J. Plasma Fusion Res. SERIES, Vol.1 (1998) 9-16

Physics of Helical Confinement Systems
IIYOSHI Atsuo
National Institute for Fusion Science, Toki 509_5292, Japan(Received: 30 September L997 / Accepted: 22 October 1997)

Abstract
Recent stimulating studies that contributed to develop the physics of the helical systems are surveyed' In addition to exploring the advantage of the potential steady state operation, resolutions for the
problem, e.g., the trapping of energetic particle, existence of stable high-beta equilibrium, ripple
transport, etc.' have been investigated. The optimization directions in magnetic structure are(i) the high ro-tationaltransform, the high shear and moderate well, and (ii) the reduced secondary current and themagnetic well. Both of them try to utilize the radial electric field for the improvement. Representativesof these two are the LHD and W7-X devices. Further optimizing approaches, like quasi-symmetry, aresubject to studies. Experimental observations have been piled up. In this article it is emphasized that,based on these active works on the helical systems, the understanding of the general toroidal plasmas
has become deeper, even including the tokamak plasma as a special example. The investigations for de-veloping the helical systems have deepened the understanding of the nature of plasmas, and are some of
the most important achievements in the physics of high temperature plasmas.

Keywords:
helical plasma, recent progress, improve confinement regime, density and beta limits, divertor,
physics of electric field

1. Development of the Concept
The concept of stellarators has been first inventedby Spitzer[l]. In the beginning, the rotational transform, which is the very essential element of the toroidal
confinement, was realized by twisting the plasma column like "figure-8". Couples of ideas have emerged forthe confining magnetic field, and a class of confinement
schemes, which would be called as helical systems, hasgrown up. The inherent problem, which is the cost of
the potential steady state sustenance of the confinement, has been known, including the trapping of energetic particle, existence of high-beta equilibrium, stability at finite beta, ripple transport, etc. The concept
has been developed aiming to resolve such problems
and to form a path to a fusion reactor.
If I dare to simplify the evolution of research, thedirections of innovations have been seen in two majorgroups. (Fig.l) The optimization directions in magnetic
Corresponding author's e-mail: iiyoshi@ nifs.ac.jp

structure are(i) the high rotational transform, the high shear
and moderate well.

PlanerFig. 1 Two streams of the concept of helical systems andnew large scale experiments, LHD and W7-X.
@1998 by The Japan Society of Plasma
Science and Nuclear Fusion ResearchIiyoshi A., Physics of Helical Confinement Systems

empirical scaling. Recently the role of the magnetic
shear has been studied on W7-AS in detail[10]. In thecase that the rotational transform l/q (q: safety factor)
is close (but not identical) to the low-order rational
numbers, the low shear is favourable. (At the low-orderrational surface, pressure gradient may be suppressed.)
In contrast, when I/q is not close to such numbers,
then the magnetic shear is effective to reduce the anomalous transport. This sheds a light on the role of themagnetic shear in the low-shear systems. In Heliotron
configurations, the magnetic shear and rotational transform vary from Heliotron-E to CHS. However, themagnetic hill, one of the possible origins of anomaly,changes simultaneously. The quantitative identificationof the roles of the magnetic shear and rotational transform in Heliotrons requires further investigations. Theories, which are based on the first principle, are still incomplete to give quantitative understanding. The progress has been made for the turbulence in Heliotrons(ii) the reduced secondary current and the magnetic well.

Both of them try to utilize the radial electric field forthe improvement of the performance. Representativesof these two are the LHD and W7-X devices. The experiment on LHD[2] is near at hand. The constructionof W7-X[3] has been started. Further optimizing approaches, like quasi-symmetry, are subject to intensive
analysis[4]. Experimental observations have been piledup[5-7]. The understanding of the general toroidal
plasmas has become deeper, even including the tokamak plasma as a special example. On this occasion, it
would be intriguing to survey some of the recent moststimulating studies that contributed to develop thephysics of the helical systems.

