Formation of cylindrical plasma equilibria with β > 1

Abstract

High-beta plasma equilibria are realized in a number of physical systems, from planetary magnetospheres, sunspots, and magnetic holes to fusion laboratory experiments. When plasma pressure becomes large enough to completely expel the magnetic field from its volume, the particle trajectories cannot be considered any more as circular gyro-orbits, and plasma pressure ceases to be gyrotropic. These non-gyrotropic effects require kinetic description and are actively studied for a long time in the magnetic reconnection problem. In this paper, we will show that non-gyrotropy of plasma pressure makes it possible to markedly exceed the limit β=1 dictated by the magnetohydrodynamics for finite-size plasmas, which may be attractive for some fusion schemes such as mirror and cusp configurations. As a first step, we study how these effects manifest themselves in a simple classical problem of confining a cylindrical plasma column by a uniform vacuum magnetic field. Using particle-in-cell simulations, we show that the equilibrium of the diamagnetic bubble type with zero internal magnetic field is formed with an electron-produced current layer of sub-ion scale and found that the gas-kinetic pressure of the central plasma exceeds the pressure of the vacuum magnetic field by 15%.