Low-frequency stability of high-current particle rings

Abstract

A theoretical study is made of the low‐frequency magnetohydrodynamic stability of high‐current particle rings embedded in a dense plasma. Two configurations are investigated in detail: astron geometry where there is no toroidal magnetic field, and tokamak geometry where a strong toroidal field exists. For an astron, a sufficient condition for stability of the kink modes (m=±1, n≠0) (excluding the n=1 precession mode) is found to be β_eg²; where β_e is the ratio of the directed beam kinetic energy density to the energy density of the external magnetic mirror field with β_e⩾ (2/πg)(R/a)² required for field cancellation at the torus center; g is a numerical factor of order unity; m (n) is the mode number for the minor (major) circumference; and R/a is the aspect ratio of the torus. For a tokamak, it is found that stability conditions for the modes (m≠0, n≠0), with n²≪ (R/a)² m², are the same as the stability conditions for these modes in a conventional plasma pinch with isotropic pressure p (r) = (1/2) n_bm_bu²_z≡ (B²_z/8π) β_t, where β_t is the ratio of the directed beam kinetic energy density to the energy density of the toroidal magnetic field (B_z).