2. Recent Progresses and Related Physics
2.1 Long-mean-free-Path regime
The possible loss of the ripple trapped particle haslong been recognized. The remedy was discussed in relation with the radial electric field[S, 9]. Recently, theelectron temperature as high as [(0) : 4 keV (or suchas f(0) : 1.6 keV) was achieved in W7-AS[10]' In116, l7l. Systematic test is required.

2.3 lmproved confinement
Owing to the intensive study, several types of improved confinement have been identified. As has been

CHS, the plasma of the temperature [(0)-2 keYwith the density of a few times 1018 m-3 is confined,

discussed. H-mode is studied on W7-AS and CHS routinely[l8, 19]. The high-Ti mode was found on Helio-

reaching much lower collisionality[11]. The radial electric field develops, together with the increased temperature, and the ripple loss is reduced. The ripple transport
could be less harmful in the present experiments than
was historically-concerned, if the enough radial electrictron-E, and was confirmed on CHS[20, 2Il. (Fig.z)
The high-Ti mode was also found on W7-AS[22], although it may not be identical to those of Heliotron-E
or CHS. The most stimulating is the improved confinement in the case of the NBI heating in W7-AS. The energy confinement time of 50 ms was achieved, which

field develops. Nevertheless, it is still a considerable
part of the total plasma loss in these cases, and thetolerance against the ripple loss in future devices
strongly depends on how the radial electric field behaves.

--c-L-mode

2.2 Anomalous transport and empirical scaling law
In present experiments, anomalous transport plays-<-high T mode

a dominant role. Empirical scaling law has been studied
Lzl mainly based on Heliotron configurations, and15,

on Wendelstein devices. A common scaling law has

90.

been proposed as International stellarator scaling law(ISS95X13] and is widely used. Comparative study in-;'0.

cluding tokamaks has been progressed[7, 1.4]. A factortwo improvement over this scaling is the immediate requirement for the future application to reactors.
Detailed study on the anomalous transport has
been piled up. Dependence on plasma Parameters has
been reported[15]. In L-mode, the effective thermal
conductivity is enhanced, if the temperature (or its

2.r5 2.2
R(m)Fig.2 lon temperature profile of the high-Ti mode

gradient) increased, as has been expected from the

Heliotron-E.
10

Iiyoshi A., Physics of Helical Confinement Systems

is twice high in comparison with the scaling law[23].
(Table 1.)

The physics of the high-Ti mode has been discussed. Common feature with the peaked profile in thepellet injection, reheat-mode[24] and high-Ti mode ispointed out[21]. One of the candidates for the origin of
the increment of the ion temperature is the enhanced
radial electric field. The neutral particles are the obstacle to establish the large radial electric field[9] andthe reduction of the neutrals is conjectured to lead tothe improvement. In conjunction with it, it should benoticed that the energy confinement is relatively improved in the case of the LID (local island divertor) experiments[25]. z, is improved, if normalized to thescaling law, by an amount of 20"/".

suggested there, but has not been discussed much further. The cause of the density limit has been consideredas the radiation instability. Study has been made, and

MARFE is observed as one cause of the density limit
on W7-AS[26].
2.5 Density profile
The knowledge of the density profile is also important: The peaked profile may be favourable for the bet-

ter fusion output. At the same time, high edge density
may be required for the high performance of the divertor functioning. So far, the high Ti mode correlates withpeaked density profile[21], and the improved confinement may require the particular types of the density

profile[7, 27]. The over-all request for the density

The absolute value of the improvement of 2", atpresent, is a few tens of percentage in many improved

profile of helical systems is not yet conclusive, but one
must clarify the rule that determines the density profile.

modes, although some parameter is improved consider-

The density peaking is dependent on the shift ofthe magnetic axis in CHS[28] (Fig.3). The direction ofably. The further study is keenly required.

2.4 Density limit
The limit of density is the key for the reactor concept. This is because the ISS95 scaling{aw suggests thatthe fusion triplet nz" Z scales likenrET q fBl'86 tor',arqz'e R0'31P-0.18 nt.02.

the 'pinch' changes. The study on the density profile
has suggested a possibility that the radial electric field
may play a role for the density peaking. Fairly flat density profile was observed on W7-AS. No strong inward

pinch was observed[7]. The impact of the magnetic
structure and the mechanism of the particle flow are theimportant future experimental subject.

