stellarator database. In this paper, thiscomparison is updated using Elmy H-mode tokamak
database and recent helical confinement databaseincluding recent LHD data.

1. lntroduction
For realization of attractive fusion reactors, better
confinement and longer-pulsed operations should beachieved in addition to ignited plasma demonstration.
The burning physics and engineering integration are

explored by ITER []and wide range of plasma

2. Achieved Operational Domain

operations will be carried out by using more advanced
toroidal systems such as advanced tokamak and helicalsystems. There are several plasma operational limits: (l)confinemenr limit, (2) stability limit, (3) density limit,and (4) pulse-length limit. Here we would like to discuss

The maximum plasma parameters obtained intokamak and helical systems are summarized in Table 1.
The highest parameters of tokamak plasmas wereobtained in various machines such as JT-60U (highest
temperature, highest fusion triple product), JET (longest

on a variety of toroidal plasma operational limits

confinement time and highest stored energy), DIII-D(highest beta), Alcator-C (highest density) and TRIAMlM (longest duration); on the other hand a number ofhelical machines is still small and the Larse Helicalfocusing on the similarities and differences between
tokamaks and helical systems. Physics for plasma
operational boundaries should be clarified, and be

extended to the higher performance limit. A
comprehensive comparison has been done by Prof.

@2O02by The Japan Society of Plasma
Science and Nuclear Fusion Research

Corresponding author's e-mail: yamazaki@ nifs.ac.jp
28

Yamazaki K. et al., High Performance Operational Limits of Tokamak and Helical Systems

Table 1 Maximum plasma parameters achieved in tokamak and helical systems.
Electron TemperatureT" (keV)lon Temperature
T, (keV)

Confinement timere (s)

Fusion Triple Productni zE Ti (m-3.s. keV)

Stored Energy
we (MJ)
Beta Valuep(%lDensityn" (1020m-3)
Plasma Durationt a",

TOKAMAK(ASDEX-U,
JT-60U)HELICAL

25

45
1.2
1.1

(LHD)

5.0

(LHD)

0.36

(LHD)

(JT-60U)(JET)(JT-60U, NS)

1020 (JT-60U)(JET)
17(JT-60U, NS)
1140 (toroidal) (START)
12 (toroidal) (Dlll-D)
15 x

20

10

0.22 x

(LHD)
(LHD)

1.0

3.0 (average) (LHD,W7-AS)

3.6(W7-AS)

2 min

(LHD)
(ATF)

(Alcator-C)

2 min(Tore-Supra)
3 hr. 10min. (Triam-1 M)

TOKAMAK

1O2ot hourHELICALTOK. ASDEX* AUG
x CMODs COMPASS
s D3D
^ JET
JFT2M
a JT60Uo PBXM:! PDX
O TCV

B

STELL

6 CHS
x FFHR
g HELE
6 HSR
a LHD

B

MHR

a SPPSr: W7-AS

.001

.01

STELL

. ASDEX". AUG* CHS
x FFHRCMOD" CoMPASS
D30." JETv*

O HELE

Vrr

JFT2M" JT60U. PBXM
. PDX
. TCV

t,IHL

S HSR
- LHD

Oz

z SPPSMHR,:: W7-AS

P*

P*

Fig. 1 Operational regimes and reactor requirements in tokamak and helical system.

Device (LHD) produces almost all highest parameters.

normalized gyro-radius, plasma beta value andAt present, ttrere is still a parameter gap between

collsionality:

tokamaks and helical systems.
Not only absolute parameters, but also normalized
parameters are very important for the extrapolation of
the present database to the future reactor. Figure I
shows the operational domain for present machines andtokamak reactor SSTR [3], LHD-type helical reactors

p.=p"/a-^[T l@B),
F = nkT l82-nT / 82 ,v* = vela / v t- na t (es rz f'z)

MHR [4], by using normalized parameters such as
29

Yamazaki K. et al., High Performance Operational Limits of Tokamak and Helical Systems

The tokamak data used here are the Elmy H-mode data-

profiles make strong effect on the production ofbase (IPB-DB3v5) [1] and data from JT-60U advanced

confinement improvement modes. On the other hand, avariety of magnetic shear configurations can be

tokamak operation [5], and helical data are the mediumsized helical machine database [6] in addition to new
LHD data [4]. For extrapolation to the reactor, a few
factor reduction in p- is required for tokamaks; on theother hand, the helical system should make access to theone order of lower p- regime in the future. Even in thepresent helical database the low collisionality regime forreactors has been already explored.

produced by choosing helical coil systems. The q-profile

is reversed or flat, and the magnetic hill region exists
near the plasma edge in the conventional helical system.

