Description
The Earth’s inner radiation belt is frequently disrupted by geomagnetic storms [1] or thunderstorm-induced electron avalanches [2]. These events inject high-energy electrons into the magnetosphere, which can damage space assets. Self-limitation of fast electron fluxes is generally observed at high latitudes $(> 55^\circ)$, as wave-particle interactions in instability-amplified wave spectra cause electron precipitation into the atmosphere [3]. Understanding this self-limitation and, more generally, the redistribution of the injected electron populations in pitch angle and energy, is crucial for assessing radiation dose risks incurred by satellite electronics. This work investigates whether such effects can rapidly occur following a low-altitude relativistic injection.
Using 2D particle-in-cell simulations, we examined the dynamics of a magnetized plasma pervaded by two symmetric loss-cone distributions of relativistic $(\sim 0.1 - 5\, \rm{MeV})$ electrons counterpropagating along a geomagnetic field line. The ratios of the hot-to-background electron densities and background electron gyro-to-plasma frequencies are $n_h / n_e = 0.01$ and $\omega_{ce} / \omega_{pe} = 0.2$, respectively.
The interaction is initially (up to $\sim 10^3 \, \omega_{pe}^{-1}$) governed by a bump-on-tail-type instability, which generates a collection of oblique Langmuir waves. This resonant instability arises primarily from the strong pitch-angle gradients in the momentum distribution of the suprathermal electrons. Its saturation leads to a significant broadening of the distribution, which both fills the loss cone and expands beyond it. Subsequently, the instability-induced Langmuir waves nonlinearly couple to excite ring-shaped wavenumber spectra of electromagnetic waves at harmonics of $\omega_{pe}$ [4], while the ponderomotive force associated with the beating Langmuir waves generates strong ion density modulations. In the later stages, the suprathermal distribution undergoes sustained diffusion due to quasi-perpendicular lower-hybrid waves; these are driven by transverse gradients in the suprathermal distribution and involve the ion response. We characterize these low-frequency waves using 3D Fourier spectra and evaluate the energy-dependent pitch-angle diffusion rate up to $\sim 2 \times 10^4\,\omega_{pe}^{-1}$ through particle tracking.
References
[1] R. M. Thorne et al., Nature 504, 411 (2013).
[2] N. G. Lehtinen et al., Geophys. Res. Lett. 27, 1095 (2000).
[3] C. F. Kennel, and H. E. Petschek, J. Geophys. Res. 71, 1 (1966).
[4] S. Y. Lee et al., Astrophys. J. 924, 36 (2022).