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

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 B0ez. 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 produ...