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

Abstract

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.Hard nonlinear evolution in the presence of particle orbits 2

On the Effect of Beating during Nonlinear Frequency Chirping

“…A generalized model that accounts for nonlinear distortions and shrinking of the field's effective potential well has been derived by Breizman [25] and further extended to expanding potential wells by Hezaveh et al [16]. A key point that is captured in these and related studies of longrange chirping [26][27][28][29], and which is closely related to the topic of the present paper, is that the generalized BGK-like modes have an active boundary layer that can dynamically expand or shrink as the field amplitude grows or decays 14 . 12 One reason for the smaller extent of the downward chirp is that it propagates away from the peak of the field mode in our setup.…”

“…The amplitude and phase modulations associated with beating may contain useful information about possible nonlinear couplings between the interfering waves. This has been exploited, for instance, in studies of coexisting EP-driven Alfvén modes and rotating kink/tearing modes [52][53][54] 28 . Since different modes generally have different spatial structures, such cases exhibit not only temporal modulation but also spatial modulation.…”

Long range frequency chirping of Alfvén eigenmodes

“…Hence, the perturbed density is assumed to be dominantly from the trapped particles inside the separatrix. Considering the small separatrix width assumption mentioned above and followed by bounce-averaging the Vlasov equation (see section 3 in [30] and appendix B in [32]), we find…”

“…More recently, a 1D theoretical framework was developed in Ref. [32], which investigates the impact of different EPs orbit topologies (magnetically trapped/passing) on long range frequency chirping of BGK modes.…”

Simulation of convective transport during frequency chirping of a TAE using the MEGA code

“…They evolve adiabatically and carry the trapped particles. Nonperturbative adiabatic models [13][14][15][16][17] suggest the slow evolution of a Langmuir wave as a 1D paradigm of the more general wave-particle interactions in realistic geometries. In Refs.…”