J. Plasma Fusion Res. SERIES, Vol. 4 (2001) I I l-116

Ouasi-Axisymmetric Stellarator GHS-qa
MATSUOKA Keisuke*, OKAMURA Shoichi, NISHIMURA Shin, ISOBE Mitsutaka. SUZUKI Chihiro.
SHIMIZU AKihiTOI, FUJISAWA AKihidC, IDA KAtSUMi, MINAMI TAKAShi, IGUCHI HAruKAZU,YOSHIMURA Yasuo, NOMURA Izumi, OSAKABE Masaki, MURAKAMI Sadayoshi,
YOKOYAMA Masayuki, NAKAJIMA Noriyoshi, HAYASHI Takaya, ITOH Kimitaka,
NUEHRENBERG Juergen2, MERKEL peter2, DREVLAK Michael2,
NUEHRENBERG Carolin2, GORI Silvio2 andZILLE Regine2
Nationa.l Institute for Fusion Science, Toki 509_5292, Japan' Nagoya University, Nagoya 464-8603, Japan
2 Max -Planck-Institut

fuer plasmaphysik, Teilinstitut Greifswald,

IPP-EUMTOM Ass., D-17491 Greifswald, Germany(Received: 5 December 2000 / Accepted: 3 October 2001)

Abstract
The physics aspects of CHS-qa, a quasi-axisymmetric helical device, which is being designed as thepost-CHS device, are discussed. Its main objective is to improve the transport in helical systems by
reducing the parallel viscosity and by applying max. J criterion to its design. The parallel viscosity ismuch reduced compared with that in CHS and the max. J criterion is fulfilled at the region near the edgein the typical CHS-qa configuration. As an experimental device, a variety of knobs for controllingmagnetic field configuration are taken into consideration in the design to study transport-related physics
subjects: bifurcation phenomena of radial electric fietd and max. J criterion. Other physics requirements
which CHS-qa should satisfy as POP experiment, such as MHD characteristics, neoclassical transpon
aspects, are also discussed.

Keywords:
helical system, drift optimization, quasi-axisymmetry, improved transport, low viscosity, maximum J

1. Introduction

divergence-free, i.e. there is no Pfirsch-Schlueter
current, which leads to no neoclassical transport. The
Palumbo condition, which is also equivalent to the

As is well recognized, helical systems are free fromdifficulties inherent of equilibria for which a plasma
current is necessary: major disruptivity, recirculatingstatement that the magnetic field strength does not vary

power and elaborate current profile control.

perpendicular.to the field lines on magnetic surfaces,

Conventional helical systems, in spite of these merits,
have an inherent helical ripple, which has been believed

can unfortunately not be met in practical toroidal
devices, then one possible solution according to thisto induce a particle loss and an enhanced neoclassicaltransport in the low collisionality regime. From the point

guiding principle is to realize quasi-symmetry in helicalsystems. QHS (quasi helical symmetric system) [2] andQAS (quasi-axisymmetric sysrem) [3,4] concepts follow
this principle. QOS (quasi-omnigenous or quasi-

of drift optimization, where the particle drift orbit
coincides with the magnetic surface, Palumbo derived
the so-called Palumbo condition, i.e. the concept ofisodynamicity []. There, the diamagnetic current is*isodynamic system) of W7-X [5] relies on a@2001 by The Japan Society of Plasma
Science and Nuclear Fusion Research

C o rr e sp ondin g aut ho r' s e - mai I : mat s uo ka @ nifs. ac.j p

ll1

Matsuoka K. et al., Quasi-Axisymmetric Stellarator CHS-qa

1 component is inevitable for adjusting the magnetic
field strength to realize quasi-axisymmetry of which

generalization of the Palumbo condition, pursuing, inparticular., the reduction in Pfirsch-Schlueter andbasic magnetic field is given by an I = 2 toroidal helicalcomponent. By pursuing the low Ao guideline adopted in
CHS, Ae lower than that of CHS is selected, i.e. about 3-

bootstrap currents.

