On the stability of plasma equilibrium in the neighborhood of a straight current conductor

The article presents a mathematical model of an equilibrium magnetoplasma configuration in a plasma cylinder containing on its axis a conductor of finite diameter with a current creating a magnetic field confining the plasma. The annular configurations considered here are the simplest elements of a wide class of galatea traps with conductors immersed in the plasma volume. The problems concerning such configurations have a simple analytical solution in terms of ordinary differential equations. A simple result on the existence of smooth equilibrium configurations with restrictions on the maximum plasma pressure related to magnetic units is obtained. The problems of the stability of the configurations–full-scale MHD stability and intermediate stability to perturbations of the same dimension–are formulated and solved. It is shown that intermediate stability takes place within a specified restrictions on pressure and MHD stability tightens this restrictions due to corrugated perturbations depending on the axial coordinate.