Charged particle nonlinear resonance with localized electrostatic wave-packets

Abstract

A resonant wave-particle interaction, in particular a nonlinear resonance characterized by particle phase trapping, is an important process determining charged particle energization in many space and laboratory plasma systems. Although an individual charged particle motion in the nonlinear resonance is well described theoretically, the kinetic equation modeling the long-term evolution of the resonant particle ensemble has been developed only recently. This study is devoted to generalization of this equation for systems with localized wave packets propagating with the wave group velocity different from the wave phase velocity. We limit our consideration to the Landau resonance of electrons and waves propagating in an inhomogeneous magnetic field. Electrons resonate with the wave field-aligned electric fields associated with gradients of wave electrostatic potential or variations of the field-aligned component of the wave vector potential. We demonstrate how wave-packet properties determine the efficiency of resonant particle acceleration and derive the nonlocal integral operator acting on the resonant particle distribution. This operator describes particle distribution variations due to interaction with one wave-packet. We solve kinetic equation with this operator for many wave-packets and show that solutions coincide with the results of the numerical integration of test particle trajectories. To demonstrate the range of possible applications of the proposed approach, we consider the electron evolution induced by the Landau resonances with packets of kinetic Alfven waves, electron acoustic waves, and very oblique whistler waves in the near-Earth space plasma.

Semianalytical findings for the dynamics of the charged particle in the Störmer problem

“…Thus, obvious close congruence of results of the approximated solution with respect to the solution of the full ODE system can be considered as the advances of the suggested approach. Meanwhile, it should be highlighted that quasi‐periodic character of the obtained solutions is in agreement with the other results available in literature (see works among [8, 17–40] which concern the problem under consideration, where [37–40] are within the framework of the analytical approach to the study of mathematical models); besides, we should note that the elegant partial semianalytical or numerical solutions have been obtained in [23–27] for the special cases of magnetic field (with zero electric field's components).…”

On the Role of Kinetic Alfven Waves in the Magnetosheath Ion Thermalization Around the Night‐Side Magnetopause

“…Such nonlinear resonances may speed up particle pitch‐angle scattering (see discussions in Allanson et al., 2022; Frantsuzov et al., 2023) and thermalization of the plasma flow. A possible further generalization of our diffusion‐based approach for nondiffusive interactions (see Isliker et al., 2017; Pommois et al., 1998; Zimbardo et al., 2006; Zimbardo & Perri, 2013) can be obtained by changing the normal probability distributions, N 1,2 , in Equation to more specific distributions describing a finite probability of nondiffusive (large) particle jumps in velocity or coordinate space (e.g., Artemyev et al., 2019; Lukin et al., 2021).…”

Particle momentum variation under interaction with wavepackets of finite spatial width

“…Single particle dynamics under the presence of monochromatic electrostatic waves has been studied as a fundamental example of Hamiltonian chaos [6][7][8][9][10][11][12][13][14][15][16][17][18]. The case of spatially modulated waves having the form of localized wavepackets, has also been studied in terms of single [19][20][21][22][23][24][25][26][27][28] and collective particle dynamics [21,22,27,[29][30][31][32], when the spatial width of the envelope is relatively large in comparison to the wavelength of the carrier wave. Studies on single particle dynamics are based in phase space analysis with the utilization of Poincare surfaces of section whereas studies on the collective particle dynamics consider Fokker-Planck or Vlasov equation for the evolution of the particle momentum distribution function under interaction with a wavepacket.…”