J. Plasma Fusion Res. SERIES, Vol.1 (1998) 17-18

lmplications of Recent Tokamak Researchfor Stellarator Design
GOLDSTON Robert J.
Princeton Plasma Physics Laboratory, Princeton University, P.O.Box 451, princeton, N108543, USA(Received: 30 September 1.997/Accepted,: 22 October 1997)

Abstract
Recent advances in tokamak physics can be used in the quest to optimize the stellarator concept. In
particular the experimental confirmation of strong bootstrap currents suggests the possibility of taking
advantage of non-zero current in steady-state stellarators. In addition the observation of neoclassical islands suggests important issues for design optimization, in order to operate in a regime in which neoclassical effects heal stellarator islands.

Keywords:
stellarator, tokamak, bootstrap current, neoclassical island

The last ten years have seen dramatic advances inexperimental and theoretical tokamak research includ-

There have, of course, also been tremendous advances recently in stellarator design. The W7-X concept

ing:

minimizes bootstrap and Pfirsh-Schliiter currents, reduces shear, and provides orbit optimization by minimizing the excursion of trapped particles from flux surfaces. The quasi-helical stellarator minimizes transport
by moving to a very nearly helically symmetric lBl spectrum, in Boozer coordinates. These optimization procedures lead, however, to rather high aspect ratio. Working from the tokamak-based intuition that low aspectratio can provide high beta, the small-aspect-ratio toroidal hybrid, SMARTH, concept [1] of Hirshman era/., moves to R/a -3, and still provides orbit optimization via very large ripple, giving rise to quasi-omnigeneity in the sense of Cary and Shasharina [2]. The
rotational transform is provided by a large /:1 helical

Experiments and theory demonstrating flow-shear
stabilization.

Confirmation of current-drive power requirement
scalings.

o Confirmation of the predicted neoclassical bootstrap
current.

e Improved theoretical models for turbulent transport,including both "standard" regimes and internal transport barriers.
o Scaling of beta limits with shaping, R/a, and current
profile (including the effect of "shear reversal").

o Neoclassical effects on resistive island growth & suppression.

component, peaked on axis, combined with externallydriven current, so that a conventional tokamak q profile

While it has often been discussed that the impressive range of research on "alternate concept" devices sheds light on the physics of tokamaks, the thesispresented here is that the insights gleaned from the last
decade of tokamak research can help illuminate physics
issues for other approaches to toroidal confinement.

obtains over most of the radius, and a substantial
equilibrium beta can be supported. The result is a device with - 25x confinement improvement over the un-

optimized configuration, stable to ballooning modes
over the inner 80 % of the radius, with volume averaqe
beta of 6 "/".
@1998 by The Japan Society of Plasma
Science and Nuclear Fusion Research

Corresponding author's e-mail: rgoldston@ pppl. gov
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Goldston R.J., Implications of Recent Tokamak Research for Stellarator Design

drive needed in the advanced tokamak should reduce
the low-n kink drive, reduce the recirculating power requirement, and allow high edge density for optimal
divertor performance. Seed transform could be provided by the stellarator fields as well. External transform may eliminate or ameliorate disruptions; in W7-A
rather modest amounts of external transform (-0.13)
allowed non-disruptive operation even at q(a) < 2. The
marriage of stellarator and advanced tokamak concepts
in the quasi-axisymmetric, high-bootstrap stellarator
may therefore offer compactness, good confinement,

Another approach, studied by Kovrizhnykh [3],Ntihrenberg [4] and Garabedian [5], and more recently
by Reiman and Zarnstorff [6], takes advantage of thefact that magnetic fields with magnitude lBl which isnearly toroidally symmetric in Boozer coordinates canprovide significant rotational transform at low aspectratio. This provides good orbit confinement in a symmetric system, which is then free to rotate toroidally,possibly providing shear flow for turbulence suppression. Furthermore, as beta increases these devices develop substantial positive bootstrap current which thenpermits less distorted modular coils, further from theplasma - key issues in stellarator reactor optimization.

high beta, low recirculating power, stability, andrelative simplicity - an attractive package if it is realizable.

Theoretical calculations indicate that these devices
share the properties of reversed-shear advanced tokamaks, including a core region which appears to be second-stable to ballooning modes. In tokamak experiments reversed shear regions, at high bootstrap current,
are stable against resistive island growth. Theoreticallythis same property should be very valuable in a stellarator, in that islands which might otherwise grow in theequilibrium as beta increases should be suppressed byabout an order of magnitude, for a radially increasing
iota, and positive bootstrap current. Specifically

In sum, the tokamak has been a very productive
vehicle for learning high-temperature plasma physics.
As embodied in the steady-state advanced tokamak, it
may itself provide the physics concept for an attractive
fusion reactor. However it also has provided a valuable
resource of physics knowledge for optimizing the stellarator approach to toroidal confinement, which may
ultimately prove to be the more attractive.

This work was supported by US DOE Contract
DE-4C02-76CH03073.

w: (wk,+ w3)t/2 - wb

Referenceswhere[1] S.P. Hirshman et al., in these Proceedings, p.152(1ee8).
J.R.
Cary and S.G. Shasharina, Phys. Rev. Lett.
[2]48,674 (1997).

:2poRh*.
" D mBt'and W"* is the island size which would have been present in the absence of the bootstrap suppression effect.
In the limit of W"".:0, this result reduces to that developed by Hegna and Callen [7], for the case of unfavorable neoclassical island drive in a helically-symmetric stellarator, due to negative bootstrap current.

[3] L.M. Kovrizhnykh, Nuclear Fusion 25, l39t
(1e8s).

[4] J. Niihrenberg, W. I-otz and S. Gori, Quasi-axi-symmetric Tokamaks, ISPP-15; Piero Caldirola,
Theory of Fusion Plasmas, E. Sindoni, F. Troyonand J. Vaclavik (eds.), Bologna, 1994.
[5] P.R. Garabedian, Phys. Plasmas 3,2483 (L996).

The presence of externally provided toroidally
quasi-symmetric transform should allow the shear[6] A.H. Reiman and M.C. Zarnstorff, in these Proceedings, p.a29 Q998).

reversal point to be moved outwards towards the edgeof the plasma, avoiding instabilities associated withq' :0 generally observed in high-performance reversedshear tokamaks. The elimination of the edee current[7] C.C. Hegna and J.D. Callen, Phys. Plasmas 1,3r3s (1994).

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