The divertor configurations strongly depend on theplasma shape. The 2-dimentional tokamak system has

poloidal divertor with remote radiation. In helical

3. Equilibrium Properties
The standard tokamak is characterized by axisymmetric plasma shaping and external plasma current;

T il

1.5

the standard helical system is 3-dimensional

uj1

configuration and net-current-free operation. These
different plasma shapings give rise to different magnetic
confinement properties. Table 2 shows similarities anddifferences between tokamak and helical systems.
Example of rotational transform for tokamak andhelical systems is shown in Fig. 2. In tokamak systems,
magnetic shear is easily modified by the plasma current
distribution, for example normal shear discharges and

LH
0.5
JT-6010

GurrerHole,

0 0.2 0.4 0.6 0.8(A) Magnetic Configuration and Equilibrium
STANDARD TOKAMAKCONVENTIONAL HELICAL

Plasma Boundary
Shape

2D

2D

Magnetic Field
Components

Toroidal (m,n) = (1,0)

Toroidal (1,0) + Helical(L,M)+ Bumpy (0,M)

Divertor

Ripples

Poloidal divertor

No net toroidal current
or BS Current
Flat or
Reversed shear profile
Helical or island divertor

2D

3D

External + BS Currents

Normal or
Reversed shear profile(B) Physics Properties

Magnetic shear
Maqnetic Well
Radial Electric Field

Toroidal Viscosity
grad-j, grad-plsland, Ergodicity

1Fig. 2 Magnetic shear for tokamak and helical systems.

Table 2 Similarities and Differences between Tokamak and Helical Systems.

q-profile

'\:.r

rho

current hole discharges in JT-60U [7]. These shear

Plasma Currents/

JT. 0U Nr rmal I hear

STANDARD TOKAMAK
Substantial Shear or
Shearless in the core
Well in whole region
driven by toroidal rotation

CONVENTIONAL HELICAL& qrad-oloss (Helical Ripple)
Large (Helical Ripple)

Small
grad-j driven
qrad-p drive
near separatrix

30

Substantial Shear
Hill near edge
driven by non ambipolar

grad-p dominant
Edge Ergodic Layer

Yamazaki K. et al., High Performance Operational Limits of Tokamak and Helical Systems

magnetic layers give rise to differences in thesystems, helical divertor concept with rather large
divertor space is adopted in LHD. In the design ofperformance of plasma confinement.
These properties shown in Table 2 are described

modular helical systems the island divertor concept is
explored and its effectiveness is demonstrated [8]. The
divertor and scrape off layer are related to ergodicity

mainly for standard tokamak and conventional helicalconfigurations. At present, various advanced plasma
shapings for helical systems are proposed as shown in
Fig. 3. Some of them are sorts of tokamak-helical hybrid

and magnetic island, and differences in stochastic

aiming at disruption-free steady-state operations.

okamaktandard |--Standard-in,:mffif=r,,

4. Gonfinementmf:\:"
nii.rfrt.
L-ifh't:;-- a! I'il^r",i:l;;

o'-.,-,o*.*!DThe global plasma confinement scaling laws intokamak and helical plasmas are well established, Elmy
H-mode IPB98(y) [1] for tokamak and ISS95 for helical

.w

QP{FO

systems [6];?fr-w = 0.0365R

U=5\

Au*lPololdll SFrndry?lssesQO
AuslOmunlgenlty

*

"=.()

p - 0 63 - 0.41 B 0'08 to.x I 0 e'7, ( 1 )-- o.o79a22tR06sP-ose ltt no"o tll\ .

Q)

Where R, a, P,i.,B, €, t26 are major radius (unit: m),minor radius (m), heating power (MW), line-averaged
density (l0te/m3), inverse aspect ratio, and rotationaltransform at p = 213 in helical systems. These two scal-

QH
Qusl hllc.l SFmDby

1 e3

Larger M

Fig. 3 Advanced 3-dimentional plasma shaping

TOKAMAKHELICAL
TOK
ASDEX
AUG
CMOD
COMPASS
O D3D

STELL

.
*
x
o

{. CHSx FFHRn HELE
s HSR
A LHD

a JET

JFT2M

a JT60UMHR

e SPPSo W7-Ar W7-ASD PBXM;:: PDX

! TCV

r';*

rtr*
TOK
ASDEX

STELL

.
f AUC
x CMOD* COMPASS
9 D3D
5 JET

. CHS
. FFHR. HELE
, HSR
. LHD
' MHR
" SPPS. w7-AS

JFT2M

i JT60Uo PBXM,:: PDX
O TCV

71S.t95

1SS95
7uE

Fig. 4 Confinement scaling laws for tokamak and helical systems.

