Nonlinear expansion and heating of a nonneutral electron plasma due to elastic collisions with background neutral gas

This paper investigates theoretically the heating and nonlinear expansion of a nonneutral electron plasma due to elastic collisions with constant collision frequency νen between the plasma electrons and a background neutral gas. The model treats the electrons as a strongly magnetized fluid (ωpe2/ωce2≪1) immersed in a uniform magnetic field B0êz. The model also assumes an axisymmetric plasma column (∂/∂θ=0) with negligible axial variation (∂/∂z=0), and that the process of heat conduction is sufficiently fast that the electrons have relaxed through electron-electron collisions to a quasi-equilibrium state with scalar pressure P(r,t)=n(r,t)T, and isothermal temperature T. Assuming that the electrons undergo elastic collisions with infinitely massive background gas atoms, global energy conservation is used to calculate the electron heating rate, dT(t)/dt, as the plasma column expands on a time scale τdiff∼(ωpe2νen/ωce2 )−1, and the electrostatic potential energy decreases. Coupled dynamical equations that describe the nonlinear evolution of the mean-square column radius r20(t) and electron temperature T(t) are derived and solved numerically.