For the given device parameters, the attainable fusion
triplet is controlled by the achievable density. Attempts
to assess the density limit have been given in[5, 1,2, L4,241. The fitting formula for experimental finding was

2.6 Beta limit and MHD activity
The MHD activity associated with the plasma current would be of secondary impact in helical systems;

Table 1 A number of improved confinement modes of helical systems arefound as in tokamaks.

Gonr linement Modesmr" (x101em-3)
Very low (<2)

low (-2.5)

mode
High
Te

CHS
2keV

high Ti r.cXS(o)
mode

H-E

= 0.7keVpelletmode
medium( - 4 )H.
ArE = 1570
mode

W7-AS
4keV

lNPAto) =1.1 keV
ATilo) < 80"/",lrtPA,cXSlO;

LrE<4@/o= 1.6 keV

tcxslo) = 0.7 keV
Alj(o) <6r/"
Mp4=0.5-1
ArE < 3oolo

rahElyy-2
te=50mshigh (-6)
reheal Lr1<2oo/omode

Iiyoshi A., Physics of Helical Confinement Systems

(c)

(a)

1 02t

Rax:92.1 cm

E l.s
?

E
o

:1
o

Rax=92.1 cm

e

I

o
-

I Rax=99.5 cm

5 lo'"

,

,a
I'

A

2*.Yr{-oq YAFArr J.
.|l|." 0.5 *fiS.'ca'i

q

o

t

I

a

0 0.2 0.4 0.6 0.8

Rax=92.1 cm

Rax:99.5 cm

1

10'-

o 0.2 0.4 0.6 0.8

1

Rax=99.5 cm

o 0.2 0.4 0.6 0.8

1

r/a

Radius (r/a)

Fig.3 Change of the density profile owing to the shift of the magnetic axis in CHS. Radial profiles of electron pressure(a),density profile (b) and' particle flux (c) are shown. Solid lines indicate the case where the major radius of the magnetic
plasma is shifted
axis is given as rgu, = g2.1 cm. Dashed lines are lor R",= 99.5 cm. Plasma is produced by ECH. As the(Seefordetails.]hollow.
even
profileflatter,(dashedbecomes[28]
thedensitylines),
outvvard

the pressure-driven activity, if any, is important. The
prospect of the achievable beta limit in future experi-

(a)

Ec)f

ments is based on the MHD theory of helical plasmas
12, 5, 291. The equilibrium study has confirmed the

..u

o_v

theoretical prediction, together with the optimization in
relation with the toroidal shift by finite beta effect[7].
The prediction for the MHD activities of high-beta
plasmas will be more dependable, if our understandingE

I 10.5111.5 112.5 113.5

is confirmed by the observations.

114.5

t (ms)

No drastic events have been found on CHS andrS

W7-AS in relation with the beta{imit up to the present
beta value (2.1 '/" for CHS[30] and 1.8 % for W7-AS[31]). An internal collapse has been observed on Heliotron-E with steep edge gradient[32], stimulating theunderstanding of the MHD activities in helical systems

(D)

uA

t331.

' --\\
-\

\\

.-

60"""

I

e-------->

Presently, the achieved beta is mainly bounded byconfinement and heating power. Under such circumstances, moderate MHD activity has been observed.

Detailed observations on the global activities havemade progress. Figure 4 shows the helical perturbationof the internal potential (CHS), and the internal struc-ila
Fig.4 Helical perturbation (m=21 is observed in the caseof NBI injection into CHS plasma. Temporal evolutions of magnetic perturbation measured byture of the perturbation is illustrated[34]. The perturbation has the wave form similar to the interchange
mode. Detailed tomographic reconstruction of the internal collapse has also been performed on Heliotron-E

Mirnov coil and static potential perturbation that is
obtained by HIBP are shown in (a). In (b), the radial
profile of the perturbed potential amplitude (fitted
by solid line) and q-profile are illustrated.

