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

This corrects the article DOI: 10.1038/ncomms8143

Electron Flux Dropouts at L ∼ 4.2 From Global Positioning System Satellites: Occurrences, Magnitudes, and Main Driving Factors

Dropouts in electron fluxes at L ∼ 4.2 were investigated for a broad range of energies from 120 keV to 10 MeV, using 16 years of electron flux data from Combined X-ray Dosimeter on board Global Positioning System (GPS) satellites. Dropouts were defined as flux decreases by at least a factor 4 in 12 h, or 24 h during which a decrease by at least a factor of 1.5 must occur during each 12 h time bin. Such fast and strong dropouts were automatically identified from the GPS electron flux data and statistics of dropout magnitudes, and occurrences were compiled as a function of electron energy. Moreover, the Error Reduction Ratio analysis was employed to search for nonlinear relationships between electron flux dropouts and various solar wind and geomagnetic activity indices, in order to identify potential external causes of dropouts. At L ∼ 4.2, the main driving factor for the more numerous and stronger 1-10 MeV electron dropouts turns out to be the southward interplanetary magnetic field B s , suggesting an important effect from precipitation loss due to combined electromagnetic ion cyclotron and whistler mode waves in a significant fraction of these events, supplementing magnetopause shadowing and outward radial diffusion which are also effective at lower energies

Electron flux dropouts at GEO: occurrences, magnitudes, and main driving factors

Large decreases of daily average electron flux, or dropouts, were investigated for a range of energies from 24.1 keV to 2.7 MeV, on the basis of a large database of 20 years of measurements from Los Alamos National Laboratory (LANL) geosynchronous satellites. Dropouts were defined as flux decreases by at least a factor 4 in 1 day, or a factor 9 in 2 days during which a decrease by at least a factor of 2.5 must occur each day. Such decreases were automatically identified. As a first result, a comprehensive statistics of the mean waiting time between dropouts and of their mean magnitude has been provided as a function of electron energy. Moreover, the Error Reduction Ratio analysis was applied to explore the possible nonlinear relationships between electron dropouts and various exogenous factors, such as solar wind and geomagnetic indices. Different dropout occurrences and magnitudes were found in three distinct energy ranges, lower than 100 keV, 100–600 keV, and larger than 600 keV, corresponding to different groups of drivers and loss processes. Potential explanations have been outlined on the basis of the statistical results

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 equation for nonlinear resonant wave-particle interaction

We investigate nonlinear resonant wave-particle interactions including effects of particle (phase) trapping, detrapping, and scattering by high-amplitude coherent waves. After deriving the relation between probability of trapping and velocity of particle drift induced by nonlinear scattering (phase bunching), we substitute this relation and other characteristic equations of wave-particle interaction into a kinetic equation for the particle distribution function. The final equation has the form of a Fokker-Planck equation with peculiar advection and collision terms. This equation fully describes the evolution of particle momentum distribution due to particle diffusion, nonlinear drift, and fast transport in phase-space via trapping. Solutions of the obtained kinetic equation are compared with results of test particle simulations

Long-term evolution of electron distribution function due to nonlinear resonant interaction with whistler mode waves

Accurately modelling and forecasting of the dynamics of the Earth’s radiation belts with the available computer resources represents an important challenge that still requires significant advances in the theoretical plasma physics field of wave–particle resonant interaction. Energetic electron acceleration or scattering into the Earth’s atmosphere are essentially controlled by their resonances with electromagnetic whistler mode waves. The quasi-linear diffusion equation describes well this resonant interaction for low intensity waves. During the last decade, however, spacecraft observations in the radiation belts have revealed a large number of whistler mode waves with sufficiently high intensity to interact with electrons in the nonlinear regime. A kinetic equation including such nonlinear wave–particle interactions and describing the long-term evolution of the electron distribution is the focus of the present paper. Using the Hamiltonian theory of resonant phenomena, we describe individual electron resonance with an intense coherent whistler mode wave. The derived characteristics of such a resonance are incorporated into a generalized kinetic equation which includes non-local transport in energy space. This transport is produced by resonant electron trapping and nonlinear acceleration. We describe the methods allowing the construction of nonlinear resonant terms in the kinetic equation and discuss possible applications of this equation