Title: Impact of energetic particle orbits on long range frequency chirping of BGK modes,
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.