Analytical solutions for hole-like equilibria for arbitrary aspect ratio high β tokamaks

Abstract

Analytical solutions for ultrahigh beta ( εβ_p»1), high safety factor q [q>O(1)], hole-like equilibria with shaped boundary have been derived for arbitrary aspect ratio tokamaks. These solutions are similar to those derived by Cowley et al. [Phys. Fluids B 3, 2066 (1991)] in the large aspect ratio limit. A high beta, high qscaling (similar to that used by Hsu et al. [Phys. Plasmas 3, 266 (1996)]) is used to obtain the various features of finite aspect ratio tokamak equilibrium with a core region occupying most of the volume where ψ = ψ (R) and a boundary layer region of thickness 1/q. It is seen from the analytical solution that there exists a critical polodial beta value (β_c) beyond which one can have hole-like equilibria. The dependency of β_c on the inverse aspect ratio (ε) is also studied.