3l

Yamazaki K. et al., High Performance Operational Limits of Tokamak and Helical Systems

ing laws are shown in Fig. 4 within solid frames. To
compare database of tokamak and helical systems, wefield shear is driven by toroidal rotation and pressure
gradient. On the other hand, in helical system, radialused the simple formula of equivalent plasma current

electric field is driven by ripple loss predicted by neoclassical transport theory. In the low density regime the/"ou1u with average minor radius auu for helical systems:

-

u

-

aB,.

RB,

-\

neo-classical ITB near the plasma center was obtainedby the appearance of positive electric field in CHS [9].
The same phenomena have recently been observed in{F;;fi"@)'a,(r)n(m)r"lue)

LHD and the detailed physics will be clarified in the
future [10].

(3):- I _< o^,(*)'a,(r)Ir,r- " R(m)I"r",,(ro)5. Stability Limit
In tokamak systems ideal beta limits agree with

Figure 4 also shows a comparison between tokamak
confinement and helical confinement using rfiLMY andzfse5. The tokamak data scaled by using both confine-ideal MHD theory, and global beta scaling law is givenbya - Fg"tp^=___:___),,<3.5.

ment laws seem better than the scaled medium-sized helical data, however, the LHD data stays on the ITER
Elmy H mode scaling using the above equivalent plasma
current. Globally, tokamak and helical transports look
similar and of gyro-Bohm type,7!r-uv* XB p o83B-osuv;o 'o ,?Lsse5€ Tu p;0.1r B-u6V;o.M ,(4)I ,/laB ,)The pressure peaking effects on plasma stability are also
explained by the ideal MHD theory. Moreover, the resistive beta limits agree with neoclassical tearing mode
(NTM) or classical tearing mode (CTM) and resistive
wall mode (RWM). The kink-ballooning modes, which
are current driven mode coupled with pressure driven
mode, are restrictive in tokamak discharges. Figure 5
shows the agreement between experimental data andtheoretical analysis in JT-60U [1 1]. On the other hand,in helical system pressure driven modes are dominant.
In the LHD experiment, achieved beta value is beyond
the Mercier local mode theory, while the global mode
analyzed by Terpschore code [12] is still marginal. The
unstable mode structure is rather broad in tokamak, on
the other hand. the localized mode is crucial in helicalsystem. The low-n mode has an interchange-like structure, and the high-n mode has a ballooning-like one.

but, local transport seems different. The standard tokamak confinement near the center is determined bysawteeth oscillations, and helical core confinement is affected by helical ripple loss especially in the high temperature and low density regime.

The local transport, especially, the internaltransport barrier (ITB) looks different between tokamak
and helical systems. The tokamak has clear internaltransport barrier on electron and ion thermal transports
as obtained in JT-60U exoeriments. The radial electric

Equilibrium

4

z3

co-

....::::::.f2
high-Bp modery v
H-mode large po/<p>
0.2 0.4 0.6 0.8- I.-r'''Magnetic Axis Position (m)eFp

Fig. 5 Stability Limits in tokamak and helical systems.

JZ

Yamazaki K. et al., High Performance Operational Limits of Tokamak and Helical Systems

The current carrying toroidal plasmas are subject tothe existence of conducting wall. The global modes areeasily stabilized by the fitted wall. In helical systems,
the local mode is not linked to the wall, however, thein this figure. The density limit of helical plasmas does
not seem to be related to the magnetic rotational transform, which is different from the tokamak density limits. The radiation collapse in tokamaks often gives riseto plasma current quench; the helical high-density collapse leads to slow plasma decay.
To produce disruption-free tokamak discharges,
one of possible methods is to add external helical field
to tokamak plasmas. The complete suppression of major
disruption by applying external rotational transform I )0.14 had been demonstrated in W7A tl5l and JIPP T-II
stellarator [16] twenty years ago. We should check
experimentally whether this method is effective even instability of bootstrap (BS) current-carrying helicalsystems still depends on wall position.

6. Density Limit
The density limit is mainly related to thermal
power balance and the radiation collapse. In tokamaks

the plasma disruption is often related to the density
limits. The operational density regime is plotted byusing tokamak scaling (Greenwald scaling [13]) andhelical scaling (new scaling with modified coefficientfrom the helical scaling [14]).

the BS driven tokamaks.

7. Steady-State Operationh zo-cp.=. The longest pulsed operation is demonstrated in the

(s)

*2,

TRIAM-IM tokamak for 3 hours and l0minuts [7].
The long-pulsed higher performance discharges arel, , , *8,n2o_h"t=2'Minlv

carried out in Tore-Supra. The reactor requirement insteady-state tokamaks is to utilize BS currents and to
reduce the circulation power of the reactor plant. The
full non-inductive operation with 80 7o BS current
fractions and 20 Vo beam driven current has been
demonstrated in JT-60U [5].

