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

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

This corrects the article DOI: 10.1038/ncomms8143

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

Very oblique whistler generation by low-energy electron streams

International audienceWhistler mode chorus waves are present throughout the Earth's outer radiation belt as well as at larger distances from our planet. While the generation mechanisms of parallel lower band chorus waves and oblique upper band chorus waves have been identified and checked in various instances, the statistically significant presence in recent satellite observations of very oblique lower band chorus waves near the resonance cone angle remains to be explained. Here we discuss two possible generation mechanisms for such waves. The first one is based on Landau resonance with sporadic very low energy (<4 keV) electron beams either injected from the plasma sheet or produced in situ. The second one relies on cyclotron resonance with low-energy electron streams, such that their velocity distribution possesses both a significant temperature anisotropy above 3–4 keV and a plateau or heavy tail in parallel velocities at lower energies encompassing simultaneous Landau resonance with the same waves. The corresponding frequency and wave normal angle distributions of the generated very oblique lower band chorus waves, as well as their frequency sweep rate, are evaluated analytically and compared with satellite observations, showing a reasonable agreement

On nonstationarity and rippling of the quasiperpendicular zone of the Earth bow shock: Cluster observations

A new method for remote sensing of the quasiperpendicular part of the bow shock surface is presented. The method is based on analysis of high frequency electric field fluctuations corresponding to Langmuir, upshifted, and downshifted oscillations in the electron foreshock. Langmuir waves usually have maximum intensity at the upstream boundary of this region. All these waves are generated by energetic electrons accelerated by quasiperpendicular zone of the shock front. Nonstationary behavior of the shock, in particular due to rippling, should result in modulation of energetic electron fluxes, thereby giving rise to variations of Langmuir waves intensity. For upshifted and downshifted oscillations, the variations of both intensity and central frequency can be observed. For the present study, WHISPER measurements of electric field spectra obtained aboard Cluster spacecraft are used to choose 48 crossings of the electron foreshock boundary with dominating Langmuir waves and to perform for the first time a statistical analysis of nonstationary behavior of quasiperpendicular zone of the Earth&apos;s bow shock. Analysis of hidden periodicities in plasma wave energy reveals shock front nonstationarity in the frequency range 0.33 &lt;I&gt;f&lt;sub&gt;Bi&lt;/sub&gt;&amp;lt;f&amp;lt;f&lt;sub&gt;Bi&lt;/sub&gt;&lt;/I&gt;, where &lt;I&gt;f&lt;sub&gt;Bi&lt;/sub&gt;&lt;/I&gt; is the proton gyrofrequency upstream of the shock, and shows that the probability to observe such a nonstationarity increases with Mach number. The profiles observed aboard different spacecraft and the dominating frequencies of the periodicities are usually different. Hence nonstationarity and/or rippling seem to be rather irregular both in space and time rather than resembling a quasiregular wave propagating on the shock surface

Non-diffusive resonant acceleration of electrons in the radiation belts

International audienceWe describe a mechanism of resonant electron acceleration by oblique high-amplitude whistlerwaves under conditions typical for the Earth radiation belts. We use statistics of spacecraftobservations of whistlers in the Earth radiation belts to obtain the dependence of the angle hbetween the wave-normal and the background magnetic field on magnetic latitude k. According tothis statistics, the angle h already approaches the resonance cone at k 15 and remains close to itup to k 30–40 on the dayside. The parallel component of the electrostatic field of whistlerwaves often increases around k 15 up to one hundred of mV/m. We show that due to thisincrease of the electric field, the whistler waves can trap electrons into the potential well via waveparticle resonant interaction corresponding to Landau resonance. Trapped electrons then move withthe wave to higher latitudes where they escape from the resonance. Strong acceleration is favoredby adiabatic invariance along the increasing magnetic field, which continuously transfers theparallel energy gained to perpendicular energy, allowing resonance to be reached and maintained.The concomitant increase of the wave phase velocity allows for even stronger relative accelerationat low energy <50 keV. Each trapping-escape event of electrons of 10 keV to 100 keV results inan energy gain of up to 100 keV in the inhomogeneous magnetic field of the Earth dipole. Forelectrons with initial energy below 100 keV, such rapid acceleration should hasten their drop intothe loss-cone and their precipitation into the atmosphere. We discuss the role of the consideredmechanism in the eventual formation of a trapped distribution of relativistic electrons for initialenergies larger than 100 keV and in microbursts precipitations of lower energy particles

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

PROBABILISTIC MODEL OF BEAM–PLASMA INTERACTION IN RANDOMLY INHOMOGENEOUS PLASMA

International audienceWe propose a new model that describes beam–plasma interaction in the presence of random density fluctuationswith a known probability distribution. We use the property that, for the given frequency, the probabilitydistribution of the density fluctuations uniquely determines the probability distribution of the phase velocity ofwaves. We present the system as discrete and consisting of small, equal spatial intervals with a linear densityprofile. This approach allows one to estimate variations in wave energy density and particle velocity, depending onthe density gradient on any small spatial interval. Because the characteristic time for the evolution of the electrondistribution function and the wave energy is much longer than the time required for a single wave–particle resonantinteraction over a small interval, we determine the description for the relaxation process in terms of averagedquantities. We derive a system of equations, similar to the quasi-linear approximation, with the conventionalvelocity diffusion coefficient D and the wave growth rate γ replaced by the average in phase space, by making useof the probability distribution for phase velocities and by assuming that the interaction in each interval isindependent of previous interactions. Functions D and γ are completely determined by the distribution function forthe amplitudes of the fluctuations. For the Gaussian distribution of the density fluctuations, we show that therelaxation process is determined by the ratio of beam velocity to plasma thermal velocity, the dispersion of thefluctuations, and the width of the beam in the velocity space