Low-frequency stability of high-current particle rings

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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 βeg2; where βe is the ratio of the directed beam kinetic energy density to the energy density of the external magnetic mirror field with βe⩾ (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) nbmbu2z≡ (B2z/8π) βt, where βt is the ratio of the directed beam kinetic energy density to the energy density of the toroidal magnetic field (Bz).