A. V. Artemyev

Thin current sheets in collisionless plasma: Equilibrium structure, plasma instabilities, and particle acceleration

The review is devoted to plasma structures with an extremely small transverse size, namely, thin current sheets that have been discovered and investigated by spacecraft observations in the Earth’s magnetotail in the last few decades. The formation of current sheets is attributed to complicated dynamic processes occurring in a collisionless space plasma during geomagnetic perturbations and near the magnetic reconnection regions. The models that describe thin current structures in the Earth’s magnetotail are reviewed. They are based on the assumption of the quasi-adiabatic ion dynamics in a relatively weak magnetic field of the magnetotail neutral sheet, where the ions can become unmagnetized. It is shown that the ion distribution can be represented as a function of the integrals of particle motion—the total energy and quasi-adiabatic invariant. Various modifications of the initial equilibrium are considered that are obtained with allowance for the currents of magnetized electrons, the contribution of oxygen ions, the asymmetry of plasma sources, and the effects related to the non-Maxwellian particle distributions. The theoretical results are compared with the observational data from the Cluster spacecraft mission. Various plasma instabilities developing in thin current sheets are investigated. The evolution of the tearing mode is analyzed, and the parameter range in which the mode can grow are determined. The paradox of complete stabilization of the tearing mode in current sheets with a nonzero normal magnetic field component is thereby resolved based on the quasi-adiabatic model. It is shown that, over a wide range of current sheet parameters and the propagation directions of large-scale unstable waves, various modified drift instabilities—kink and sausage modes—can develop in the system. Based on the concept of a turbulent electromagnetic field excited as a result of the development and saturation of unstable waves, a mechanism for charged particle acceleration in turbulent current sheets is proposed and the energy spectra of the accelerated particles are obtained.

Consequences of geomagnetic activity on energization and loss of radiation belt electrons by oblique chorus waves

Statistics of amplitudes and obliquity of lower band chorus whistler mode waves have been obtained from Cluster measurements in Earths outer radiation belt and fitted as functions of L, latitude, magnetic local time, and three geomagnetic activity ranges for Dst ∈ [+10,-80] nT. Very oblique chorus waves have generally a much smaller average intensity than quasi-parallel waves, especially on the nightside. Nevertheless, analytical estimates and full numerical calculations of quasi-linear diffusion rates show that dayside very oblique waves (θ>60°) dominate pitch angle scattering of energetic electrons during moderately disturbed periods. As geomagnetic activity increases, leading to higher wave amplitudes, electron lifetimes are only slightly reduced, due to a decrease of the wave obliquity probably related to Landau damping by stronger incoming fluxes from the plasma sheet. As a result, electron energization by chorus waves for Dst>-80 nT generally occurs in a loss-dominated regime in which energization increases at lower L. However, at L≥6 the most disturbed periods (Dst<-40 nT) produce a stronger energization independent of losses. Double-belt structures may therefore arise when Dst<-40 nT, with two peaks of energization located just outside the plasmapause and at L~6. The variability of lower band chorus wave obliquity with geomagnetic activity could actually account for some part of the observed variability of energization and loss in the outer belt. It is also suggested that quasi-linear pitch angle diffusion by very oblique waves together with energy diffusion by parallel waves might contribute to the steep wave growth observed in the day sector between the equator and 25°.

Time domain structures: What and where they are, what they do, and how they are made

Time domain structures (TDS) (electrostatic or electromagnetic electron holes, solitary waves, double layers, etc.) are ≥1ms pulses having significant parallel (to the background magnetic field) electric fields. They are abundant through space and occur in packets of hundreds in the outer Van Allen radiation belts where they produce magnetic-field-aligned electron pitch angle distributions at energies up to a hundred keV. TDS can provide the seed electrons that are later accelerated to relativistic energies by whistlers and they also produce field-aligned electrons that may be responsible for some types of auroras. These field-aligned electron distributions result from at least three processes. The first process is parallel acceleration by Landau trapping in the TDS parallel electric field. The second process is Fermi acceleration due to reflection of electrons by the TDS. The third process is an effective and rapid pitch angle scattering resulting from electron interactions with the perpendicular and parallel electric and magnetic fields of many TDS. TDS are created by current-driven and beam-related instabilities and by whistler-related processes such as parametric decay of whistlers and nonlinear evolution from oblique whistlers. New results on the temporal relationship of TDS and particle injections, types of field-aligned electron pitch angle distributions produced by TDS, the mechanisms for generation of field-aligned distributions by TDS, the maximum energies of field-aligned electrons created by TDS in the absence of whistler mode waves, TDS generation by oblique whistlers and three-wave-parametric decay, and the correlation between TDS and auroral particle precipitation, are presented.

