Impact of energetic particle orbits on long range frequency chirping of BGK modes

TL;DR

This paper investigates how the bounded orbits of energetic particles influence the long-range frequency chirping of BGK modes, providing a more realistic 1D model that captures the effects of particle energy and orbit topology on mode evolution.

Contribution

It introduces an extended model incorporating bounded particle orbits and equilibrium potentials, enhancing the understanding of frequency chirping in plasma waves beyond previous free-particle models.

Findings

Mode shape and saturation depend on initial energy and frequency deviation.

Different equilibrium orbits lead to varying rates of frequency evolution.

Frequency sweeps are slower compared to previous models.

Abstract

Long range frequency chirping of Bernstein-Greene-Kruskal modes, whose existence is determined by the fast particles, is investigated in cases where these particles do not move freely and their motion is bounded to restricted orbits. An equilibrium oscillating potential, which creates different orbit topologies of energetic particles, is included into the bump-on-tail instability problem of a plasma wave. With respect to fast particles dynamics, the extended model captures the range of particles motion (trapped/passing) with energy and thus represents a more realistic 1D picture of the long range sweeping events observed for weakly damped modes, e.g. global Alfven eigenmodes, in tokamaks. The Poisson equation is solved numerically along with bounce averaging the Vlasov equation in the adiabatic regime. We demonstrate that the shape and the saturation amplitude of the nonlinear mode structure depends not only on the amount of deviation from the initial eigenfrequency but also on the initial energy of the resonant electrons in the equilibrium potential. Similarly, the results reveal that the resonant electrons following different equilibrium orbits in the electrostatic potential lead to different rates of frequency evolution. As compared to the previous model [Breizman B.N. 2010 Nucl. Fusion 50 084014], it is shown that the frequency sweeps with lower rates. The additional physics included in the model enables a more complete 1D description of the range of phenomena observed in experiments.