J. Plasma Fusion Res. SERIES, Vol.5 (2002) 149-155

Stellarator Fusion Reactors - an Overview
BEIDLER Craig D., HARMEYER Ewald, HERRNEGGER Franz, KISSLINGER Johann,
IGITKHANOV Yuri and WOBIG Horstr
Max-Planck Institut ftir Plasmaphysik, EUMTOM Association D-85740 Garching bei Miinchen, Germany(Received: 11 December 2OOl I Accepted: 4 June 2OO2)

Abstract
The stellarator system offers a distinct alternative to the mainline approaches to magnetic fusion
power and has several potentially major advantages. Since the first proposal of the stellarator concept
many reactor studies have been published and these studies reflect the large variety of stellarator
configurations. The main representatives are the continuous-coil configurations and the modular-coilconfigurations. As a continuation of the LHD experiment two reactor configurations, FFHRI andFFHR2, have been investigated, which use continuous helical windings for providing the magnetic field.
The modular coil concept has been realized in the MHH-reactor study (USA 1997) and in the Helias
reactor. The Helias reactor combines the principle of plasma optimisation with a modular coil system.
The paper also discusses the issues associated with the blanket and the maintenance process. Stellarator
configurations with continuous coils such as LHD possess a natural helical divertor, which can be usedfavourably for impurity control. In advanced stellarators with modular coils the same goal can beachieved by the island divertor. Plasma parameters in the various stellarator reactors are computed on thebasis o1'presently known scaling laws showing that confinement is sufficiently good to provide ignitionand self--sustained burn.

Keywords:
stellarator, fusion reactor, modular coil, helical system, power balance

1. Introduction

current drive. Its coil configuration permits access to thedevice from all sides and facilitates a modular approach

The main properties of a stellarator reactor are thepotential of steady-state operation and the absence of
current disruption; a summary of the main features is

to blanket and shield design. Since stellarators andtorsatrons can operate free of induced toroidal current

given in Table 1. The steady-state magnetic fields

and do not suffer from major plasma disruptions, themajor concern of an excessive energy dump on the firstwall and plasma facing components can be eliminated.

simplify superconducting magnet design, remove theneed for pulsed superconducting coils, and eliminate
energy storage required to drive pulsed coils. Plasma

2. Stellarator Reactors

confinement during startup and shutdown is aided by thepresence of magnetic surfaces at all times during this

Early stellarator reactor designs 11,2,3,4) concluded
that the coupled problems of high coil cost and low
system power density (i.e., low beta) were particularly

phase. Steady-state plasma operation after ignition is an

outstanding advantage of the stellarator concept.
A stellarator can have a relatively high aspect ratio
and does not require expensive complicating auxiliary
magnets for field shaping, position control coils andsevere for the classical stellarator. A particulardisadvantage of the classical stellarator configuration@20O2 by The Japan Society of Plasmat

C o rre s p ondin.g autho r' s e -mail : w obi g @ ipp. mp g. de

Science and Nuclear Fusion Researcht49

Beidler C.D. et al., Stellmator Fusion Reactors - an Overview

Table 1 Main features of a stellarator reactor

Table 2 Helical system reactors

o Steady-state magnetic fields. No induced eddy
.
r
r
r
.
.

currents. No enhanced fatigue of the structure
due to pulsed thermal load.
Steady-state operation at high A, A-> *.
No energy storage and low recirculating power
requirements.
Moderate plasma aspect ratio (8-12) which offers
good access to the reactor core.
Start-up on existing magnetic surfaces with good
confinement at all instances.
No positioning or field shaping coils necessary.
No major disruptions that could lead to an energy

dump on the first wall or on the divertor target.
r

plates.

Several potential methods for impurity control
and ash removal exist. Magnetic islands at theplasma edge can be used for divertor action
No toroidal current drive is required.