Lower aspect ratio (Ao), which is characteristic of
CHS, is satisfied in QAS configurations more easily

4, which results in the toroidal period number N of 2 for
CHS-qa according to the long pitch. The major radiusthan in other configurations, although recent QOS
design [6] can be of low Ao. Low Ao is practicallyand the magnetic field strength of CHS-qa are
determined to be 1.5 m and 1.5 Tesla, respectively,
mainly from facility constraints. Design studies haveimportant for an experimental device because it gives
large plasma volume and accessibility to ports. As wasshown in CHS experiment [7], helical ripples
substantially reduce the toroidal rotation velocity

been done from physics and engineering viewpoints

trr,r2l.

induced by NBI. The central rotation velocity increases
as the vacuum magnetic axis R"* is shifted inward,
where the central helical ripple is reduced from several
7o to almost zero with the shift. The velocity is mainly
determined by the parallel viscosity except for the
inward-shifted case. Low parallel viscosity is required
not to damp the rotation velocity induced spontaneously,
which should be one of necessary conditions to obtain

The optimization process on CHS-qa has been doneby using 43 variables (R., and Z.) to adjust theoutermosl magnelic surface. The rotational transform t,

QA-ness, magnetic well, local ballooning stability
criterion and a particle confinement are taken into
account in the process. Up to now the configuration
called 2b32, where the priority in the process was put on

the local ballooning stability, is considered to be mostthe velocity shear for the transport improvement.

preferable from the purpose of CHS-qa experimentbecause the optimization is also directed to the max. J
criterion. Fourier components of its magnetic fieldOn the other hand, as was shown in FM-l spherator

experiment [8], where trapped particles were located in
the good curvature region by controlling its magnetic

strength are shown in Fig. I as a function of thenormalized minor radius rla. As is seen from the figure

field structure with the vertical field, the particle
confinement time was strikingly improved because themax. J criterion was satisfied. The criterion is effective
to reduce the growth rate of micro-instabilities, i.e.

the 866 component, the measure of vacuum magnetic
well, is several Vo at the boundary, and B1s showing thetoroidicity is the dominant one. Typical cross-sections of
the magnetic surfaces along with the averaged magnetic
surface are shown in Fig. 2. It might be said that thecross-sections are decomposed into the axisymmetric
one and 3D shaping applied to it. The axisymmetricshape in the figure looks like a typical tokamak crosssection with moderate elongation and triangularity,
which are favorable for max. J criterion. It can also beseen from the vertically and horizontally elongatedcollisionless trapped particle instabilities, 4; modes andso on, and it is partially satisfied in the verticallyelongated tokamaks where the triangularity makes thecriterion to be satisfied more [9]. The confinement
improvement in the reversed shear tokamak
configuration may result from this criterion. Applicationof the max. J criterion to helical plasmas has been
discussed in the design study of LHD [10].
Unfortunately it was not successful for the criterion to
be realized in its design because of technical problems
on computation time. Because this criterion has beenshown to be effective for the confinement improvement

cross-sections that the outermost magnetic surfaces arestrongly affected with elongation and triangularity. The

in real experiments, the design effort incorporating thecriterion in helical systems should be one of most

optimized stellarators. It should be noted that the comet-

important subjects for toroidal plasma confinement.

account of the max. J criterion.

3D shaping determines physics characteristics oflike cross-section [3] is derived by taking primary
Neoclassical transport calculations on CHS-qa
without the radial electric fields show tokamak-likebehavior in the low collisionality regime [12,14], which
is much better than that of drift-optimized configurationof CHS where the bottom of helical ripple has the samevalue by shifting the position Ru* inward. The a particle
confinement is estimated in the reactor-relevant CHS-qa
configuration (5 Tesla, plasma volume of 1000 mr) [tS].

2. Physics Aspects of CHS-qa
Generally speaking, drift-optimized helical systems(QHS, QAS, QOS) inevitably require arather long pitchin their magnetic field configurations compared withheliotron / torsatrons. This is because of the role of an I

= I helical component which should be of long pitch,otherwise it becomes a simple solenoid. In QAS, the I =tt2

Matsuoka K. et al., Quasi-Axisymmetric Stellarator CHS-qa

aDN@
c)

.€
Helical ripple components

6 -0.05
{t)

(b)

o

8{1,0iB(0,1)- - --B(2,0)
- -

-o.1

Btl ,-r )-----B(2,-2)- --- B(r,1)
--

-0.15

- B(1 ,-2)-----B(4,-3)
-o.2

o

o.2

0.4
(r/a)

0.6

- B(3,-4)

Fig. 2 Magnetic surfaces of 2b32 configuration at three
typical toroidal cross-sections. (a) d = 0. (bl Q =4, lcl Q = nl2. The averaged cross-section is shown

B(0,0)

0.8

rl

Iin (d). lt is seen that the axisymmetric crosssection is composed of elongation andtriangularity.

