Monte Carlo Treatment of 𝛼 Particle Collisional Dynamics in Magnetic Mirrors

Abstract

Harnessing the energy of alpha particles produced in fusion reactions is desirable for building economically feasible fusion power plants. A key consideration for maximizing alpha particle energy extraction and removal from the machine is how the alpha particle distribution is affected by diffusive processes such as wave-induced diffusion and Coulomb collisions. The evolution of the alpha particle distribution function subject to diffusive processes can be modeled using the Fokker-Planck equation. In transforming the Fokker-Planck equation into the equivalent Langevin formulation for use in Monte Carlo simulations, we find a geometric effective drift arising from non-uniformity of the measure. We study the effects of this geometric correction for a collision operator of alpha particles colliding with a deuterium-tritium plasma. For this process, the geometric correction enforces the expected isotropic Maxwellian distribution. In a magnetic mirror fusion device, we demonstrate that neglecting this geometric correction leads to overestimating losses while alpha particles initially slow down and then underestimating the total confinement time. This treatment can be extended to other diffusive processes and particle species for applications such as alpha channeling, direct energy conversion, and impurity transport.