Analytic Approximations of the Steady State Particle Distribution Function in Rotating Magnetic Mirrors

Magnetic mirrors have recently experienced renewed interest as a potential alternative fusion concept. One way of addressing particle loss via diffusion into the mirror loss cone is through rotating the plasma, which introduces a centrifugal potential that improves confinement. However, less is known about the distribution function of particles in a rotating mirror configuration compared to the standard non-rotating mirror. Characterizing this distribution could help in understanding effects in the confinement system such as instabilities. We examine the steady state behavior of the particle distribution function, specifically near the loss cone boundary. Using finite-element simulations of the Fokker Planck diffusion equation on cold particle sources, we find analytic approximations to the distribution function for a range of parameters that cover both non-relativistic and relativistic speeds. In particular, we investigate the distribution function's dependency on the confining potential, mirror ratio, and temperature as well as the regimes where typical distribution functions such as the Maxwellian with loss cone cutouts no longer sufficiently model the simulated results.