Parameters

FFHRl

Major radius[m]
Av. radius of coils[m]
Coil current[MAturns]
Plasma radius[m]
Plasma volume[mt]Magnetic field B(0)tTl
Max. field on coils
tTl
Average beta
l%1
Density n(0)[m-']Temperature f(0)[keV]
Fusion power
IMW]
Polarity /Field periods
Magnet. energy
IGJI

20
3.33

66.6
2

FFHR2
10

2.3
50
1.2

579

284

12

14
0.7

10
13
1.8

2x1O2o2.8x1020

22

27
1000
2

1

3000
3
18

1290

10

147

coils. The thermal output is on the order of 4000 MW.

The study on the modular stellarator ASRA6C was
carried out in 1987 as a joint effort of IPP Garching,
KfK Karlsruhe and the University of Wisconsin [14].
This study was based on the Wendelstein 7-AS
configuration and the aim was directed towards theclarification of critical issues of an advanced modular

arises from the interaction between the toroidal fieldcoils and the helical windings. The torsatron [5,6] andmodular-coil configurations [7,8], however, show strong
promise for alleviating the coil problem per se.

The MIT T-l torsatron design [6] was the firststudy of a torsatron reactor. It reflects an attempt toreduce the total power output to < 4 GWt under theassumption of conservative beta limits. Helical reactor

stellarator reactor and was not meant as a point design.
The MHH is a 4-period modular stellarator reactor,
which has been designed in ajoint effort by a group of

fusion laboratories in the USA [5]. The approach issimilar to that used in the ARIES-tokamak reactor

design studies are based on the LHD-concept, which has

been developed at the National Institute of Fusion
Studies (NIFS) in Toki, Japan. The LHD-experiment is
a torsatron with / = 2 helical windings and 10 field
periods [9] and the advantage of the LHD-concept is thestudies [16]: an integrated physics, engineering, reactor
component and cost optimisation. This stellarator power
plant study is the first attempt at an integrated design ofnatural divertor with two X-points, which helicallya stellarator reactor addressing all major components ofencircle the plasma. Apart from this helical structure it

the plant: the physics base, the coil system, the blanket,

has many features in common with the tokamak

maintenance, the power balance and, last but not least,
the cost analysis. The magnetic configuration isbasically a Heliac including elements of optimisation as

divertor. Two versions of the LHD-type reactor exist:
the Force-Free Helical Reactor (FFHR [10,] l]) and theModular Helical Reactor (MHR t12l). The main featureof the FFHR is the arrangement of the helical windings

have been developed in the Helias concept. This
explains the name: Modular Helias-like Heliac (MHH,in such a way that the forces on the helical windings areminimized. This requirement leads to an I = 3 systemwith l8 field periods (see Table 2).
The first studies of modular stellarator reactors

see Table 3).

The method to calculate the coil system after themagnetic field has been specified offers the chance tooptimize the magnetic field first according to criteria of
optimum plasma performance [17] and then to compute

started from the well-known magnetic field
configurations, which before have been realized byhelical windings and toroidal field coils. The UWTORM reactor [13], designed at the University of Wisconsin,
is one of the first devices utilising the concept of

the coil system after this procedure has come to amodular coils. The modular stellarator reactor (MSR)

the Wendelstein 7-X device U9l, which will
demonstrate the reactor capability of the advanced

satisfying result. Along this line the advanced stellarator[18] has been developed. The concept of modular coils
and the principle of optimisation have been combined indeveloped at the Los Alamos Laboratories is a classicalI = 2, m = 6 configuration generated by 24 modular

stellarator line. HSR5/22 and HSR4/18 are fusion
r50

Beidler C.D. et al., Stellarutor Fusion Reactors - an Overvrew

Table 3 Modular coil reactors
Parameters

Major radius[m]
Av. radius of coils[m]
Coil current[MAturns]
Number of modular coils
Av. plasma radius[m]
Plasma volume[mt]Magnetic field B(0)ITI
Max. field on coils
ITI
Average beta
I%l

