An official website of the United States government
Abstract Electron diffusion by whistler‐mode chorus waves is one of the key processes controlling the dynamics of relativistic electron fluxes in the Earth's radiation belts. It is responsible for the acceleration of sub‐relativistic electrons injected from the plasma sheet to relativistic energies as well as for their precipitation and loss into the atmosphere. Based on analytical estimates of chorus wave‐driven quasi‐linear electron energy and pitch‐angle diffusion rates, we provide analytical steady‐state solutions to the corresponding Fokker‐Planck equation for the relativistic electron distribution and flux. The impact on these steady‐state solutions of additional electromagnetic ion cyclotron waves, and of ultralow frequency waves are examined. Such steady‐state solutions correspond to hard energy spectra at 1–4 MeV, dangerous for satellite electronics, and represent attractors for the system dynamics in the presence of sufficiently strong driving by continuous injections of 10–300 keV electrons. Therefore, these analytical steady‐state solutions provide a simple means for estimating the most extreme electron energy spectra potentially encountered in the outer radiation belt, despite the great variability of injections and plasma conditions. These analytical steady‐state solutions are compared with numerical simulations based on the full Fokker‐Planck equation and with relativistic electron flux spectra measured by satellites during one extreme event and three strong events of high time‐integrated geomagnetic activity, demonstrating a good agreement.
more »
« less
Upper Limit on Outer Radiation Belt Electron Flux Based on Dynamical Equilibrium
Abstract In the Earth's radiation belts, an upper limit on the electron flux is expected to be imposed by the Kennel‐Petschek mechanism, through the generation of exponentially more intense whistler‐mode waves as the trapped flux increases above this upper limit, leading to fast electron pitch‐angle diffusion and precipitation into the atmosphere. Here, we examine a different upper limit, corresponding to a dynamical equilibrium in the presence of energetic electron injections and both pitch‐angle and energy diffusion by whistler‐mode chorus waves. We first show that during sustained injections, the electron flux energy spectrum tends toward a steady‐state attractor resulting from combined chorus wave‐driven energy and pitch‐angle diffusion. We derive simple analytical expressions for this steady‐state energy spectrum in a wide parameter range, in agreement with simulations. Approximate analytical expressions for the corresponding equilibrium upper limit on the electron flux are provided as a function of the strength of energetic electron injections from the plasma sheet. The analytical steady‐state energy spectrum is also compared with maximum electron fluxes measured in the outer radiation belt during several geomagnetic storms with strong injections, showing a good agreement at 100–600 keV.
more »
« less
- Award ID(s):
- 2019914
- PAR ID:
- 10444076
- Publisher / Repository:
- DOI PREFIX: 10.1029
- Date Published:
- Journal Name:
- Journal of Geophysical Research: Space Physics
- Volume:
- 128
- Issue:
- 8
- ISSN:
- 2169-9380
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract Energetic particle injections are commonly observed in Jupiter's magnetosphere and have important impacts on the radiation belts. We evaluate the roles of electron injections in the dynamics of whistler‐mode waves and relativistic electrons using Juno measurements and wave‐particle interaction modeling. The Juno spacecraft observed injected electron flux bursts at energies up to 300 keV atMshell ∼11 near the magnetic equator during perijove‐31. The electron injections are related to chorus wave bursts at 0.05–0.5fcefrequencies, wherefceis the electron gyrofrequency. The electron pitch angle distributions are anisotropic, peaking near 90° pitch angle, and the fluxes are high during injections. We calculate the whistler‐mode wave growth rates using the observed electron distributions and linear theory. The frequency spectrum of the wave growth rate is consistent with that of the observed chorus magnetic intensity, suggesting that the observed electron injections provide free energy to generate whistler‐mode chorus waves. We further use quasilinear theory to model the impacts of chorus waves on 0.1–10 MeV electrons. Our modeling shows that the chorus waves could cause the pitch angle scattering loss of electrons at <1 MeV energies and accelerate relativistic electrons at multiple MeV energies in Jupiter's outer radiation belt. The electron injections also provide an important seed population at several hundred keV energies to support the acceleration to higher energies. Our wave‐particle interaction modeling demonstrates the energy flow from the electron injections to the relativistic electron population through the medium of whistler‐mode waves in Jupiter's outer radiation belt.more » « less
-
Abstract Electron precipitation by chorus whistler‐mode waves generated by the same electron population is expected to play an important role in the dynamics of the outer radiation belt, potentially setting a hard upper limit on trapped energetic electron fluxes. Here, we statistically analyze the relationship between equatorial electron fluxes and the power of mid‐latitude cyclotron‐resonant chorus waves precipitating these electrons, both inferred from ELFIN low‐altitude energy and pitch‐angle resolved electron flux measurements in 2020–2022. We provide clear evidence of a flux limitation coinciding with an exponential increase of precipitation. We statistically demonstrate that the actual inferred resonant wave power gains are well correlated with theoretical linear gains, as in the classical Kennel‐Petschek model, for moderately high linear gains and high fluxes. However, we also find a finite occurrence of very high fluxes, corresponding to resonant waves of moderate average amplitude, implying a softer, more dynamical upper limit than traditionally envisioned.more » « less
-
Abstract In planetary radiation belts, the Kennel‐Petschek flux limit is expected to set an upper limit on trapped electron fluxes at 80–600 keV in the presence of efficient electron loss through pitch‐angle diffusion by whistler‐mode chorus waves generated around the magnetic equator by the same 80–600 keV electron population. Comparisons with maximum measured fluxes have been relatively successful, but several key assumptions of the Kennel‐Petschek model have not been experimentally tested. The Kennel‐Petschek model notably assumes an exponential growth of chorus waves as the trapped electron flux increases, and a fixed maximum wave power gain of about 3. Here, we describe a method for inferring the near‐equatorial wave power gain using only measurements of trapped, precipitating, and backscattered electron fluxes at low altitude. Next, we make use of Electron Losses and Fields Investigation (ELFIN) CubeSats measurements of such electron fluxes during two moderate geomagnetic storms with sustained electron injections to infer the corresponding chorus wave power gains as a function of time, energy, and equatorial trapped electron flux. We show that wave power increases exponentially with trapped flux, with a wave power gain roughly proportional to the theoretical linear convective gain, and that the maximum inferred gain near the upper flux limit is roughly 10, with a factor of 2 uncertainty. Therefore, two key theoretical underpinnings of the Kennel‐Petschek model are borne out by the present results, although the strong inferred gains should correspond to higher flux limits than in traditional estimates.more » « less
-
Abstract Whistler‐mode chorus and hiss waves play an important role in Earth's radiation belt electron dynamics. Direct measurements of whistler wave‐driven electron precipitation and the resultant pitch angle distribution were previously limited by the insufficient resolution of low Earth orbit satellites. In this study, we use recent measurements from the Electron Losses and Fields INvestigation CubeSats, which provide energy‐ and pitch angle‐resolved electron distributions to statistically evaluate electron scattering properties driven by whistler waves. Our survey indicates that events with increasing precipitating‐to‐trapped flux ratios (evaluated at 63 keV unless otherwise specified) correlate with increasing trapped flux at energies up to ∼750 keV. Weak precipitation events (precipitation ratio <0.2) are evenly distributed, while stronger precipitation events tend to be concentrated atL > 5 over midnight‐to‐noon local times during disturbed geomagnetic conditions. These results are crucial for characterizing the whistler‐mode wave driven electron scattering properties and evaluating its impact on the ionosphere.more » « less
