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

Rotating the plasma in magnetic mirrors introduces a centrifugal potential, which better confines particles compared to non-rotating mirror configurations. Steady state particle distribution functions of ion species are especially essential in understanding radiative losses and instabilities in these confinement systems. However, no definitive analytic model exists for these distribution functions in rotating mirror configurations. Using finite-element-based simulations of the Fokker-Planck diffusion equation for cold Maxwellian sources, we examine the mirror ratio and confining potential dependencies of the steady state ion distribution. By parametrizing momentum pitch-angle space into pseudo loss cone contours, we find a simple analytic approximation that smoothly decays to zero at the loss cone boundary while remaining Maxwellian for the bulk of the distribution. This analytic approximation outperforms the Maxwellian model with loss cone cutouts in that it provides a more accurate model for applications ranging from synchrotron and bremsstrahlung losses to stabilization conditions of loss cone modes.