Expansion and nonlinear relaxation of a strongly magnetized non-neutral electron plasma due to elastic collisions with background neutral gas

Abstract

The expansion and nonlinear relaxation of a non-neutral electron plasma due to elastic collisions with constant collision frequency νen between the plasma electrons and a low-density background neutral gas are investigated theoretically. The model treats the electrons as a strongly magnetized fluid (ω2pe/ω2ce≪1) with isothermal temperature T=const immersed in a uniform magnetic field B0êz. The model also assumes an axisymmetric plasma column (∂/∂θ=0) with negligible axial variation (∂/∂z=0). Introducing the scaled radial coordinate ρ=r/r0(t), and the density profile shape function η(ρ,t)=[2πr20(t)/N]n(r,t), a diffusion equation is derived that describes the nonlinear evolution and relaxation of η(ρ,t) in response to electron collisions with the neutral gas. A very important consequence of the present analysis is that electron–neutral collisions (νen≠0) cause the electron density profile to relax to a (slowly expanding) quasiequilibrium state with identical profile shape ηeq(ρ) to that which would be produced by relaxation to thermal equilibrium by electron–electron collisions in the absence of background neutral gas (νen=0).