Butterfly pitch-angle distribution of relativistic electrons in the outer radiation belt: Evidence of nonadiabatic scattering

In this paper we investigate the scattering of relativistic electrons in the nightside outer radiation belt (around the geostationary orbit). We consider the particular case of low geomagnetic activity (|Dst|\u3c20 nT), quiet conditions in the solar wind, and absence of whistler wave emissions. For such conditions we find several events of Van Allen probe observations of butterfly pitch angle distributions of relativistic electrons (energies about 1–3 MeV). Many previous publications have described such pitch angle distributions over a wide energy range as due to the combined effect of outward radial diffusion and magnetopause shadowing. In this paper we discuss another mechanism that produces butterfly distributions over a limited range of electron energies. We suggest that such distributions can be shaped due to relativistic electron scattering in the equatorial plane of magnetic field lines that are locally deformed by currents of hot ions injected into the inner magnetosphere. Analytical estimates, test particle simulations, and observations of the AE index support this scenario. We conclude that even in the rather quiet magnetosphere, small scale (magnetic local time (MLT)-localized) injection of hot ions from the magnetotail can likely influence the relativistic electron scattering. Thus, observations of butterfly pitch angle distributions can serve as an indicator of magnetic field deformations in the nightside inner magnetosphere. We briefly discuss possible theoretical approaches and problems for modeling such nonadiabatic electron scattering

Publisher Correction: Wave energy budget analysis in the Earths radiation belts uncovers a missing energy.

This corrects the article DOI: 10.1038/ncomms8143

Approximate analytical formulation of radial diffusion and whistler-induced losses from a preexisting flux peak in the plasmasphere

International audienceModeling the spatiotemporal evolution of relativistic electron fluxes trapped in the Earth's radiation belts in the presence of radial diffusion coupled with wave-induced losses should address one important question: how deep can relativistic electrons penetrate into the inner magnetosphere? However, a full modeling requires extensive numerical simulations solving the comprehensive quasi-linear equations describing pitch angle and radial diffusion of the electron distribution, making it rather difficult to perform parametric studies of the flux behavior. Here we consider the particular situation where a localized flux peak (or storage ring) has been produced at low L < 4 during a period of strong disturbances, through a combination of chorus-induced energy diffusion (or direct injection) at low L together with enhanced wave-induced losses and outward radial transport at higher L. Assuming that radial diffusion can be further described as the spatial broadening within the plasmasphere of this preexisting flux peak, simple approximate analytical solutions for the distribution of trapped relativistic electrons are derived. Such a simplified formalism provides a convenient means for easily determining whether radial diffusion actually prevails over atmospheric losses at any particular time for given electron energy E and location L. It is further used to infer favorable conditions for relativistic electron access to the inner belt, providing an explanation for the relative scarcity of such a feat under most circumstances. Comparisons with electron flux measurements on board the Van Allen Probes show a reasonable agreement between a few weeks and 4 months after the formation of a flux peak

Wave-particle interactions in the outer radiation belts

Data from the Van Allen Probes have provided the first extensive evidence of non-linear (as opposed to quasi-linear) wave-particle interactions in space with the associated rapid (fraction of a bounce period) electron acceleration to hundreds of keV by Landau resonance in the parallel electric fields of time domain structures (TDS) and very oblique chorus waves. The experimental evidence, simulations, and theories of these processes are discussed. {\bf Key words:} the radiation belts, wave-particle interaction, plasma waves and instabilitiesComment: 9 pages, 2 figure

Acceleration of radiation belts electrons by oblique chorus waves

International audience[1] The redistribution of energy during the recovery phase of geomagnetic storms related to the acceleration of electrons in the Earth's outer radiation belt by cyclotron-resonant chorus waves is an important and challenging topic of magnetospheric plasma physics. An approximate analytical formulation of energy diffusion coefficients is derived in this paper, on the basis of a quasi-linear formalism valid for large enough bandwidths or for successive random scatter by uncorrelated waves of different frequencies and moderate average amplitudes. We make use of chorus wave parameterizations derived from CLUSTER measurements to show that oblique whistler waves can significantly increase the energy diffusion rate of small pitch angle electrons on the dayside. On the other hand, the energization rate of the more numerous high pitch angle electrons is typically reduced by a factor of 2 on the dayside, while it remains nearly unchanged on the nightside where high-intensity waves are less oblique. Besides, lifetimes are strongly reduced on the dayside, which could also impact the long-term time-integrated acceleration rates of injected electrons. Comparison between the analytical formulas and full numerical results demonstrates a good agreement and provides new scaling laws as a function of whistler mean frequency, plasma density and particle energy. It is also suggested that the enhancement of energy diffusion of low energy electrons (<100 keV) at small pitch angles with oblique waves could result in an intensification of wave growth at latitudes higher than 15. This might contribute to explain high chorus intensities measured by CLUSTER on the dayside at high latitudes. Citation: Mourenas, D., A. Artemyev, O. Agapitov, and V. Krasnoselskikh (2012), Acceleration of radiation belts electrons by oblique chorus waves