DensiV <n>Temperature <I>
Fusion power
Field periods
Magnet. energy

superconductor, which avoids heat treatment after the
MHH

HSR4/18

14

18
5.5
10.8

4.75
13.8
32
1.63

735
4.94
14.5
5

winding procedure. Modular coils offer the chance tobe fabricated separately and be tested before installingthese into the reactor. Heat treatment is possible also
after finishing the winding process. Spacing beween
modular coils should be small to avoid ripple trappingof localized particles, however this conflicts with therequirements for maintenance. Maintenance throughportholes needs sufficiently large gaps between adjacentcoils. In the Helias reactor HSR5/22 or HSR4/18, l0

40
2.1

1567
5
10.3
3.7

[m-t]
[keV]

1.3x1020
10

2x1O2o

tMWl

1730
4

3000
4

IGJI

80

100

coils per period turned out to be a compromise between
physics requirements and the need for sufficient access.

15

In MHH the alternative method has been choosen: awhole sector of the coil system together with the blanket
will be moved horizontally and replacement of blanket
and divertor components occurs through the horizontal

This list displays only the recent stellarator reactors.
(MHH data from ref. [15]).

gaps. The critical issue of this procedure is theseperation and reconnection of the sector, which must be
done by remote control in a radioactive environment.
With respect to maintenance the continuous helical coilapproach is the ideal one, since sufficiently large gaps
between helical windings exist and access to the blanket
and the divertor is possible nearly everywhere.

reactors based on this concept.

The main criteria in designing stellarator reactors
are the space needed for a breeding blanket and shield

and the conditions of self-sustained bum. The size ofblanket and shield depends on atomic physics and ismore or less the same in all fusion devices; it is on theorder of 1-1.3 m. Any stellarator reactor must be large
enough to accomodate a blanket. The confinement timemust satisfy the Lawson conditon ntE> 2xl02o, which

3. Blanket in Stellarator Reactors
As in any toroidal fusion device the purpose of theblanket is to provide sufficient breeding of tritium andto shield the superconducting coils against neutrons. The

implies that the confinement time must be about 1-2
seconds. Any chance to operate the reactor at highsize of the blanket and its radial width is an absolute
figure and any fusion device has to provide enoughspace to accomodate a blanket with about l.3m radialbuild. In contrast to tokamaks the stellarator, however,requires a 3-dimensional design of the blanket, which

density relaxes the requirements on the confinement
time.

Another design parameter is the magnetic fieldstrength, which should be large enough to provide

sufficient confinement and high magnetic pressure(small beta values) while on the other hand it should bemust conform to the 3-dimensional shape of the plasma.

small to avoid large mechanical forces in the coils andexpensive superconductors. Feasibility of the coilsystem and maintainability of the blanket are otherreplaceable through portholes, therefore a stellarator

Blanket segments must be small enough to beneeds a large variety of different modules, which in caseof the Helias reactor HSR22 are 25O comprising 25
different shapes. The various blanket concepts, which

important design criteria. Since there is no consensus yet
on a priority list among these criteria, stellarator reactor

have been studied for tokamak reactors [20], are also
suited for stellarators. The MHH-design favours a selfcooled lithium blanket while in the FFHRI and FFHR2
molten salt FLIBE (LiF-BeF2) has been selected [21].
Either a solid breeder blanket (HCPB [22]) or a liquid
LiPb blanket with additional cooling [23] are the options

concepts differs appreciably with respect to size,
magnetic field and layout of the blanket.
The magnet system is the most expensive
component of the reactor core and for this reason acareful optimisation is required. The continuous coilsystem as realized in FFHR1 and FFHR2 is a large item,
which must be fabricated on the site of the reactor.
Since superconducting coils on Nb3Sn basis require thewind-and-react technique large helical windings must
either use NbTi-superconductors or anotherin the Helias reactor HSR5/22 [24]. Blanket design
developed for NET and DEMO reactors have been
adapted to the stellarator reactor by W. Daenner [251.

