Quasi-equilibrium electron density along a magnetic field line

A methodology is developed to determine the density of high-energy electrons along a magnetic field line for a low-β plasma. This method avoids the expense and statistical noise of traditional particle tracking techniques commonly used for high-energy electrons in bombardment plasma generators. By preserving the magnetic mirror and assuming a mixing timescale, typically the elastic collision frequency with neutrals, a quasi-equilibrium electron distribution can be calculated. Following the transient decay, the analysis shows that both the normalized density and the reduction fraction due to collision converge to a single quasi-equilibrium solution.