On non-linear frequency chirping in connection with collisions

Abstract

The non-linear behaviour of toroidicity-induced Alfvén eigenmodes, destabilized by fast ions, is investigated in tokamak geometry and for a Wendelstein 7-X high-mirror equilibrium. Both cases show frequency chirping in the non-linear phase. The focus of this paper is on how particle collisions influence the non-linear dynamics and the associated frequency chirping. Pitch-angle scattering and fast-ion drag, which together are described by the fast-ion collision operator, are considered. We study the effect of a Krook operator, relaxing the distribution function to its unperturbed value, on the non-linear dynamics. The Krook operator leads to a periodic re-appearance of the chirping. This is also observed in experiments in which a fast-particle source is usually present.