Tokamak equilibria with arbitrary cross-section

Abstract

Magnetohydrodynamic equilibria are obtained by semi-analytic means for large-aspect-ratio tokamaks with fixed, non-circular boundaries and slightly non-uniform currents. The method uses the fact that there is a conformal map of any simple closed region onto the unit circle. Solutions are expressed as quadratures which involve the conformal maps. These quadratures are evaluated numerically for specific examples. Results for equilibria with circular, elliptical, dee-shaped and doublet-shaped cross-sections are presented and compared. Toroidal and finite-beta effects are noted and stability against flutes is examined by Mercier's criterion for the various configurations.

Design constraints for steady-state tokamak reactors driven by lower hybrid waves

“…In this case the best value of e was about 4.2%. This best case requires R = 8.2 m, which confirms the trend to larger e at smaller R, suggested by expression (12).…”

“…In the range of interest to fusion power ( o v ( T i o ) ) ^ T io' a n d we can illustrate the dominant influences on reactor design by rewriting expression (11) as -1 (12) This last expression supports the claim in Section 2 that higher plasma temperatures are beneficial to reactor economics for fixed j3 t . In addition, large R, B o , and j3 t are desirable, which suggests that large high-power reactors are more favourable.…”

“…This particular case is for A = 3.0, K= 1.3, and d = 0.25. The non-circular plasma shape may be conducive to higher beta stability [11][12][13][14][15]; if, for example, q(i//) varies between 1.3 and 3.9 then j3 t = 0.07 while if q varies between 1.0 and 3.0, then 0 t = 0.12. This current profile is hollow in the centre and is typical of what may be termed a surface current equilibrium.…”

Local, ideal and resistive stability in tokamaks with non-circular cross-section

“…The numerical evaluations of local stability for a PDX-like equilibrium [10] and various tokamak reactor designs [11] have been performed. The local stability of doublet configurations appropriate to Doublet IIA [12] has been numerically analysed.…”