Ideal magnetohydrodynamic stability of tokamak plasmas

Abstract

Variational theory is used to derive a generalized Euler equation and a new energy functional which are convenient for analytical studies of ideal magnetohydrodynamic stability in tokamaks. This generalized Euler equation, which is an explicit function of the magnetic surface coordinate ψ only, represents an infinite set of equations coupled together by poloidal m mode coupling. In the infinite aspect ratio limit, the toroidal curvature and mode coupling terms disappear and an infinite set of uncoupled Euler equations for the diffuse linear pinch (Hain–Lüst equation) for each m value results. The continuous spectra are discussed for the circular toroidal case. In this case, the equations are further specialized to three modes (m, m−1, m+1) and in the marginal stability limit reduce to known results. Analytically eliminating the m−1 and m+1 modes for arbitrary current profiles provides results on limiting β poloidal for tokamaks.