Low-Beta Plasma Equilibrium and Stability in Linear Filamentary Multipole Magnetic Fields

Abstract

Analytical results are presented for two stability integrals along a field line and for a class of low-β plasma equilibria in linear multipole magnetic fields. The integral \\ointdl calculated for quadrupole and hexapole fields, \\ointdl/B for quadrupole, hexapole and octopole fields. They are expressed in terms of the complete elliptic integral of the first kind. The stability limit lines defined by (∂/∂ψ)\\ointdl=0 and (∂/∂ψ)\\ointdl/B=0 (ψ: flux function) are determined together with the magnetic mirror ratio on those field lines. The magnetic well depth is also estimated. Low-β plasma equilibria in multipole fields are obtained by the perturbation technique. Variations of the field lines due to the plasma diamagnetism are calculated up to the linear terms in plasma pressure.