Fig. 1 Fourier components of the magnetic field strengthof 2b32 configuration in the Boozer coordinare.

the direction to augment the external rotational

although it is different from the configuration of 2b32.

transform like in a tokamak. The increase in r brings
about a favorable effect on MHD properties, however

By shifting the residual ripples into the high field side,a particle confinement is improved. This might bebecause the banana tip has less possibility to encounterthe residual ripples. Compatibility with the 2b32

care should be taken for t not to cross the dangerous low
order rational surface. The current is estimated with the
NIFS bootstrap code under the temperature and density
profiles plausible for the experiment and the resultant r

configuration awaits a future work.
The Pfirsch-Schlueter current can not be eliminatedprofile for <B> of 1.37o is shown in Fig. 3. At present
the calculation is reliable up to <B> of about 1.52o.
When the rotational transform has the positive shear (drldY> 0, Y: the normalized toroidal flux) shown in the
figure, the bootstrap current, which is supposed topreferentially flow at the node of island, creates theradial magnetic field of which direction is to cancel the
perturbing radial magnetic field producing the island; it

in QA configurations. Nevertheless, the associatedproblem of the Shafranov shift is eliminated by plasma

shaping: the configuration 2b32 shows a nearly
vanishing Shafranov shift compared with other CHS-qa

configurations. The strong reduction in the parallelviscosity in the toroidal direction, described later, isselected at the expense of P.S. current in CHS-qa. By
using 3D MHD equilibrium code HINT [16] where thestabilizes the neoclassical tearing mode.

existence of magnetic surfaces is not assumed a priori,

MHD calculation on the Mercier criterion gives
stability <f> of about 5Vo under the pressure profile ofthe fragility of magnetic surfaces is examined. It isshown that up to the volume averaged beta <B> of about(1-Y';t s. In CHS and LHD, <B> values obtained in the

3Vo clean magnetic surfaces are kept under the condition

real experiments are higher than those predicted by thecriterion tl7-191. However, in the CHS configuration
shifted more inward than the optimized one, where themagnetic hill is even enhanced, MHD instabilities

of no net current and rather flattened pressure profile.
The calculation taking account of net current due to thebootstrap and Ohkawa currents is under way. It is
expected that rotational transform profile shaping by thenet current may help to avoid resonances.
In QA configuration, the bootstrap cuffent flows inlimiting the stored energy have been observed, showingthat the Mercier criterion is valid as a rough guideline of

the achievable <F> prediction. Because min. B is113

Matsuoka K. et al., Quasi-Axisymmetric Stellarator CHS-qa(a)profile giving <p> of l.3%o. Beyond the current ofaround 150 kA corresponding to <p> of about 4Vo, t
crosses over 0.5 and the mln=Zll external kink modegets unstable. In the experiments in JIPP T-II and W7-n"(O) {ixed to be 2.0x101e m-3

scanning T from 0.3 lo 7 keV

250

200

O tbs(zt'3e) {kA) i wc
r lbs(2b32) (kA) ; NWC

A, no current disruption was observed when the externalr is larger than 0.14 t20,211. The external t is shown toenlarge the stability window l22l and to produce the(ilc reachs 20)

g 150
o
E 1oo

restoring force against the displacement of the currenttt

carrying plasma column, irrespective of theIdisplacement direction. These have been considered tobe the cause of no disruption, however, recent W7-AS

.,II

50

.I

0.5

.f-.

1 1.s 2experiments [23] show that major disruptions occur
occasionally. The situation, where the disruption is
avoided even when the total I crosses over 0.5, is alsostudied in W7-AS, and it gives us the clue to operate
CHS-qa by controlling r profile with Ohkawa and OH
currents when the total t exceeds 0.5 because of thebootstrap current as <B> increases up to 4 ot 57o,although more calculation studies on external kink and2.5

Ave. beta (%)

tearing modes are needed.

The velocity shear is known to be one of thestabilizing mechanisms of micro-instabilities. The
motivation of the QA concept is in obtaining a strong
toroidal rotation velocity. Actually in CHS-qa the

E 4.4
o
o
F

toroidal velocity will be determined primarily by theanomalous perpendicular viscosity as in a tokamak andi.E 0.2
6

will be up to the level where VH-mode and H-mode areobserved in DIII-D l24l and JFT-2M [25]' respectively'

E o.t

The poloidal viscosity is also calculated for CHS-qa andis shown to be determined mainly by its high effective

6

v.J

-o

0

A, i.e. relatively small B1e component [26]. The low
o.2

0.4

(r/a)

0.6

0.8

toroidal and poloidal viscosities will be helpful forachieving transport improvement. The H-mode in W7AS is correlated with the reduction in the poloidal
viscosity [27]. Bifurcation phenomena observed intokamaks can be expected to occur in CHS-qa' and ITB
observed in CHS [28] is also expected to occur by

1

Fig. 3 lota profiles for vacuum magnetic field and thatwith finite beta of .F> = 1.3%. At the finite B
oositive shear of dt/dY> 0 is realized.

