Approximating the Particle Distribution in Rotating and Tandem Mirror Traps

Abstract: Steady state distribution functions can be used to calculate stability conditions for modes, radiation energy losses, and particle loss rates. Heuristic analytic approximations to these distributions can capture key behaviors of the true distributions while possessing computational advantages over their numerical counterparts. In this paper, we motivate and present a closed-form analytic model for a distribution of particles in a centrifugal or tandem mirror. We find that our model outperforms other known models in approximating numerical steady-state simulations outside of a narrow range of low confining potentials. We demonstrate the model's suitability in the high confining potential regime for applications such as loss cone stability thresholds, fusion yields, and available energy.