Formation process of relativistic electron flux through interaction with chorus emissions in the Earth's inner magnetosphere

Abstract

We perform test particle simulations of energetic electrons interacting with whistler mode chorus emissions. We compute trajectories of a large number of electrons forming a delta function with the same energy and equatorial pitch angle. The electrons are launched at different locations along the magnetic field line and different timings with respect to a pair of chorus emissions generated at the magnetic equator. We follow the evolution of the delta function and obtain a distribution function in energy and equatorial pitch angle, which is a numerical Green's function for one cycle of chorus wave‐particle interaction. We obtain the Green's functions for the energy range 10 keV–6 MeV and all pitch angles greater than the loss cone angle. By taking the convolution integral of the Green's functions with the distribution function of the injected electrons repeatedly, we follow a long‐time evolution of the distribution function. We find that the energetic electrons are accelerated effectively by relativistic turning acceleration and ultrarelativistic acceleration through nonlinear trapping by chorus emissions. Further, these processes result in the rapid formation of a dumbbell distribution of highly relativistic electrons within a few minutes after the onset of the continuous injection of 10–30 keV electrons.

Kinetic equation for nonlinear resonant wave-particle interaction

“…2, 3, 6, and 18), but the problem of their proper inclusion into a Fokker-Planck equation for a full description of the long-term evolution of a particle ensemble has, so far, eluded solution (e.g., see discussion in Ref. 16).…”

“…This effect corresponds to particle acceleration via trapping. 2,3,16,18 Since the duration of trapping acceleration can be rather long and variations of I can be large (both being independent of e), this process cannot be described as a local diffusion.…”

“…These general characteristics of nonlinear wave-particle resonant interaction have been derived analytically and tested numerically many times for different plasma systems. [1][2][3]16,18 However, to our best knowledge, no equation providing the relationship between P and V(I) has been yet available. Hereafter, we shall derive this relationship and use it to construct (for the first time) a generalized Fokker-Planck equation which will include all effects described by PðIÞ, V(I), and D(I).…”

Probabilistic approach to nonlinear wave-particle resonant interaction

“…Thus, integral operators were proposed to include them into a kinetic equation [40][41][42] to take this process into account. However, in many plasma systems with nonlinear wave-particle interaction, trapping effects are somehow compensated by effects of nonlinear scattering [35,43,44], i.e.…”

Statistical Distribution of Whistler Mode Waves in the Radiation Belts With Large Magnetic Field Amplitudes and Comparison to Large Electric Field Amplitudes

“…Of these waves, a type of whistler mode wave dubbed "magnetospheric chorus" has been demonstrated to be one of the primary mechanisms for accelerating radiation belt electrons to such high energies (Omura et al, 2015;Summers et al, 1998;Thorne et al, 2013). Of these waves, a type of whistler mode wave dubbed "magnetospheric chorus" has been demonstrated to be one of the primary mechanisms for accelerating radiation belt electrons to such high energies (Omura et al, 2015;Summers et al, 1998;Thorne et al, 2013).…”