I. Y. Vasko

Magnetic field depression within electron holes

We analyze electron holes that are spikes of the electrostatic field (up to 500 mV/m) observed by Van Allen Probes in the outer radiation belt. The unexpected feature is the magnetic field depression of about several tens of picotesla within many of the spikes. The earlier observations showed amplification or negligible perturbations of the magnetic field within the electron holes. We suggest that the observed magnetic field depression is due to the diamagnetic current of hot and highly anisotropic population of electrons trapped within the electron holes. The required trapped population should have a density up to 65% of the background plasma density, a temperature up to several keV, and a temperature anisotropy T⊥/T∥∼2. We argue that the observed electron holes could be generated due to injections of highly anisotropic plasma sheet electrons into the outer radiation belt. These electron holes may present a source of the seed population due to transport of trapped electrons to higher latitudes and can be potentially used for distant probing of plasma properties in their source region.

Electron holes in inhomogeneous magnetic field: Electron heating and electron hole evolution

Electron holes are electrostatic non-linear structures widely observed in the space plasma. In the present paper, we analyze the process of energy exchange between electrons trapped within electron hole, untrapped electrons, and an electron hole propagating in a weakly inhomogeneous magnetic field. We show that as the electron hole propagates into the region with stronger magnetic field, trapped electrons are heated due to the conservation of the first adiabatic invariant. At the same time, the electron hole amplitude may increase or decrease in dependence on properties of distribution functions of trapped and untrapped resonant electrons. The energy gain of trapped electrons is due to the energy losses of untrapped electrons and/or decrease of the electron hole energy. We stress that taking into account the energy exchange with untrapped electrons increases the lifetime of electron holes in inhomogeneous magnetic field. We illustrate the suggested mechanism for small-amplitude Schamels [Phys. Scr. T2, 228–237 (1982)] electron holes and show that during propagation along a positive magnetic field gradient their amplitude should grow. Neglect of the energy exchange with untrapped electrons would result in the electron hole dissipation with only modest heating factor of trapped electrons. The suggested mechanism may contribute to generation of suprathermal electron fluxes in the space plasma.

Diffusive scattering of electrons by electron holes around injection fronts

Van Allen Probes have detected nonlinear electrostatic spikes around injection fronts in the outer radiation belt. These spikes include electron holes (EH), double layers, and more complicated solitary waves. We show that EHs can efficiently scatter electrons due to their substantial transverse electric fields. Although the electron scattering driven by EHs is diffusive, it cannot be evaluated via the standard quasi-linear theory. We derive analytical formulas describing local electron scattering by a single EH and verify them via test particle simulations. We show that the most efficiently scattered are gyroresonant electrons (crossing EH on a time scale comparable to the local electron gyroperiod). We compute bounce-averaged diffusion coefficients and demonstrate their dependence on the EH spatial distribution (latitudinal extent and spatial filling factor) and individual EH parameters (amplitude of electrostatic potential, velocity, and spatial scales). We show that EHs can drive pitch angle scattering of ≲5 keV electrons at rates 10 −2 − 10 −4 s −1 and, hence, can contribute to electron losses and conjugated diffuse aurora brightenings. The momentum and pitch angle scattering rates can be comparable, so that EHs can also provide efficient electron heating. The scattering rates driven by EHs at L shells L ∼ 5–8 are comparable to those due to chorus waves and may exceed those due to electron cyclotron harmonics.

Electron-acoustic solitons and double layers in the inner magnetosphere: ELECTRON-ACOUSTIC SOLITONS

The Van Allen Probes observe generally two types of electrostatic solitary waves (ESW) contributing to the broadband electrostatic wave activity in the nightside inner magnetosphere. ESW with symmetric bipolar parallel electric field are electron phase space holes. The nature of ESW with asymmetric bipolar (and almost unipolar) parallel electric field has remained puzzling. To address their nature, we consider a particular event observed by Van Allen Probes to argue that during the broadband wave activity electrons with energy above 200 eV provide the dominant contribution to the total electron density, while the density of cold electrons (below a few eV) is less than a few tenths of the total electron density. We show that velocities of the asymmetric ESW are close to velocity of electron-acoustic waves (existing due to the presence of cold and hot electrons) and follow the Korteweg-de Vries (KdV) dispersion relation derived for the observed plasma conditions (electron energy spectrum is a power law between about 100 eV and 10 keV and Maxwellian above 10 keV). The ESW spatial scales are in general agreement with the KdV theory. We interpret the asymmetric ESW in terms of electron-acoustic solitons and double layers (shocks waves).

Effects of electron pressure anisotropy on current sheet configuration

Recent spacecraft observations in the Earths magnetosphere have demonstrated that the magnetotail current sheet can be supported by currents of anisotropic electron population. Strong electron currents are responsible for the formation of very thin (intense) current sheets playing the crucial role in stability of the Earths magnetotail. We explore the properties of such thin current sheets with hot isotropic ions and cold anisotropic electrons. Decoupling of the motions of ions and electrons results in the generation of a polarization electric field. The distribution of the corresponding scalar potential is derived from the electron pressure balance and the quasi-neutrality condition. We find that electron pressure anisotropy is partially balanced by a field-aligned component of this polarization electric field. We propose a 2D model that describes a thin current sheet supported by currents of anisotropic electrons embedded in an ion-dominated current sheet. Current density profiles in our model agree w...

