Energy Spectrum of Lost Alpha Particles in Magnetic Mirror Confinement

TL;DR

This paper provides analytical solutions for the energy loss, velocity, and timing of alpha particles in magnetic mirror confinement, aiding the design of energy recovery mechanisms in fusion reactors.

Contribution

It introduces a general analytical framework for predicting alpha particle losses in magnetic mirrors, applicable across various device parameters.

Findings

Derived closed-form solutions for alpha particle loss distributions.

Applicable to any high-energy species in mirror devices.

Framework valid for any potential and mirror ratio R > 1.

Abstract

In a magnetic mirror fusion reactor, capturing the energy of fusion-produced alpha particles is essential to sustaining the reaction. However, since alpha particles are born at energies much higher than the confining potential, a substantial fraction are lost due to pitch-angle scattering before they can transfer their energy to the plasma via drag. The energy of lost alpha particles can still be captured through direct conversion, but designing an effective mechanism requires a description of the energies and times at which they become deconfined. Here we present analytical solutions for the loss velocity, energy, and time distributions of alpha particles in a magnetic mirror. After obtaining the Fokker-Planck collision operator, we asymptotically solve for the eigenfunctions of the Legendre operator to reveal a closed-form solution. Our framework applies to any high-energy species, for any applied potential and mirror ratio R > 1, making this work broadly applicable to mirror devices.