On the linear stability of a toroidal plasma with resistivity viscosity and Hall current

AbstractThe purpose of this paper is to study several mathematical questions regarding the linear stability analysis of a toroidal plasma equilibrium on the basis of the magnetohydrodymic equations with finite resistivity, viscosity, and Hall current. We show that the spectrum of the operator in an abstract evolution equation consists of at most finitely many unstable eigenvalues and infinitely many stable eigenvalues, and the set of the eigenfunctions is complete. The existence and uniqueness of a solution to the initial-boundary value problem of the linearized equations is proved. Finally the existence of a toroidal plasma equilibrium subject to a prescribed velocity with small norm on the boundary is established and its linear stability is proved