At present no decision can be made as to whichblanket concept is the optimum for stellarators. The
151

Beidler C.D. et al., Stellarator Fusion Reactors - an Overview

three-dimensional geometry requires a careful

Depending on the stellarator type, divertors are
realized in different ways. In moderate to high-shear
heliotrons like Heliotron E. CHS and LHD. one canmake use of intrinsic diverting field lines to create aengineering design taking into account the maintenanceprocedure and the safety requirements. With respect tosafety a helium-cooled ceramic breeder is very

helical divertor. By employing additional field
perturbation coils these devices benefit from theadditional flexibility to create externally imposedfavourable, however the large amount of beryllium andthe accumulation of tritium in the blanket makes
reprocessing of the breeder cassettes necessary. Also theislands, which allow the installation of a so-called local
island divertor [ID). In low-shear advanced stellarators
like W7-AS and W7-X, one makes use of the intrinsic
islands [26]. Recent experiments in Wendelstein 7-AS
have demonstrated the efficiency of the island divertor
in realizing a high density plasma detached from thedivertor target plates [27].

size of the blanket segments depends on the available
space, the accessibility and the type of the breeder. Witha liquid breeder relatively large segments can beinstalled in a Helias reactor; before maintenance thebreeder material will be drained into a dump tank andthe empty container can be removed through portholes.

In all stellarator-reactor concepts the average
neutron wall load turned out to be rather small, peakvalues are below 2 MWm-2. This results from the ratio
between plasma surface and plasma volume, which
increases with major radius. This simple geometrical
relation makes a large aspect ratio stellarator morefavourable for neutron wall load than a small aspectratio tokamak, provided the plasma volume and thefusion power are the same. This circumstance has abeneficial effect on the lifetime of first wall and blanket;
in MHH a lifetime of 11 years has been estimated. Thisestimate also holds for the Helias reactors while in
FFHR the lifetime is 10 years. However, the number ofblanket elements to be replaced during down time islarger than in the equivalent tokamak, and therefore thelong lifetime of the structural material in stellarators isonly an advantage if by parallel operation the time formaintenance in stellarators is the same as in a tokamak

5. Operational Limits
In stellarators the density limit and the beta limit
define the operational regime of the fusion plasma.
Since a large toroidal current does not exist, also nolimit on the rotational transform exists, which isnecessary to prevent tearing modes and disruptions.

Even if in quasi-axisymmetric stellarators a finite
bootstrap current exists, any disruption of this current

will be mitigated by the external stellarator field. In
contrast to tokamak reactors, where the Greenwald
limit keeps the average density in the range of<n>=lx!O2o m-3, stellarators can reach a line averaged
density of 3.5x1020 m-3 1271. The density limit is aradiative limit and can be explained as the result of thepower balance. In a fusion plasma, however, the alphaheating power grows with the square of the density,
which implies that a radiative density limit, in principle,
does not exist in a fusion plasma. But in the start-up
phase, when the external heating power is large and thealpha-heating power is small, the radiative losses areimportant and an appropriate route to ignition must bereactor.

4. Divertor
In early stellarator reactor studies little attention has
been paid to the divertor problem. In the meantime,
however, theoretical and experimental results havestrongly increased the data base on divertor action, andfound.

Numerical investigations of the MHD-stability inHelias configurations have shown stability up to an
averaged beta of 5Vo [28]. Stability analysis using
CAS3D has shown that the equilibrium of HSR4/18 atthe design activity of Wendelstein l-X and theexperiments in LHD and Wendelstein 7-AS havecontributed a large amount of experience to the physics
and technology of divertors in stellarator geometry. The
basic requirement for the divertor in stellarators is thesame as in tokamaks: the divertor should protect the firstwall from excessive thermal load and thus diminish the<F>=4.37o is unstable against global modes in theboundary regions, while at <F>=3.5Vo these modes arestable. In tokamaks neoclassical tearing modes threaten
to lower the MHD-beta limit. Even if small bootstrap

influx of impurity ions released from the wall. In

currents occur in stellarators the positive shear t'

tokamaks the separatrix and the associated X-point arestabilizes neoclassical tearing modes.
Neoclassical ripple losses provide a special loss
mechanism in stellarators and due to the strong increase
with temperature (1n"o-(e" rr1t'sT3 I 182 R2;; the ripple-

axisymmetric while in stellarators the X-point-likestructure follows the coil system or the helical shape ofsthe last masnetic surface.
152

