Pitch angle scattering of fast particles by low frequency magnetic fluctuations

Abstract

The adiabatic invariance of the magnetic moment during particle motion is of fundamental importance to the dynamics of magnetized plasma. The related rate of pitch angle scattering is investigated here for fast particles that thermally stream through static magnetic perturbations. For a uniform magnetic field with a localized perturbation, it is found that the curvature parameter κ2=min(Rc/ρL) does not predict the level of pitch angle scattering. Instead, based on numerical integration of particle orbits in prescribed magnetic fields, we derive predictions for the particle scattering rates, which can be characterized by the relative perturbation amplitude A≃δB/B, and the particle Larmor radius normalized by the field-aligned wavelength of the perturbations, ρL/λ||. Particles with ρL/λ||≃1 are subject to strong pitch angle scattering, while the level of scattering vanishes for both the limits of ρL/λ||≪1 and ρL/λ||≫1. The results are summarized in terms of a scattering operator, suitable for including the described scattering in basic kinetic models.

Nonresonant scattering of relativistic electrons by electromagnetic ion cyclotron waves in Earth's radiation belts

“…Such contours are shown in Figures 3(a) and 3(b) for resonant and nonresonant energies, respectively. Interestingly, the underlying structure of the contour integral for nonresonant energies is similar to that of field line curvature scattering [39][40][41]. It turns out that, for either resonant or nonresonant regimes, the phase integral only survives on the branch cuts labeled C L and C U .…”

Properties of Intense H‐Band Electromagnetic Ion Cyclotron Waves: Implications for Quasi‐Linear, Nonlinear, and Nonresonant Wave‐Particle Interactions

“…Since EMIC wave frequencies ω are lower than the proton gyrofrequency Ω ci and much lower than the electron gyrofrequency Ω ce = 1,836 Ω ci , the cyclotron resonance condition for parallel EMIC waves can be rewritten as kv/Ω ce = 1/(γ cos α), with γ the Lorentz factor, v and α the electron velocity and pitch-angle (Angelopoulos et al, 2023;Summers & Thorne, 2003). Consequently, any magnetic fluctuation of sufficiently low frequency, ω ≪Ω ce , can resonantly scatter low energy electrons if its wave number k is sufficiently high to satisfy the above resonance condition (e.g., see Xu & Egedal, 2022). For typical high-k EMIC waves of low amplitudes (Denton et al, 2019), this resonant scattering is proportional to the wave power and much more efficient than purely nonresonant scattering (X.…”

“…For typical high-k EMIC waves of low amplitudes (Denton et al, 2019), this resonant scattering is proportional to the wave power and much more efficient than purely nonresonant scattering (X. An, Artemyev, et al, 2022;Angelopoulos et al, 2023;Xu & Egedal, 2022). Therefore, the nonresonant electron interactions with EMIC waves could be more precisely recast as nonresonant with the main EMIC waves (at peak wave power) while still resonant with much lower intensity EMIC waves at higher wave numbers k, which usually correspond to higher ω/Ω ci values based on the EMIC wave dispersion relation (Denton et al, 2019;Summers & Thorne, 2003).…”

Inclusion of Nonresonant Effects Into Quasi‐Linear Diffusion Rates for Electron Scattering by Electromagnetic Ion Cyclotron Waves

“…In the fourth mechanism to explain subrelativistic precipitation, nonresonant interactions, the scattering is provided by interactions with wave numbers significantly higher than the wave numbers of the peak‐power frequency, highest amplitude waves composing H‐band EMIC wave packets, implying that this interaction is indeed nonresonant with the peak‐power frequency waves (An et al., 2022, 2024), although it is still resonant with the lower amplitude, higher wavenumber (higher frequency) waves (An et al., 2024; Shi et al., 2024; Xu & Egedal, 2022). This second approach assumes that the observed short duration EMIC wave packets correspond to spatially short wave packets, and further assumes that an FFT in space of these short spatial packets provides the actual distribution of wavenumbers inside such packets (An et al., 2022, 2024).…”