Bounce‐averaged advection and diffusion coefficients for monochromatic electromagnetic ion cyclotron wave: Comparison between test‐particle and quasi‐linear models

Abstract

[1] The electromagnetic ion cyclotron (EMIC) wave has long been suggested to be responsible for the rapid loss of radiation belt relativistic electrons. The test-particle simulations are performed to calculate the bounce-averaged pitch angle advection and diffusion coefficients for parallel-propagating monochromatic EMIC waves. The comparison between test-particle (TP) and quasi-linear (QL) transport coefficients is further made to quantify the influence of nonlinear processes. For typical EMIC waves, four nonlinear physical processes, i.e., the boundary reflection effect, finite perturbation effect, phase bunching and phase trapping, are found to occur sequentially from small to large equatorial pitch angles. The pitch angle averaged finite perturbation effect yields slight differences between the transport coefficients of TP and QL models. The boundary reflection effect and phase bunching produce an average reduction of >80% in the diffusion coefficients but a small change in the corresponding average advection coefficients, tending to lower the loss rate predicted by QL theory. In contrast, the phase trapping causes continuous negative advection toward the loss cone and a minor change in the corresponding diffusion coefficients, tending to increase the loss rate predicted by QL theory. For small amplitude EMIC waves, the transport coefficients grow linearly with the square of wave amplitude. As the amplitude increases, the boundary reflection effect, phase bunching and phase trapping start to occur. Consequently, the TP advection coefficients deviate from the linear growth with the square of wave amplitude, and the TP diffusion coefficients become saturated with the amplitude approaching 1 nT or above. The current results suggest that these nonlinear processes can cause significant deviation of transport coefficients from the prediction of QL theory, which should be taken into account in the future simulations of radiation belt dynamics driven by the EMIC waves.Citation: Su, Z., H. Zhu, F. Xiao, H. Zheng, C. Shen, Y. Wang, and S. Wang (2012), Bounce-averaged advection and diffusion coefficients for monochromatic electromagnetic ion cyclotron wave: Comparison between test-particle and quasi-linear models,

Contemporaneous EMIC and whistler mode waves: Observations and consequences for MeV electron loss

“…But scattering by each type of wave alone cannot completely explain the observed MeV electron dynamics. On the other hand, scattering by EMIC waves alone [Thorne and Kennel, 1971;Summers and Thorne, 2003;Sandanger et al, 2007;Su et al, 2012;Blum et al, 2015] usually entails fast precipitation of only a small part of the MeV electron population Usanova et al, 2014]. On the other hand, scattering by EMIC waves alone [Thorne and Kennel, 1971;Summers and Thorne, 2003;Sandanger et al, 2007;Su et al, 2012;Blum et al, 2015] usually entails fast precipitation of only a small part of the MeV electron population Usanova et al, 2014].…”

“…Whistler mode hiss (inside the plasmasphere) or chorus (outside the plasmasphere) waves alone induce relatively slow losses of whole populations of relativistic electrons, with lifetimes L > 2 − 5 days ("lifetimes" denoting loss time scales of the entire particle population up to equatorial pitch angles 0 ≈ 90 ∘ ) [Artemyev et al, 2013;Ni et al, 2013;Ma et al, 2015;Artemyev et al, 2016;Orlova et al, 2016]. This occurs because the upper cutoff frequency of quasi-parallel EMIC waves of realistic amplitudes (∼0.1-1 nT, such that nonlinear effects remain weak [Su et al, 2012]) is often sufficiently far from the corresponding ion gyrofrequency Zhang et al, 2016b] to prevent these waves from resonantly scattering MeV electrons at high equatorial pitch angles ( 0 > 0,max (EMIC) ∼ 45 ∘ -70 ∘ ) Usanova et al, 2014;Mourenas et al, 2016] where most of the MeV electron population is found [e.g., Ni et al, 2015]. This occurs because the upper cutoff frequency of quasi-parallel EMIC waves of realistic amplitudes (∼0.1-1 nT, such that nonlinear effects remain weak [Su et al, 2012]) is often sufficiently far from the corresponding ion gyrofrequency Zhang et al, 2016b] to prevent these waves from resonantly scattering MeV electrons at high equatorial pitch angles ( 0 > 0,max (EMIC) ∼ 45 ∘ -70 ∘ ) Usanova et al, 2014;Mourenas et al, 2016] where most of the MeV electron population is found [e.g., Ni et al, 2015].…”

Comparison of formulas for resonant interactions between energetic electrons and oblique whistler-mode waves

“…25,[31][32][33] But in the second-order resonance given by d 2 g=dt 2 ¼ 0, which enables the stable trapping of a resonant electrons, 34 this centripetal acceleration force plays an important role. Although this centripetal term had already been included in some numerical studies, 14,16 but was usually not taken into account in theoretical analysis. 1,26,29,[34][35][36][37][38] The motion of phase trapped electrons is dominated not by the ambient magnetic field, but by the wave field, 26,39 which enables the particle parallel velocity to follow the resonant velocity all the way in the wave field.…”

“…[7][8][9][10][11][12][13] However, the quasilinear approach inherently neglects nonlinear effects arising from the interactions between radiation belt electrons and various magnetospheric waves, and these nonlinear effects have been studied using test-particle simulations. [14][15][16][17] The motion of charged particles in an electromagnetic field is governed by the Lorentz force, and thus can be modeled by integrating the Lorentz equation directly. 18 But it is often more instructive and computationally economical to gyro-average the equations so that numerical integration can proceed on time scales comparable to the gyro-period.…”

Scattering of relativistic and ultra-relativistic electrons by obliquely propagating Electromagnetic Ion Cyclotron waves

“…It was shown in 333 the past that for EMIC waves with amplitude of several nT nonlinear effects such as phase 334 bunching and phase trapping may play important role and cause significant deviations form theresults of quasi-linear model [e.g. Albert and Bortnik, 2009;Su et al, 2012;. Thus, the 336 assumption of non-thermal motion of plasma particles, as well as quasi-linear approach, has to 337 be challenged in our future studies.…”