Non-diffusive resonant acceleration of electrons in the radiation belts

We describe a mechanism of resonant electron acceleration by oblique high-amplitude whistler waves under conditions typical for the Earth radiation belts. We use statistics of spacecraft observations of whistlers in the Earth radiation belts to obtain the dependence of the angle θ between the wave-normal and the background magnetic field on magnetic latitude λ. According to this statistics, the angle θ already approaches the resonance cone at λ∼15° and remains close to it up to λ∼30°–40° on the dayside. The parallel component of the electrostatic field of whistler waves often increases around λ∼15° up to one hundred of mV/m. We show that due to this increase of the electric field, the whistler waves can trap electrons into the potential well via wave particle resonant interaction corresponding to Landau resonance. Trapped electrons then move with the wave to higher latitudes where they escape from the resonance. Strong acceleration is favored by adiabatic invariance along the increasing magnetic field, wh...

The quasi‐electrostatic mode of chorus waves and electron nonlinear acceleration

Selected Time History of Events and Macroscale Interactions During Substorms observations at medium latitudes of highly oblique and high-amplitude chorus waves are presented and analyzed. The presence of such very intense waves is expected to have important consequences on electron energization in the magnetosphere. An analytical model is therefore developed to evaluate the efficiency of the trapping and acceleration of energetic electrons via Landau resonance with such nearly electrostatic chorus waves. Test-particle simulations are then performed to illustrate the conclusions derived from the analytical model, using parameter values consistent with observations. It is shown that the energy gain can be much larger than the initial particle energy for 10 keV electrons, and it is further demonstrated that this energy gain is weakly dependent on the density variation along field lines.

Very oblique whistler generation by low‐energy electron streams

Whistler mode chorus waves are present throughout the Earths 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.

Evidence of stronger pitch angle scattering loss caused by oblique whistler‐mode waves as compared with quasi‐parallel waves

Wave normal distributions of lower-band whistler-mode waves observed outside the plasmapause exhibit two peaks: one near the parallel direction and the other at very oblique angles. We analyze a number of conjunction events between the Van Allen Probes near the equatorial plane and Polar Orbiting Environmental Satellites (POES) at conjugate low altitudes, where lower-band whistler-mode wave amplitudes were inferred from the two-directional POES electron measurements over 30–100 keV, assuming that these waves were quasi-parallel. For conjunction events, the wave amplitudes inferred from the POES electron measurements were found to be overestimated as compared with the Van Allen Probes measurements primarily for oblique waves and quasi-parallel waves with small wave amplitudes (< ~20 pT) measured at low latitudes. This provides plausible experimental evidence of stronger pitch angle scattering loss caused by oblique waves than by quasi-parallel waves with the same magnetic wave amplitudes, as predicted by numerical calculations.

Thermal electron acceleration by localized bursts of electric field in the radiation belts

In this paper we investigate the resonant interaction of thermal ∼10–100 eV electrons with a burst of electrostatic field that results in electron acceleration to kilovolt energies. This single burst contains a large parallel electric field of one sign and a much smaller, longer-lasting parallel field of the opposite sign. The Van Allen Probe spacecraft often observes clusters of spatially localized bursts in the Earths outer radiation belts. These structures propagate mostly away from the geomagnetic equator and share properties of soliton-like nonlinear electron acoustic waves: a velocity of propagation is about the thermal velocity of cold electrons (∼3000–10,000 km/s), and a spatial scale of electric field localization along the field lines is about the Debye radius of hot electrons (∼5–30 km). We model the nonlinear resonant interaction of these electric field structures and cold background electrons.

Electron pitch‐angle diffusion in radiation belts: The effects of whistler wave oblique propagation

[1] We calculated the electron pitch-angle diffusion coefficients in the outer radiation belt for L-shell

Wave energy budget analysis in the Earth/'s radiation belts uncovers a missing energy

4.5 taking into account the effects of oblique whistler wave propagation. The dependence of the distribution of the angle q between the whistler wave vector and the background magnetic field on magnetic latitude is modeled after statistical results of Cluster wave angle observations. According to in-situ observations , the mean value and the variance of the q distribution rapidly increase with magnetic latitude. We found that inclusion of oblique whistler wave propagation led to a significant increase in pitch-angle diffusion rates over those calculated under the assumption of parallel whistler wave propagation. The effect was pronounced for electrons with small equatorial pitch-angles close to the loss cone and could result in as much as an order of magnitude decrease of the electron lifetimes. We show that the intensification of pitch-angle diffusion can be explained by the contribution of higher order cyclotron resonances. By comparing the results of calculations obtained from two models of electron density distribution along field lines, we show that the effect of the intensification of pitch-angle diffusion is stronger when electron density does not vary along field lines. The intensification of pitch-angle diffusion and corresponding decrease of energetic electron lifetime result in significant modification of the rate of electron losses and should have an impact on formation and dynamics of the outer radiation belt. Citation: Artemyev, A., O. Agapitov, H. Breuillard, V. Krasnoselskikh, and G. Rolland (2012), Electron pitch-angle diffusion in radiation belts: The effects of whistler wave oblique propagation, Geophys.