[3s1.

The other issue is Alfv6n eigen mode' Energetic
particles can drive fluctuations of Alfv6n waves, which
in turn could expel the high energy particles out of theplasma. The fluctuations of the family of the Alfv6n
eigenmode are identified in W7-AS when the plasma

beta value is increased[36]. High frequency oscillations,of which the frequency is well scaled to the real frequency of the toroidal Alfu6n eigen mode, are also
L2

Iiyoshi A., Physics of Helical Confinement Svstems

observed on CHS associated with the NBI injection

importance for the absolute trapping, neoclassical loss
and anomalous transport. CHS has provided a pictureof electric potential €ig. 6)[a3]. The interface of theradial electric field, across which the field changes
strongly, is observed. This is a hint for the momenturn[37]. At the moment, the fluctuation of the Alfu6n
eigenmode in W7-AS does not cause substantial loss.
However, the Alfu6n eigenmode in an asymmetricplasma has its own merit of study, ,'.e., how the continuous spectrum behaves in nonsymmetric plasmas[3g].

2.7 Divertor and edge control
In Heliotron configurations, helical divertor traces

200

bound the plasma-wall interactions[39]. In W7-AS theuse of intrinsic islands is planned[7].
The island divertor is applied to CHS. Enriched
plasma density at the pump duct and the reduction ofo w/O;tl ctr
W/O;r1co
I WlOir2coooothe effective particle confinement have been confirmed.

I25, 401 (Fig. 5.) Experiment on particle control shallbe studied. The reduced edge neutral density is led, and

E

!

D

I
50

islands has been demonstrated. It is expected that there

I

o1

100

F

the edge electron temperature is increased. On W7-AS.
the confinement of the dense-cold plasma in the edge

W Blid;tlctt
W Blid;rlco
W Blid:t26

o
A
tr

150

A
A

u

arises an E X B flow in the edge islands[7].

o3. Physics of Electric Field
3.1 Reduction of transport
Physics of the radial electric field has attracted

012345nel101scm-3]

Fig. 5 Reduction of the effective particle confinement (i.e.,much attention in the research of toroidal plasmas. One
is the suppression of neoclassical loss: This effect isbetter controllability of particles) is realized by the
local island divertor on CHS. Effective particle confinement time without LID (solid symbols) and with
LID (open symbols) are shown. Co and Ctr indicate
the direction of neutral beams. (See [40] for details.]

partly confirmed by the achievement of the high temperature plasmas in W7-AS experiment[10].
The other important subject is the reduction of
anomalous transport. In discharges which are illustrated

in Section 2.3, the strong electric field is generated.
There are experimental suggestions, e.g., for the pellet
mode, high-Ti mode and the case with high electron
temperature, though to be confirmed in future, thatstrong radial electric field is either one of causes of or isrelated with the improved confinement. More directcomparison has been made for tokamaks[41]. Theory
has been advanced associated with the H-mode physics[9]. A formula likexc(. 1I C(dE,/dr)2
was obtained for helical systems[l7, 421. The dependence of the coefficient Cin this formula was given, andtheoretical prediction has been discussed on the necessary level of E',. In present experiments of CHS, thegradient is not enough or marginal. Future experiments-1 -0.5-0.5 00.5

1pFig.6 Electric field structure which is measured by thewith stronger gradients are particularly interesting.

HIBP in the CHS plasmas. Low density ECH plasma(open circle), combined NBI and ECH heating

3.2 Structure
The structure of the radial electric field has vital

plasma (solid circle) and NBI heating case (opensquare). (See [45] for derails.)
13

Iiyoshi A., Physics of Helical Confinement Systems

future. More generally, there are abundant magnetic
activities in current-carrying systems like tokamaks. In
contrast, the electric dynamics could be dramatic intransport barrier. Such a situation will be a basis for the
future finding of the new state of improved confinement. Theoretical method for the analysis of the radial
electric field has been developed[9], and has been ap-

helical systems. The observations on the electric field in
CHS, combined with the knowledge on tokamaks, provide a physics basis to study the dynamical structuralformation and to explore the future progress of theplied to helical systems[44]. Qualitative agreement has
been reported except the interface, but further analysis
is still required.

physics in general.

