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Long range frequency chirping of Bernstein-Greene-Kruskal modes, whoseexistence is determined by the fast particles, is investigated in cases wherethese particles do not move freely and their motion is bounded to restrictedorbits. An equilibrium oscillating potential, which creates different orbittopologies of energetic particles, is included into the bump-on-tailinstability 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 rangesweeping events observed for weakly damped modes, e.g. global Alfveneigenmodes, in tokamaks. The Poisson equation is solved numerically along withbounce averaging the Vlasov equation in the adiabatic regime. We demonstratethat the shape and the saturation amplitude of the nonlinear mode structuredepends not only on the amount of deviation from the initial eigenfrequency butalso on the initial energy of the resonant electrons in the equilibriumpotential. Similarly, the results reveal that the resonant electrons followingdifferent equilibrium orbits in the electrostatic potential lead to differentrates 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 lowerrates. The additional physics included in the model enables a more complete 1Ddescription of the range of phenomena observed in experiments.

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