Beidler C.D. et al., Stellarator Fusion Reactors - an Overvrew

induced loss can be prohibitive to ignition. For thisTable 4 Exponents of empirical scaling laws

reason the effective helical ripple has been minimised to

LGS lSS95 \M795 New New
LHD1 LHD2
t31l I32l

Iess than 0.01 in the Helias configuration. In the LHD

device this effective ripple can also be reducedc"appreciably. Furthermore, operating the fusion plasma at

low temperature helps to make ripple losses small. Thus
it is expected lhat an effective helical ripple of 0.01 is
tolerable.
The most desirable temperature regime in a fusion
plasma is the region between l0 keV and 20 keV since(with plasma beta fixed) the fusion power output has amaximum in this region. The Lawson parametet <n>tE
has its minimum in this region and the requirements on
the energy confinement are the weakest: <n>re>2x1020.
The possibility to choose the average density in the
Helias reactor in the range of <n>=2-3x1020 m-3 puts

-0.6

0.256
-0.59

1

0.263

0.115

-0.58
0.64

-0.64

0.65

0.36
-0.54
0.74

2

2.21

2.21

2.59

2.09

0.8

0.83
0.4

0.73
0.43

1.01

0.85

0.0

0.0

0.51

0.5

0.51

0.54

0.21

Pa5
Ral
aa2
Ba3
ta7
<n> a4

0.4
0.6

1.O2

= C oR"r aaz Ba3 arra4 Pa5 ra6,
The coefficients are listed in Table 4. Units: s, m, m,
Tn

Tesla, l02om-3, MW.
A possible isotope effect has not been included inless stringent requirements on the necessaryconfinement tirne than in a tokamak reactor with lower

the empirical scaling laws. The geometry of the plasma
column is described by two parameters only, the major

densities. In summary, the parameter regime of astellarator fusion plasma isr Average density <n> = 2-3xl02o m-3
o Average beta< 4Vo
o Temperature regime Z-u* < 20 keV. Energy confinement time z6 = | - 2 s
Due to the chance to operate at high density the requirement on the confinement time in the stelllarator reactor
is reduced; the required confinement time is beween I
and 2 seconds. The fusion triple product <n><T>r"isroughly a factor of two smaller than in a tokamak powerreactor, where the temperature is about a factor of two
higher.

radius and the effective minor radius a, ellipticalelongation or triangularity have not yet been introduced
as in tokamaks. The toroidal variation of the plasma
cross section is included in the definition of the effective
minor radius. NLHDl-scaling and NlHD2-scaling [33]do not depend on the rotational transform, however theexperimental data of Wendelstein 7-AS indicate adependence on the rotational transform and therefore
they support the Lackner-Gottardi scaling law in thisrespect.

Good confinement of highly energetic alphaparticles is a necessary condition for self-sustaining burnof the fusion process in a stellarator reactor. In thiscontext the following problems are of importance:

6. Fusion Plasma in Stellarators
Power balance in stellarator reactors has been

sufficient confinement of trapped alpha particles, a small
number of particles trapped in the modular ripple,
anomalous losses of alpha particles by plasma
oscillations. In the present reactor configurations HSR5/
22 and HSR4/18, the number of lost alphas is smaller or
equal to 2.5Vo; thus only 2.5Vo of the heating power islost by poorly confined alpha particles. Further finetuning of the magnetic field is possible to improve theconfinement of alpha particles further.

