This study analyzes the effects of electromagnetic ion cyclotron (EMIC) waves on relativistic electron scattering and losses in the Earth’s outer radiation belt. EMIC emissions are commonly observed in the inner magnetosphere and are known to reach high amplitudes, causing significant pitch angle changes in primarily > 1 MeV electrons via cyclotron resonance interactions. We run test-particle simulations of electrons streaming through helium band waves with different amplitudes and wave normal angles and assess the sensitivity of advective and diffusive scattering behaviors to these two parameters, including the possibility of very oblique propagation. The numerical analysis confirms the importance of harmonic resonances for oblique waves, and the very oblique waves are observed to efficiently scatter both co-streaming and counter-streaming electrons. However, strong finite Larmor radius effects limit the scattering efficiency at high pitch angles. Recently discussed force-bunching effects and associated strong positive advection at low pitch angles are, surprisingly, shown to cause no decrease in the phase space density of precipitating electrons, and it is demonstrated that the transport of electrons into the loss cone balances out the scattering out of the loss cone. In the case of high-amplitude obliquely propagating waves, weak but non-negligible losses are detected well below the minimum resonance energy, and we identify them as the result of non-linear fractional resonances. Simulations and theoretical analysis suggest that these resonances might contribute to subrelativistic electron precipitation but are likely to be overshadowed by non-resonant effects.
more »
« less
Nonlinear Interactions Between Radiation Belt Electrons and Chorus Waves: Dependence on Wave Amplitude Modulation
We use test particle simulations to model the interaction between radiation belt electrons and whistler mode chorus waves by focusing on wave amplitude modulations. We quantify the pitch angle and energy changes due to phase trapping and phase bunching (including both advection and scattering) for electrons with various initial energies and pitch angles. Three nonlinear regimes are identified in a broad range of pitch angle‐energy space systematically, each indicating different nonlinear effects. Our simulation results show that wave amplitude modulations can extend the nonlinear regimes, while significantly reducing electron acceleration by phase trapping. By including amplitude modulations, the “advective” changes in pitch angle and energy caused by phase bunching are reduced, while the “diffusive” scattering due to phase bunching is enhanced. Our study demonstrates the importance of wave amplitude modulations in nonlinear effects and suggests that they need to be properly incorporated into future theoretical and numerical studies.
more » « less- NSF-PAR ID:
- 10374836
- Publisher / Repository:
- DOI PREFIX: 10.1029
- Date Published:
- Journal Name:
- Geophysical Research Letters
- Volume:
- 47
- Issue:
- 4
- ISSN:
- 0094-8276
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
more » « less
Abstract Discovery of the Earth's Van Allen radiation belts by instruments flown on Explorer 1 in 1958 was the first major discovery of the Space Age. The observation of distinct inner and outer zones of trapped megaelectron volt (MeV) particles, primarily protons at low altitude and electrons at high altitude, led to early models for source and loss mechanisms including Cosmic Ray Albedo Neutron Decay for inner zone protons, radial diffusion for outer zone electrons and loss to the atmosphere due to pitch angle scattering. This scattering lowers the mirror altitude for particles in their bounce motion parallel to the Earth's magnetic field until they suffer collisional loss. A view of the belts as quasi‐static inner and outer zones of energetic particles with different sources was modified by observations made during the Solar Cycle 22 maximum in solar activity over 1989–1991. The dynamic variability of outer zone electrons was measured by the Combined Radiation Release and Effects Satellite launched in July 1990. This variability is caused by distinct types of heliospheric structure that vary with the solar cycle. The launch of the twin Van Allen Probes in August 2012 has provided much longer and more comprehensive measurements during the declining phase of Solar Cycle 24. Roughly half of moderate geomagnetic storms, determined by intensity of the ring current carried mostly by protons at hundreds of kiloelectron volts, produce an increase in trapped relativistic electron flux in the outer zone. Mechanisms for accelerating electrons of hundreds of electron volts stored in the tail region of the magnetosphere to MeVenergies in the trapping region are described in this review: prompt and diffusive radial transport and local acceleration driven by magnetospheric waves. Such waves also produce pitch angle scattering loss, as does outward radial transport, enhanced when the magnetosphere is compressed. While quasilinear simulations have been used to successfully reproduce many essential features of the radiation belt particle dynamics, nonlinear wave‐particle interactions are found to be potentially important for causing more rapid particle acceleration or precipitation. The findings on the fundamental physics of the Van Allen radiation belts potentially provide insights into understanding energetic particle dynamics at other magnetized planets in the solar system, exoplanets throughout the universe, and in astrophysical and laboratory plasmas. Computational radiation belt models have improved dramatically, particularly in the Van Allen Probes era, and assimilative forecasting of the state of the radiation belts has become more feasible. Moreover, machine learning techniques have been developed to specify and predict the state of the Van Allen radiation belts. Given the potential Space Weather impact of radiation belt variability on technological systems, these new radiation belt models are expected to play a critical role in our technological society in the future as much as meteorological models do today.
