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 B̃r/B0, the number of alphas lost via diffusion scales as (B̃r/B0)2. For TAE amplitudes B̃r/ B0≥10−3, α orbit stochasticity sets in and, depending on the radial width of the fast α density nα(r), a substantial fraction of alphas can be lost in one slowing down time. For B̃r/ B0<10−4, the losses become insignificant.