studied by various methods: local transport calculations

using ASTRA [29] and the TOTAL_P-code, andextrapolation of empirical scaling laws of stellarator

confinement to reactor conditions [30]. The lattermethod allows one to make quick parameter studies. In
order to check whether the empirical confinement times
allow for ignition the following procedure is applied:
starting from the design parameters including the plasma
profiles the required confinement and the confinement
times from empirical laws are computed. As a guideline
to model the plasma profiles the results of the ASTRAcode were usecl. Parameter studies have been made to
explore the dependence on the shape of the profiles.
The scaling laws used in the following procedure
are described by a power law

7. Conclusions
In comparing the various reactor candidates thesame temperature and density profiles have been
assumed. The results are listed in Table 5. Alpha heating
power minus bremsstrahlung is the available heating

power; also 3Vo loss of alpha particles has been
assumed. In all cases the required confinement time lies
153

Beidler C.D. et al., Stellafttor Fusion Reactors - an Overview

Table 5 Fusion plasma in stellarator reactors
HSR4/18

MHH

FFHR2

FFHR2Il

18

10
1.2

15

lml

1.8

lml

lm'l
il

Major radius
Av. minor radius
Plasma Volume

2.1

14
1.6

1567

734

284

960

lota

1.0

Magnetic field

5.0

0.7
5.0

0.7
10.0

0.7
6.0

Line av. density <t>2.056x1020

2.12x102o2.12x102o

IT]
Im-']

Electron Density n(0)Temperature f(0)Av. Electron Temperature

2.94Ox1On
15

2.2x102o
3.1x1020

3.04 x1020

3.04 x1020

lm-'l

15
5.0

15

5.0

3.5
0.96

9.8
2.66
2.O9

lkeVl
lkeVl
t%l
t%l
IGWI

Beta(0)

13.7

15
5.0
14.6

Average Beta

3.67

3.95

3.1 55

1.72
1.56
1.08
1.34

o.62
1.72
1.6
1.7

1.79

0.74

1.0
2.02

0.96

Fusion power P*"
Energy Conf.Time (req.)
Energy Conf.Time (NLHD2)
Energy Conf.Time (LGS)
Energy Conf.Time (lSS95)
Energy Conf.Time (NLHD1 )

4.96

1.71

1.57
2.22
1.20
2.37

1.53

1.M
1.5

2.2

lsl
lsl
lsl
lsl
lsl

References

between 1.5 and I .75 s; it is about a factor of two larger
than the ISS95 confinement time. However, predictions
on the basis of LGS and NlHD-scaling are moretll

L. Spitzer, D. Grove, W. Johnson, L. Tonks and W.

Westendorp, USAEC Report NYo-6047 (1954).
I2l K. Miyamoto, Nucl. Fusion 18,243 (1978).
t3l A. Gibson. Proc. BNES Nuclear Fusion Reactor
Conf. at Culham Laboratory, 233 (September,

favourable: in HSR4/18 LGS and NLHD1 predict
confinement times which are larger than the required
ones, in FFHR2 the result is marginal and the MHH
device needs a small improvement factor. The
configuration FFHR2/1 is an enlarged version of1969).

t4l A. Gibson, R. Hancox and R.J. Bickerton, Proc. 4thInter. Conf. on Plasma Physics and Controlled
Nuclear Fusion Research. IAEA-CN-28/K-4, III,375 (June 17-23, l97L).
lsl C. Gourdon, D. Marty, E.K. Maschke and J. Touche, Nucl. Fusion 11, 161 (I971).
t6l P.A. Politzer, L.M. Lidsky and D.B. Montgomery,
Massachusetts Institute of Technology report PFC/
TR-79-1 (March, 1979).
t7l W. Wobig and S. Rehker, Proc. 7th Symp. on Fu-

