Alpha-particle losses from toroidicity-induced Alfvén eigenmodes. Part II: Monte Carlo simulations and anomalous alpha-loss processes

Abstract

Fusion‐born α particles moving parallel to the magnetic field can resonate with toroidal Alfvén eigenmodes (TAE) leading to anomalous α‐orbit diffusion across the α‐loss boundaries in a tokamak. This is analyzed using the Hamiltonian guiding center code orbit in conjunction with the kinetic magnetohydrodynamics (MHD) eigenmode solving code nova‐k. Resonant single α orbits are studied below and above the threshold for orbit stochasticity and Monte Carlo randomized ensembles of alphas subjected to a finite amplitude time‐dependent TAE are followed with respect to their radial losses using realistic MHD equilibria and numerically computed toroidal Alfvén eigenfunctions for one toroidal eigenmode n=1 and the full Fourier spectrum of poloidal harmonics m involved in the ‘‘gap mode.’’ The α‐loss mechanisms are resonant drift motion across the loss boundaries of alphas born near these boundaries and stochastic diffusion to the boundaries in constants of the motion (phase) space. After a first transient of resonant drift losses scaling as B̃_r/B₀, the number of alphas lost via diffusion scales as (B̃_r/B₀)². For TAE amplitudes B̃_r/ B₀≥10⁻³, α orbit stochasticity sets in and, depending on the radial width of the fast α density n_α(r), a substantial fraction of alphas can be lost in one slowing down time. For B̃_r/ B₀−⁴, the losses become insignificant.