increasing the mirror ripple which is to be controlled bysatisfied in a sense of the average in CHS-qa' thechanging the current ratio of two groups of main
modular coils [29,30]. In Fig. 4 the particle flux
determining the radial electric field is schematicallyshown as a function of the helical ripple. Here, the flux
due to the bulk viscosity is also shown as an example

stability against local ballooning modes is examined by

TERPSICHORE code. The local ballooning modestability, which should be more pessimistic than realplasmas, gives <B> stable up to 3Vo. Ideal kink modes
are also estimated by TERPSICHORE under the plasma
current of which value is 100 kA and of which profile isother than the neoclassical flux. It is shown that theradial electric field is uniquely determined by theelaborately tailored, and it is shown that 3D shaping of
CHS-qa stabilizes the modes although the modes are
unstable for the averaged cross-section without the 3D
shaping. Ideal kink modes are examined by using
CAS3D code, too. Here is assumed the current profile toneoclassical non-ambipolar diffusions when the ripple isabott l\Vo, under which situation the bifurcation withpositive radial electric field is expected as in CHS.
When the ripple is reduced to about l%o, the fluxes due
to such as bulk viscosity, loss-cone loss and charge

be the bootstrap current one obtained from the pressure

tt4Matsuoka K. er c/., Quasi-Axisymmetric Stellarator CHS-qa

Finally, the flexibility is important for an
experimental device; the current ratio not only of 3 pairsof poloidal field coils (for R* shift, quadrupole magnetic

CtxE

field, OH current) but also of main and additional
modular coils (for mirror ripple and r controls,

nr

respectively) can be controlled in CHS-qa. In addition tothis, Ohkawa current will play an important role incontrolling the r profile. Further, a divertor study which

0.01

also is of great experimental importance awaits future
work.
gH

3. Discussion and Conclusion
So-called optimized stellarators might becharacterized by a variety of 3D shaping which isFig. 4 The particle flux as a function of helical ripple.
When the ripple is large (about 10%) the radial

electric field is uniquely determined by theapplied to an axisymmetric magnetic field configuration.

neoclassical fluxes. At the reduced ripple (about
1%l the flux due to the bulk viscosity becomescomparable to the neoclassical one. The fluxes
due to such as bulk viscosity, loss cone loss andcharge exchange loss, will also play an importantrole in determining the radial electric field.

It should be necessary for the axisymmetric shape tohave one with both of elongation and triangularity forgood confinement properties, which has been wellestablished in tokamak experiments. If the omnigeneity
is not lost by the 3D shaping, it might bring about goodeffects on toroidal plasma confinement. One example isthe stabilizing effect on MHD modes related to the net
plasma current. Among knobs for flexible experiments

exchange loss become comparable to the neoclassicalone. There the bifurcation with negative radial electricfield seen in tokamaks is expected.
The max. J criterion is satisfied in the magnetic
configuration with the magnetic well and the shear of

the most important one should be the mirror ripple,
because this is related to conflicting requirements. For
the a particle confinement it might be necessary to shift
the residual ripples to the high field side, on the other

dtldY> 0 [9]. Collisionless trapped particle instabilities
are excited when the toroidal drift velocity of ion

hand, to satisfy max. J criterion the banana has to(electron) banana is parallel to the toroidal componentof ion (electron) diamagnetic drift velocity. The criterion
is satisfied more for barely trapped bananas than forexperience some bumpiness at the low field side [31] toreduce its parallel velocity.

deeply trapped ones, because the former experiences thecompactness, low disruptivity, low recirculationg power

good curvature region more than the latter. In usual
tokamak configurations without the reversed shear, it isdifficult for banana particles to satisfy the drift reversal
because of the negative shear of dt/dY < 0. However, in
CHS-qa the magnetic field configuration has a favorable
characteristics that the average magnetic well in vacuum
and the positive shear (stellarator shear) of drldy > 0
due to the bootstrap current are satisfied as is shown in
Fig. I and 3, respectively. Recent detailed calculationshows that because of small non-axisymmetric Fouriercomponents growing outwards shown in Fig. I theparallel velocity for max. J calculation gets reduced near
the boundary, which results in max. J configuration
there. The extent of the region where the criterion issatisfied can be changed, for example, by controlling thevacuum magnetic axis position Ru* [31]. Controllabilityof max. J with other means, for example the mirror
ripple, awaits a future work.

CHS-qa can place itself in a unique position to study theconfinement improvement among a variety of toroidal

In conclusion, by keeping advantages ofplasma confinement devices. This experiment will
elucidate the role of magnetic field structures on theplasma confinement.

Acknowledgements
The authors would like to acknowledge Dr. W.A.
Cooper for his calculation on ideal kink modes with his
TERPSICHORE code and also to express their gratitude

to Director-general M. Fujiwara for his continuing
encouragement.

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