FFHR2, where the increase of size has been
compensated by a reduction of the magnetic field. Alsoin this case empirical scaling laws predict ignition
without the need of an improvement factor. In all cases
the average beta value stays below 47o,which in view ofthe highest beta values in LHD and W 7-AS seems to be
an achievable goal. Also the assumed density of<n>=2x1020 m-3 is below the highest density in W 7-AS.
Thus, only a moderate amount of optimism is needed to
extrapolate present stellarator results to a self-sustainedsion Technology, Grenoble, 333 (1972).

fusion plasma.

t8l R.L. Miller and R.A. Krakowski. Los Alamos Na-

The economic viability of stellarator reactors is
mainly determined by the magnet system and thecomplexity of the blanket. These are the cost-driving
components and for this reason any chance should betaken to operate the stellarator at low magnetic fields,
even if this requires an increase in size. In this casethere are good prospects that superconducting coils on
NbTi basis can be used. Concerning the blanket, several
options as in tokamaks are available, a preference,
however, cannot yet be made. In this respect further

tional Laboratory report (June, 1981).
t9l A. Iiyoshi et cl., Fusion Technol. 17,169 (1990).
ll0l A. Sagara et al.,Fusion Eng. Des. 41,349 (1998).

studies are necessary taking into account thell4l G. Btihme et al.,IPP-rcport IPP 2/285, KfK-report

tlll K. Yamazaki et al.,Proc.25'h EPS Conf. On Contr.
Fusion and Plasma Physics, Maastricht, June 14-18,
1999.

Ilz)K. Yamazaki et al., l6th IAEA-Conf. Montreal
1996, paper IAEA-CN-64/GI-5.

[13] B. Badger et al.,University of Wisconsin Report
LTWFDM-55O (1982).

KfK 4268, Fusion Power Assoc./Univ. Wisc. FPA-

maintenance concept.
154

Beidler C.D. el a/., Stellarator Fusion Reactors - an Overview

l24lH. Wobig, E. Harmeyer, F. Herrnegger, J.
Kisslinger, IPP-Report IPP IM44.

87-2.

|51 Stellarator power plant study, UCSD-ENG-O04(1997).

[25] W. Daenner, IPP-report lPP2l33l (1996) p.262.
l26lH. Wobig, J. Kisslinger and V. Welge, Rep.IPP 2/116l The Aries - I Tokamak Reactor Study, UCLA-PPG1323 Volume II.

313, p.189.

[17] J. Niihrenberg, R. Zille, Proc. of the workshop on
Theory of Fusion Plasmas, Varenna 1987, EditriceComp., Bologna 1987, EUR 11336 EN.

[27] Grigull et al.,28th EPS-Conf. on Plasma Phys. andt18l U. Brossmann et al.,Plasma Phys. and Contr. Nucl.
Fusion Res., (Proc. 9th Int. Conf., Baltimore 1982)
Vol. III, 141 (IAEA Vienna 1983).
t19l C.D. Beidler et al.,Fusion Technol. 17,148 (1990).
[20] Malang, S, Fusion Eng. and Des. 46, 193 (1999)[21] H. Yamanishi et al., Fusion Eng. Des. 41, 583

35, Br 15-8128 (1993).
[29] N.E. Karulin, IPP Report IPP 2/337 (1997).

Contr. Fusion (Madeira 2001) to be published.

[28] J. Ntihrenberg et a/., Plasma Phys. Control. Fusion[30] Beidler, C.D. et al.,Proc lTth IAEA Conf. on Fus.
Energy, Yokohama I 998, IAEA-FI -CN-69IFTP/01.
t3ll K. Lackner and E. Gottardi, Nucl. Fusion 30,767
1990.

(1998).

I32lU. Stroth et a/., Nucl. Fusion 36, 1063 (19965[22]M. dalle Donne, KfK-report 5429 (1994).
[23] S. Malang et al., FZKA 5581 (1995).

[33] K. Yamazaki et al. IAEA-Conf. on Fusion Energy,
Sorrento 2000, paper (FTPzllz).

r55