Quantifying the nonlinear dependence of energetic electron fluxes in the Earth's radiation belts with radial diffusion drivers

In this study, we use mutual information to characterise statistical dependencies of seed and relativistic electron fluxes in the Earth's radiation belts on ultra low frequency (ULF) wave power measured on the ground and at geostationary orbit . The benefit of mutual information, in comparison to measures such as the Pearson correlation, lies in the capacity to distinguish nonlinear dependencies from linear ones. After reviewing the property of mutual information and its relationship with the Pearson correlation for Gaussian bivariates of arbitrary correlation, we present a methodology to quantify and distinguish linear and nonlinear statistical dependencies that can be generalised to a wide range of solar wind drivers and magnetospheric responses. We present an application of the methodology by revisiting the case events studied by Rostoker et al. (1998). Our results corroborate the conclusions of Rostoker et al. (1998) that ULF wave power and relativistic electron fluxes are statistically dependent upon one another. However, we find that observed enhancements in relativistic electron fluxes correlate modestly, both linearly and nonlinearly, with the ULF power spectrum when compared with values found in previous studies (Simms et al., 2014), and with values found between seed electrons and ULF wave power for the same case events. Our results are indicative of the importance in incorporating data analysis tools that can quantify and distinguish between linear and nonlinear interdependencies of various solar wind drivers.

Electrification of Dielectric Satellites under the Influence of Electron Flows of the Earth’s Radiation Belts

The effect of electron fluxes from the Earth’s radiation belts on satellites made of dielectric materials is studied theoretically. Spherical shaped nanosatellites of the BLITS and BLITS-M types are considered as a model. An analytical solution is obtained for the dependence of the electric field on the distance to the center of the satellite. Empirical formulas are used for the electron flux density and the track length in matter depending on the electron energy. The energy losses of incident electrons in the Debye shielding layer that surrounds the satellite, as well as the appearance of radiation conductivity in the surface layer of the dielectric, are taken into account. The reasons for the nonmonotonic dependence of the electric field on the satellite radius are established. Despite the fact that the electric field inside the satellite is smaller than the electrical breakdown threshold of the solid dielectric, it can be assumed that the dielectric micro-breakdown can occur in the surface layer of the dielectric and near inhomogeneities.

Distribution of Earth's radiation belts' protons over the drift frequency of particles

Using data on the proton fluxes of the Earth's radiation belts (ERBs) with energy ranging from 0.2 to 100 MeV on the drift L shells ranging from 1 to 8, the quasi-stationary distributions over the drift frequency fd of protons around the Earth are constructed. For this purpose, direct measurements of proton fluxes of the ERBs during the period from 1961 to 2017 near the geomagnetic equator were employed. The main physical processes in the ERB manifested more clearly in these distributions, and for protons with fd>0.5 mHz at L>3, their distributions in the {fd,L} space have a more regular shape than in the {E,L} space. It has also been found that the quantity of the ERB protons with fd ∼ 1–10 mHz at L∼2 does not decrease, as it does for protons with E > 10–20 MeV (with fd>10 mHz), but increases with an increase in solar activity. This means that the balance of radial transport and loss of ERB low-energy protons at L∼2 is disrupted in favor of transport of these protons: the effect of an increase in the radial diffusion rates with increasing solar activity overpowers the effect of an increase in the density of the dissipative medium.

Distribution of the Earth's radiation belts protons over the drift frequency of particles

On the base of generalized data on the proton fluxes of the Earth's radiation belts (ERB) with energy from E ~ 0.2 MeV to 100 MeV at drift shells L from ~ 1 to 8, constructed stationary distributions of the ERB protons over the drift frequency fd of protons around the Earth. For this, direct measurements of proton fluxes of the ERB in the period 1961–2017 near the plane of the geomagnetic equator were used. The main physical processes in the ERB manifested more clearly in these distributions, and for protons with fd > 0.5 mHz at L > 3 distributions of the ERB protons in the space {fd, L} have a more orderly form than in the space {E, L}. It has been found also that the quantity of the ERB protons with fd ~ 1–10 mHz at L ~ 2 does not decrease, as for protons with E > 10–20 MeV (with fd > 10 mHz), but increases with an increase in solar activity. This means that the balance of radial transport and losses of the ERB low-energy protons at L ~ 2 is disrupt in advantage of transport: for these protons, the effect of an increase in the radial diffusion rates with increasing in solar activity overpowers the effect of an increase in the density of the dissipative medium.

Effect of finite correlation time on the wave-particle interactions of nonlinear electrostatic structures with electrons in the Earth's radiation belts.

<p><em>In situ</em> measurements of electron scale fluctuations by the Van Allen Probes and MMS have demonstrated the ubiquitous occurrence of phase-space holes and various kinetic nonlinear structures in the Earth's magnetosphere. However it remains an open question whether phase-space holes have to be incorporated into global magnetospheric models describing the energisation and acceleration of electrons. In this communication we will review current wave-particle models of electron phase-space holes interacting with energetic electrons (e.g. >1 keV in the Earth's radiation belts)  and present new theoretical results showing that finite correlation times of phase-space holes results in enhanced pitch-angle scattering. The pitch-angle scattering by phase-space holes is shown to be on par with that produced by chorus waves, and in some instances outgrows the chorus contribution. </p><p> </p>