Electron-acoustic solitary waves in the Earth's inner magnetosphere

The broadband electrostatic turbulence observed in the inner magnetosphere is produced by large-amplitude electrostatic solitary waves of generally two types. The solitary waves with symmetric bipolar parallel (magnetic field-aligned) electric field are electron phase space holes. The solitary waves with highly asymmetric bipolar parallel electric field have been recently shown to correspond to the electron-acoustic plasma mode (existing due to two-temperature electron population). Through theoretical and numerical analysis of hydrodynamic and modified Korteweg-de Vries equations, we demonstrate that the asymmetric solitary waves appear due to the steepening of initially quasi-monochromatic electron-acoustic perturbation arrested at some moment by collisionless dissipation (Landau damping). The typical steepening time is found to be from a few to tens of milliseconds. The steepening of the electron-acoustic waves has not been reproduced in self-consistent kinetic simulations yet, and factors controlling t...

Evolution of electron phase space holes in inhomogeneous plasmas

Electron phase space holes or vortices (EHs) are electrostatic solitary waves with a bipolar parallel (magnetic field-aligned) electric field. They are formed in a nonlinear stage of electron streaming type instabilities and exist due to electrons trapped within the EH electrostatic potential. The background plasma density gradients, characteristic for both space and laboratory plasmas, can affect the evolution of EHs. In this paper, we use a one-dimensional electrostatic Vlasov–Ampere code (ions are immobile) with periodic boundary conditions to study the evolution of a single EH in inhomogeneous plasmas. We find that the EH propagating along a positive (negative) plasma density gradient is accelerated (decelerated) and narrowed (widened). EH propagating along a positive density gradient results in the acceleration of a relatively small population of trapped electrons to suprathermal energies. Interestingly, a decelerating EH is reflected at the point with the plasma density value dependent only on EH pa...

Pulsating auroras produced by interactions of electrons and time domain structures

Previous evidence has suggested that either lower band chorus waves or kinetic Alfven waves scatter equatorial kilovolt electrons that propagate to lower altitudes where they precipitate or undergo further low altitude scattering to make pulsating auroras. Recently, time domain structures (TDS) were shown, both theoretically and experimentally, to efficiently scatter equatorial electrons. To assess the relative importance of these three mechanisms for production of pulsating auroras, eleven intervals of equatorial THEMIS data and a four-hour interval of Van Allen Probe measurements have been analyzed. During these events, lower band chorus waves produced only negligible modifications of the equatorial electron distributions. During the several TDS events, the equatorial 0.1-3 keV electrons became magnetic-field-aligned. Kinetic Alfven waves may also have had a small electron scattering effect. The conclusion of these studies is that time domain structures caused the most important equatorial scattering of ~1 keV electrons toward the loss cone to provide the main electron contribution to pulsating auroras. Chorus wave scattering may have provided part of the highest energy (>10 keV) electrons in such auroras.

Evolution of electron phase space holes in inhomogeneous magnetic fields

Electron phase space holes (EH) are electrostatic solitary waves that are widely observed in the space plasma often permeated by inhomogeneous magnetic fields. Understanding of the EH evolution in inhomogeneous magnetic fields is critical for accurate interpretations of spacecraft data. To study this evolution we use 1.5D gyrokinetic electrostatic Vlasov code (magnetized electrons and immobile ions) with periodic boundary conditions. We find that EHs propagating into stronger (weaker) magnetic field are decelerated (accelerated) with deceleration (acceleration) rate dependent on the magnetic field gradient. Remarkably, decelerating EHs are reflected at the magnetic field dependent only on EH parameters (independent of the magnetic field gradient). A magnetic field inhomogeneity results in development of a net potential drop along EHs. Our simulations suggest that slow EHs recently observed in the plasma sheet boundary layer can appear due to braking of initially fast EHs by magnetic field gradients and that a large number of even fast EHs can contribute to macroscopic parallel potential drops.

Kinetic models of sub-ion cylindrical magnetic hole

Magnetic holes are magnetoplasma structures very similar to the classical θ–pinch. They are widely observed in the space plasma and identified by the substantial magnetic field depressions on scales from magnetohydrodynamic range to electron scales. In this paper, we develop the kinetic models of cylindrically symmetric magnetic holes with sub-ion scales using two types of charged particle distribution functions (both current-carrying and background plasma populations are included). We demonstrate that developed magnetic holes have configurations very similar to those revealed in the recent spacecraft observations in the Earth magnetosphere: both localized electron currents and strong radial electric fields are found at the magnetic hole boundary. We demonstrate that for realistic plasma parameters, the inclusion of ion currents into the model produces magnetic holes with double-scale magnetic field profile. We find that the magnetic hole depth (amplitude of the magnetic field depression) depends on the m...