Whistler-mode chorus waves play a crucial role in accelerating electrons in Earth’s outer radiation belt to relativistic and ultrarelativistic energies. While this electron evolution is typically modeled using a diffusion approximation for scattering, high-amplitude chorus waves induce nonlinear resonant effects that challenge this approach on short time scales. The long-term influence of these nonlinear interactions on radiation belt dynamics remains an unresolved issue. Recent simplified models suggest rapid nonlinear acceleration to ultrarelativistic energies, with formation of butterfly distributions during parallel wave propagation. In this study, we introduce a novel numerical approach based on Liouville phase space density mapping to investigate nonlinear scattering by high-amplitude waves over extended periods (minutes and beyond). We use a numerical wave field model of lower-band chorus risers that includes realistic fine-spectral features including subpacket modulations, phase decoherence, and jumps in wave normal angle. By incorporating these detailed spectral characteristics of the waves, we demonstrate that the rapid acceleration occurs across a broader pitch-angle range, forming a flat-top distribution. Similar effect is observed as the repetition period of chorus elements becomes shorter, with the additional effect of increased electron precipitation due to transition from bursty to continuous flux profiles in the loss cone. These findings highlight the importance of incorporating nonlinear effects and fine-scale wave properties in the future development of high-energy electron models for the outer radiation belt.

AbstractElectromagnetic ion cyclotron waves in the Earth's outer radiation belt drive rapid electron losses through wave-particle interactions. The precipitating electron flux can be high in the 100s keV energy range, well below the typical minimum resonance energy. One of the proposed explanations relies on nonresonant scattering, which causes pitch-angle diffusion away from the fundamental cyclotron resonance. Here we propose the fractional sub-cyclotron resonance, a second-order nonlinear effect that scatters particles at resonance order $n = 1/2$, as an alternate explanation. Using test-particle simulations, we evaluate the precipitation ratios of sub-MeV electrons for wave packets with various shapes, amplitudes, and wave normal angles. We show that the nonlinear sub-cyclotron scattering produces larger ratios than the nonresonant scattering when the wave amplitude reaches sufficiently large values. The ELFIN CubeSats detected several events with precipitation ratio patterns matching our simulation, demonstrating the importance of sub-cyclotron resonances during intense precipitation events.

Nonlinear wave-particle interactions contribute to the acceleration and precipitation of electrons in the outer radiation belt. Recent simulations and spacecraft observations suggest that oblique whistler-mode chorus can cause loss cone overfilling through nonlinear Landau resonance and thus break the strong diffusion limit of quasilinear theories. Here we show with test-particle simulations that a single element of parallel-propagating chorus can also break the diffusion limit through nonlinear cyclotron resonance, as long as its amplitude remains high. This is due to the strong scattering at low pitch angles caused by individual chorus subpackets. We further demonstrate that the subpacket modulations create a discernible pattern in the precipitating electron fluxes, with peaks correlated with the largest subpackets. Such flux patterns may be connected to weak micropulsations within diffuse auroras.

We present a test particle study of perturbations of a weakly relativistic electron distribution interacting with a rising-tone lower band chorus emission. Trajectories of interacting electrons are traced back in time from the equator to reconstruct the perturbed velocity distribution. The wave field is precalculated from a model based on the nonlinear growth theory and features a realistic subpacket structure. The perturbed distribution reveals a series of stripes of increased and decreased phase space density. This perturbation is associated with the electromagnetic hole structure which exists along the resonance velocity curve of each subpacket. Time-averaging of the final distribution shows that rising-tone lower band chorus emissions produce a sharp decrease in density at low parallel velocities, which might be detectable by spacecraft particle instruments.

The chorus whistler-mode emission, a major driver of radiation belt electron energization and precipitation, exhibits significant amplitude modulations on millisecond timescales. These subpacket modulations are accompanied by fast changes in the wave normal angle. Understanding the evolution of wave propagation properties inside chorus elements is essential for modeling nonlinear chorus-electron interactions, but the origin of these rapid changes is unclear. We propose that the variations come from propagation inside thin, field-aligned cold plasma enhancements (density ducts), which produce differing modulations in parallel and perpendicular wave magnetic field components. We show that a full-wave simulation on a filamented density background predicts wave vector and amplitude evolution similar to Van Allen Probes spacecraft observations. We further demonstrate that the commonly assumed wide density ducts, in which wave propagation can be studied with ray tracing methods, cannot explain the observed behavior. This indirectly proves the existence of wavelength-scale field-aligned density fluctuations.

Equatorial noise is an electromagnetic emission with line spectral structure, predominantly located in the vicinity of the geomagnetic equatorial plane at radial distances ranging from 2 to 8 Earth’s radii. Here we focus on the rare events of equatorial noise occurring at ionospheric altitudes during periods of strongly increased geomagnetic activity. We use multicomponent electromagnetic measurements from the entire 2004–2010 DEMETER spacecraft mission and present a statistical analysis of wave propagation properties. We show that, close to the Earth, these emissions experience a larger spread in latitudes than they would at large radial distances and that their wave normals can significantly deviate from the direction perpendicular to local magnetic field lines. These results are compared to ray tracing simulations, in which whistler mode rays with initially nearly perpendicular wave vectors propagate down to the low altitudes with wave properties corresponding to the observations. We perform nonlinear fitting of the simulated latitudinal distribution of incident rays to the observed occurrence and estimate the distribution of wave normal angles in the source. The assumed Gaussian distribution provides the best fit with a standard deviation of $2^{\circ}$ from the perpendicular direction. Ray tracing analysis further shows that small initial deviations from the meridional plane can rapidly increase during the propagation and result in deflection of the emissions before they can reach the altitudes of DEMETER.

The nonlinear growth theory of chorus emissions is used to develop a simple model of the subpacket formation. The model assumes that the resonant current, which is released from the source to the upstream region, radiates a new whistler mode wave with a slightly increased frequency, which triggers a new subpacket. Saturation of the growth in amplitude is controlled by the optimum amplitude. Numerical solution of advection equations for each subpacket, with the chorus equations acting as the boundary conditions, produces a chorus element with a subpacket structure. This element features an upstream shift of the source region with time and an irregular growth of frequency, showing small decreases between adjacent subpackets. The influence of input parameters on the number of subpackets, the shift of the source, the frequency sweep rate and the maximum amplitude is analyzed. The model well captures basic features of instantaneous frequency measurements provided by the Van Allen Probes spacecraft. The modeled wave field can be used in future particle acceleration studies.