Approximating the Particle Distribution in Rotating and Tandem Mirror Traps

TL;DR

This paper introduces a new analytic model for particle distributions in rotating and tandem mirror traps, improving approximation accuracy over existing models and aiding in stability and energy calculations.

Contribution

It presents a novel closed-form analytic distribution model that outperforms previous models in most regimes for centrifugal and tandem mirror traps.

Findings

Model outperforms existing models outside low confining potentials

Suitable for high confining potential applications like stability thresholds

Enhances calculations of fusion yields and energy availability

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 such as the relative speeds of different transport processes 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.