-
Radiation belt electrons are strongly affected by resonant interactions with cyclotron-resonant waves. In the case of a particle passing through resonance with a single, coherent wave, a Hamiltonian formulation is advantageous. With certain approximations, the Hamiltonian has the same form as that for a plane pendulum, leading to estimates of the change at resonance of the first adiabatic invariant I , energy, and pitch angle. In the case of large wave amplitude (relative to the spatial variation of the background magnetic field), the resonant change in I and its conjugate phase angle ξ are not diffusive but determined by nonlinear dynamics. A general analytical treatment of slow separatrix crossing has long been available and can be used to give the changes in I associated with “phase bunching,” including the detailed dependence on ξ , in the nonlinear regime. Here we review this treatment, evaluate it numerically, and relate it to previous analytical results for nonlinear wave-particle interactions. “Positive phase bunching” can occur for some particles even in the pendulum Hamiltonian approximation, though the fraction of such particles may be exponentially small.more » « less
-
more » « less
Abstract Radiation belt electrons are strongly affected by resonant interactions with cyclotron‐resonant waves. For broad band, small amplitude waves the interactions are well described by quasi‐linear diffusion in pitch angle and energy, but coherent, large amplitude waves such as strong whistler mode chorus call for a different treatment. The standard nonlinear framework reduces the problem to that of a classical pendulum. This picture has generally been confirmed by many numerical simulations, but recent studies have uncovered additional, complex behavior, not captured by the pendulum model, for particles with low pitch angle. We show that avoiding a commonly made approximation leads to a more general but still tractable “second fundamental model” Hamiltonian, which involves not one but two regions of phase trapping. We analyze its phase portraits in detail, and perform representative test particle simulations with slowly changing parameters. We find that the trajectories encompass traditional phase bunching and phase trapping as well as additional behavior best understood using the new model.
-
more » « less
Abstract Electron losses from the outer radiation belt are typically attributed to resonant electron scattering by whistler‐mode waves. Although the quasi‐linear diffusive regime of such scattering is well understood, the observed waves are often quite intense and in the nonlinear regime of resonant wave‐particle interaction. Such nonlinear resonant interactions are still being actively studied due to their potential for driving fast precipitation. However, direct observations of nonlinear resonance of whistler‐mode waves with electron distributions are scarce. Here, we present evidence for such resonance with high‐resolution electron energy and pitch angle spectra acquired at low‐altitudes by the dual Electron Losses and Fields INvestgation (ELFIN) CubeSats combined with conjugate measurements of equatorial plasma parameters, wave properties, and electron energy spectra by the Time History of Events and Macroscale Interactions during Substorms and Magnetospheric MultiScale missions. ELFIN has obtained numerous conjunction events exhibiting whistler wave driven precipitation; in this study, we present two such events which epitomize signatures of nonlinear resonant scattering. A test particle simulation of electron interactions with intense whistler‐mode waves prescribed at the equator is employed to directly compare modeled precipitation spectra with ELFIN observations. We show that the observed precipitating spectra match expectations to within observational uncertainties of wave amplitude for reasonable assumptions of wave power distribution along the magnetic field line. These results indicate the importance of nonlinear resonant effects when describing intense precipitation patterns of energetic electrons and open the possibility of remotely investigating equatorial wave properties using just properties of precipitation energy and pitch angle spectra.
