In the outer radiation belt, the acceleration and loss of high-energy electrons is largely controlled by wave-particle interactions. Quasilinear diffusion coefficients are an efficient way to capture the small-scale physics of wave-particle interactions due to magnetospheric wave modes such as plasmaspheric hiss. The strength of quasilinear diffusion coefficients as a function of energy and pitch angle depends on both wave parameters and plasma parameters such as ambient magnetic field strength, plasma number density, and composition. For plasmaspheric hiss in the magnetosphere, observations indicate large variations in the wave intensity and wave normal angle, but less is known about the simultaneous variability of the magnetic field and number density. We use in situ measurements from the Van Allen Probe mission to demonstrate the variability of selected factors that control the size and shape of pitch angle diffusion coefficients: wave intensity, magnetic field strength, and electron number density. We then compare with the variability of diffusion coefficients calculated individually from colocated and simultaneous groups of measurements. We show that the distribution of the plasmaspheric hiss diffusion coefficients is highly non-Gaussian with large variance and that the distributions themselves vary strongly across the three phase space bins studied. In most bins studied, the plasmaspheric hiss diffusion coefficients tend to increase with geomagnetic activity, but our results indicate that new approaches that include natural variability may yield improved parameterizations. We suggest methods like stochastic parameterization of wave-particle interactions could use variability information to improve modeling of the outer radiation belt. Plain Language SummaryThe electrons in Earth's radiation belts exist in a highly rarefied part of space where collisions between particles is very rare. The only way in which the energy or direction of the trapped high-energy electrons can be changed is through interactions with electromagnetic waves. The efficacy of the interaction is a function of the energy and direction of travel of the electrons. In physics-based models of the radiation belts, the efficacy of the wave-particle interactions is captured in diffusion coefficients. These functions are constructed from information about the amplitude and frequency properties of the waves in the interaction, the magnetic field strength, ion composition, and density of the local plasma. We build up collections of observations of these properties from multiple passes of one of the NASA Van Allen probes through the same three small regions of space. The observations display significant temporal variability. We report on the statistical distributions of wave intensity, magnetic field strength and plasma number density and investigate the statistical distribution of the resulting diffusion coefficient. We find that the diffusion coefficients are highly variable and suggest that, by borrowing methods from other branches of geophysics...
The Van Allen Probes mission provides unique measurements of the most energetic radiation belt electrons at ultrarelativistic energies. Simultaneous observations of plasma waves allow for the routine inference of total plasma number density, a parameter that is very difficult to measure directly. On the basis of long-term observations in 2015, we show that the underlying plasma density has a controlling effect over acceleration to ultrarelativistic energies, which occurs only when the plasma number density drops down to very low values (~10 cm–3). Such low density creates preferential conditions for local diffusive acceleration of electrons from hundreds of kilo–electron volts up to >7 MeV. While previous models could not reproduce the local acceleration of electrons to such high energies, here we complement the observations with a numerical model to show that the conditions of extreme cold plasma depletion result in acceleration up to >7 MeV.
Test particle codes indicate that electron dynamics due to interactions with low amplitude incoherent whistler mode‐waves can be adequately described by quasi‐linear theory. However there is significant evidence indicating that higher amplitude waves cause electron dynamics not adequately described using quasi‐linear theory. Using the method that was introduced in Allanson et al. (2019, https://doi.org/10.1029/2019JA027088), we track the dynamical response of electrons due to interactions with incoherent whistler‐mode waves, across all energy and pitch angle space. We conduct five experiments each with different values of the electromagnetic wave amplitude. We find that the electron dynamics agree well with the quasi‐linear theory diffusion coefficients for low amplitude incoherent waves with (Bw,rms/B0)2≈3.7·10−10, over a time scale T of the order of 1,000 gyroperiods. However, the resonant interactions with higher amplitude waves cause significant nondiffusive dynamics as well as diffusive dynamics. When electron dynamics are extracted and analyzed over time scales shorter than T, we are able to isolate both the diffusive and nondiffusive (advective) dynamics. Interestingly, when considered over these appropriately shorter time scales (of the order of hundreds or tens of gyroperiods), the diffusive component of the dynamics agrees well with the predictions of quasi‐linear theory, even for wave amplitudes up to (Bw,rms/B0)2≈5.8·10−6. Quasi‐linear theory is based on fundamentally diffusive dynamics, but the evidence presented herein also indicates the existence of a distinct advective component. Therefore, the proper description of electron dynamics in response to wave‐particle interactions with higher amplitude whistler‐mode waves may require Fokker‐Planck equations that incorporate diffusive and advective terms.
Electrically charged particles are trapped by the Earth’s magnetic field, forming the Van Allen radiation belts. Observations show that electrons in this region can have energies in excess of 7 MeV. However, whether electrons at these ultra-relativistic energies are locally accelerated, arise from betatron and Fermi acceleration due to transport across the magnetic field, or if a combination of both mechanisms is required, has remained an unanswered question in radiation belt physics. Here, we present a unique way of analyzing satellite observations which demonstrates that local acceleration is capable of heating electrons up to 7 MeV. By considering the evolution of phase space density peaks in magnetic coordinate space, we observe distinct signatures of local acceleration and the subsequent outward radial diffusion of ultra-relativistic electron populations. The results have important implications for understanding the origin of ultra-relativistic electrons in Earth’s radiation belts, as well as in magnetized plasmas throughout the solar system.
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