3.3 Dynamics

4. Summary and Discussion

The dynamics of the electric field bifurcation is experimentally observed. Nonlinear relation in the radialcurrent and the electric field has been observed on CHS[+5]. (Fig.7) The nonlinear relation is the essence ofMany innovative physics ideas have been investigated in past to explore the concept of helical systems.
Many of the proposed schemes ofrthe improvements
have now been examined in experiments. Encouraging
observations have been obtained progressively, but

field bifurcation of toroidal plasma in general.
More exciting is the discovery of the potential pul-

there remain substantial challenges; they could be overcome only if all the intellectual efforts and innovations
will be put forward. Two streams of considerations will

the transition in the radial electric field. This measurement on CHS is the basis for understanding the electric

sation[46]. Electric bifurcation occurs periodically,

be experimentally tested in a near future, 1.e., LHD and
W7-X. Alternative approaches for optimization are in-realizing a new dynamical stationary state. In relation
with the H-mode physics, the periodic formation anddecay of the transport barrier have been predicted in
the theory[47]. This finding of the periodic pulsation
sheds a new insight of the stationary state in helical systems, as well as of the generation of the strong radial
electric field shear. The impact of these oscillations on
the achievable radial electric filed must be studied in(a)tr t=54.5 ms X(r=sz.o ms)

a t=55.0 ms

tt tl

5

"il*.

-o.5 0
p

0

^5

-1 0_

E

Bn

'--

cE

Ao
I

a

\r

I

t=5 6.6m

wry
-\

-5

N

-5

'f \t

.C

1

to

t'
t=54.7ms.lDynamic change is observed
I rl/ilfrililL(c) rotested fully on the coming new devices' The empirical
database may imply that there could be a difference ofthe confinement between the Heliotron and optimized
stellarator, but this could be concluded after LHD and(b) 10S"ttrrL...,'iU5(t=51-59rns) Y | !

.rrn-"

vestigated and shall be tested. The principles of optimization and the physics for the improvements should be

-\

vlllF

tl'"

'

v uavelet.

,r-\{"r, !l[rr:8$9P.
''

Er (V/cm)

-10

rl

-2 0

-- -- - f ittinq

2_4

rlrll

6

8

E,, (kV/m)
Fig.7 Electric field bifurcation is observed on CHS. Potential profile (solid line) and measured potential lust before (opensquare) and just after (solid circle) the transition are shown in (a). The E-J curve in (b) shows clearly the nonlinear bifurcation. Example of the neoclassical estimate is shown in (c). (See [45] for details')
T4

Iiyoshi A., Physics of Helical Confinement Systems

W7-X are operated at full performance with divertors.
The investigations for developing the helical systems have deepened the understanding of the nature of[15] F. Sano et a/., Nucl. Fusion 30, 81 (1990).
[16] K. ltoh et al,, Phys. Rev. I_Ett. 69,1050 (1992).
[17] K. ltoh et a/., Plasma Phys. Contr. Fusion 36, 123

plasmas, e.g., in the problems of the symmetry break-(ree4).

ing-and ergodization, turbulent transport, electric fieldbifurcation, etc. This understanding is some of the mostimportant achievements in the physics of high temperature plasmas. We wish that the science of the helicalconfinement systems could be judged by its academic
standard as well as by its impact to fusion research.

[18] V. Erckmann et al., Phys. Rev. Lett. 70, 2086
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Acknowledgmentof Fusion Energy (Montr6al, IAEA) IAEA-CN-

The Author would like to thank the help of Professors, K. Itoh, K. Matsuoka, K. Ida and A. Fujisawa,whose contribution forms the basis for the paper.

64/Ft-CP-s (1996).

l22lR. Jaenike et al.,Plasma Phys. Control. Fusion 37,
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16