_,;'Figure 6 denotes the density domain of the transport database used in Figs. I and 4, not real density limits. This
helical scaling can roughly fit to tokamak data as shown

TOKAMAKHELICALTOK. ASDEX
t AUG
x cMoor COMPASS
a o3D
r JET
. Jfl2M
e JT60U

ler20

n EXP

C PBXM

I TCV

lerl9

I e+21

STELL

. CHS
. HEE
"sD
1.+20

ft axp

I.;,

IMA
=.+
I8{lm
lerl8

le+18

le+19

1d2O

l.+18

1e+21

tr^ cn

1e+20

l6+18

1e+21

GR
TOK
. ASDEX

I
I

STELL

t CHS
r HEE
r LHD

x CMOD. COMPASS
. D3D
A JET
. Jfl2M
5 JT60U

I
I---t-----

: TCV

I

16+20

fl rno

lc+19

16+21

1.+20

h tno

Fig. 6 Operational density regime of tokamak and helical systems.

-t -fYamazaki K. et al., High Performance Operational Limits of Tokamak and Helical Systems

In helical system, it is easy to keep its magnetic

economical reactors based on quasi-axisymmetric (QA)

configuration in steady state, and the remained issue isto check compatibility between divertor and plasmaor quasi-poloidal (QP) configurations [18]. A lot ofcommon reactor engineering issues will be sheared

confinement.

between tokamak and helical desisns.

8. Reactor Prospect

9. Summary

As for reactor designs, one of critical issues forboth tokamak and helical systems is compatibility

Finally we can summarize the operational limits oftokamak and helical plasmas in Table 3. The magnetic
configuration in tokamak system can be easily changed

between system compactness and remote maintenancescheme. Especially, helical systems are supposed to be

by modifying plasma current distribution; in helicalrather large and not attractive from economicalsystems various plasma shapings by adopting the helicalcoil system give rise to a variety of magnetic properties.
Both global confinement properties are same such as
gyro-Bohm scaling. However, local transport is notsimilar between tokamak and helical system, especiallyradial electric field formation and internal transport

viewpoint. Figure 7 shows progress on reactor designfor making compact systems. Previous helical reactor
design has major radius of -20 meter, and now lowaspect-ratio designs with major radius of less than 10
meters are explored for the realization of compact andbarrier (ITB) properties. The plasma stability oftokamak might be determined by MHD theory related tocurrent driven and pressure driven modes; in helicalsystem the pressure-driven mode is dominant and theachieved pressure gradient is beyond Mercier mode
limits.
The realization of attractive fusion reactors, better
confinement and longer-pulsed operations should beachieved, in addition to burning plasma physics
clarification that will be performed in ITER [1]. In
tokamak systems, critical issue is to avoid disruption
and to demonstrate steady-state operation; in helical

30
25
20
R(m)

10

systems high performance discharges should bedemonstrated with reliable divertor, and compact design1970 1975 1980 1985 1990 1995 2000 2005 2010

concepts should be explored. Each magnetic
confinement concepts should be developed
complementally focusing on above critical issues
keeping their own merits, for realization of attractive

Year
Fig. 7 Progress on reactor design for making compact
and economical systems.

Table 3 Operational limits in tokamak and helical systems.
STANDARD TOKAMAK

Confinement

Beta Limit

Density Limit
Pulse-Length Limit

Beyond limit

Gyro-Bohm
Kink-Ballooning Mode
Resistive Wall Mode
Neoclassical Tearinq Mode
Radiation & MHD
Collapses
Recycling Control
Resistive Wall Mode
Neoclassical Tearinq Mode

Thermal collapse
Current quench

34

CONVENTIONAL HELICAL
Gyro-Bohm (Global)
Helical Ripple Effect(Local)Low-n Pressure-Driven Mode

Radiation Collapse
Recycling Control
Resistive mode (?)

Thermal collapse

Yamazaki K. et al., High Performance Operational Limits of Tokamak and Helical Systems

reactors and for clarification of common toroidal plasma

16l U. Stroth e/ a/., Nucl. Fusion 36, 1063 (1996).

confinement physics.

[7] T. Fujita et al., this conference.
[8] P. Grigull, this conference.
t9l A.Fujisawa et al.,Phy. Rev. Lett. 82,2669 (1999).
[0] K.Yamazaki et al., this conference.
I I ll S. Takeji. private communication.

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[3] Y. Seki, M. Kikuchi er al.. I3'h IAEA Conf. Plasma
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35