Analytical estimates of electron quasi-linear diffusion by fast magnetosonic waves

International audience[1] Quantifying the loss of relativistic electrons from the Earth's radiation belts requires to estimate the effects of many kinds of observed waves, ranging from ULF to VLF. Analytical estimates of electron quasi-linear diffusion coefficients for whistler-mode chorus and hiss waves of arbitrary obliquity have been recently derived, allowing useful analytical approximations for lifetimes. We examine here the influence of much lower frequency and highly oblique, fast magnetosonic waves (also called ELF equatorial noise) by means of both approximate analytical formulations of the corresponding diffusion coefficients and full numerical simulations. Further analytical developments allow us to identify the most critical wave and plasma parameters necessary for a strong impact of fast magnetosonic waves on electron lifetimes and acceleration in the simultaneous presence of chorus, hiss, or lightning-generated waves, both inside and outside the plasmasphere. In this respect, a relatively small frequency over ion gyrofrequency ratio appears more favorable, and other propitious circumstances are characterized. This study should be useful for a comprehensive appraisal of the potential effect of fast magnetosonic waves throughout the magnetosphere. Citation: Mourenas, D., A. V. Artemyev, O. V. Agapitov, and V. Krasnoselskikh (2013), Analytical estimates of electron quasi-linear diffusion by fast magnetosonic waves

Kinetic models of tangential discontinuities in the solar wind

TN acknowledges financial support by the UK's Science and Technology Facilities Council (STFC) via Consolidated Grant ST/S000402/1. OA was supported by the Natural Environment Research Council (NERC) Highlight Topic Grant #NE/P017274/1 (Rad-Sat).Kinetic-scale current sheets observed in the solar wind are frequently approximately force-free despite the fact that their plasma β is of the order of one. In-situ measurements have recently shown that plasma density and temperature often vary across the current sheets, while the plasma pressure is approximately uniform. In many cases these density and temperature variations are asymmetric with respect to the center of the current sheet. To model these observations theoretically we develop in this paper equilibria of kinetic-scale force-free current sheets that have plasma density and temperature gradients. The models can also be useful for analysis of stability and dissipation of the current sheets in the solar wind.PostprintPeer reviewe

Electron pitch-angle diffusion: resonant scattering by waves vs.nonadiabatic effects

International audienceIn this paper we investigate the electron pitchanglediffusion coefficients in the night-side inner magnetospherearound the geostationary orbit (L 7) due to magneticfield deformation. We compare the effects of resonantwave–particle scattering by lower band chorus waves and theadiabaticity violation of electron motion due to the strongcurvature of field lines in the vicinity of the equator. Fora realistic magnetic field configuration, the nonadiabatic effectsare more important than the wave–particle interactionsfor high energy (> 1 MeV) electrons. For smaller energy,the scattering by waves is more effective than nonadiabaticone. Moreover, the role of nonadiabatic effects increases withparticle energy. Therefore, to model electron scattering andtransport in the night-side inner magnetosphere, it is importantto take into account the peculiarities of high-energy electrondynamics

K-shell ionization of heavy hydrogen-like ions

A theoretical study of the K-shell ionization of hydrogen-like ions, colliding with bare nuclei, is performed within the framework of the time-dependent Dirac equation. Special emphasis is placed on the ionization probability that is investigated as a function of impact parameter, collision energy and nuclear charge. To evaluate this probability in a wide range of collisional parameters we propose a simple analytical expression for the transition amplitude. This expression contains three fitting parameters that are determined from the numerical calculations, based on the adiabatic approximation. In contrast to previous studies, our analytical expression for the transition amplitude and ionization probability accounts for the full multipole expansion of the two-center potential and allows accurate description of nonsymmetric collisions of nuclei with different atomic numbers, $Z_1 \neq Z_2$. The calculations performed for both symmetric and asymmetric collisions indicate that the ionization probability is reduced when the difference between the atomic numbers of ions increases.Comment: 8 pages, 6 figure