Electron Kinetic Entropy across Quasi-Perpendicular Shocks

We use Magnetospheric Multiscale (MMS) data to study electron kinetic entropy per particle Se across Earth’s quasi-perpendicular bow shock. We have selected 22 shock crossings covering a wide range of shock conditions. Measured distribution functions are calibrated and corrected for spacecraft potential, secondary electron contamination, lack of measurements at the lowest energies and electron density measurements based on plasma frequency measurements. All crossings display an increase in electron kinetic entropy across the shock ΔSe being positive or zero within their error margin. There is a strong dependence of ΔSe on the change in electron temperature, ΔTe, and the upstream electron plasma beta, βe. Shocks with large ΔTe have large ΔSe. Shocks with smaller βe are associated with larger ΔSe. We use the values of ΔSe, ΔTe and density change Δne to determine the effective adiabatic index of electrons for each shock crossing. The average effective adiabatic index is 〈γe〉=1.64±0.07.

Electron Energy Partition across Interplanetary Shocks. I. Methodology and Data Product

Analyses of 15,314 electron velocity distribution functions (VDFs) within ±2 hr of 52 interplanetary (IP) shocks observed by the Wind spacecraft near 1 au are introduced. The electron VDFs are fit to the sum of three model functions for the cold dense core, hot tenuous halo, and field-aligned beam/strahl component. The best results were found by modeling the core as either a bi-kappa or a symmetric (or asymmetric) bi-self-similar VDF, while both the halo and beam/strahl components were best fit to bi-kappa VDF. This is the first statistical study to show that the core electron distribution is better fit to a self-similar VDF than a bi-Maxwellian under all conditions. The self-similar distribution deviation from a Maxwellian is a measure of inelasticity in particle scattering from waves and/or turbulence. The ranges of values defined by the lower and upper quartiles for the kappa exponents are κ ec ~ 5.40-10.2 for the core, κ eh ~ 3.58-5.34 for the halo, and κ eb ~ 3.40-5.16 for the beam/strahl. The lower-to-upper quartile range of symmetric bi-self-similar core exponents is s ec ~ 2.00-2.04, and those of asymmetric bi-self-similar core exponents are p ec ~ 2.20-4.00 for the parallel exponent and q ec ~ 2.00-2.46 for the perpendicular exponent. The nuanced details of the fit procedure and description of resulting data product are also presented. The statistics and detailed analysis of the results are presented in Paper II and Paper III of this three-part study.

Electron Bulk Acceleration and Thermalization at Earth's Quasiperpendicular Bow Shock

Electron heating at Earth's quasiperpendicular bow shock has been surmised to be due to the combined effects of a quasistatic electric potential and scattering through wave-particle interaction. Here we report the observation of electron distribution functions indicating a new electron heating process occurring at the leading edge of the shock front. Incident solar wind electrons are accelerated parallel to the magnetic field toward downstream, reaching an electron-ion relative drift speed exceeding the electron thermal speed. The bulk acceleration is associated with an electric field pulse embedded in a whistler-mode wave. The high electron-ion relative drift is relaxed primarily through a nonlinear current-driven instability. The relaxed distributions contain a beam traveling toward the shock as a remnant of the accelerated electrons. Similar distribution functions prevail throughout the shock transition layer, suggesting that the observed acceleration and thermalization is essential to the cross-shock electron heating.

Dependence of the Spectrum of Shock-Accelerated Ions on the Dynamics at the Shock Crossing

Diffusive shock acceleration (DSA) of ions occurs due to pitch-angle diffusion in the upstream and downstream regions of the shock and multiple crossing of the shock by these ions. The classical DSA theory implies continuity of the distribution at the shock transition and predicts a universal spectrum of accelerated particles, depending only on the ratio of the upstream and downstream fluid speeds. However, the ion dynamics at the shock front occurs within a collision-free region and is gyrophase dependent. The ions fluxes have to be continuous at the shock front. The matching conditions for the gyrophase-averaged distribution functions at the shock transition are formulated in terms of the transition and reflection probabilities. These probabilities depend on the shock angle and the magnetic compression as does the power spectrum of accelerated ions. Their spectral index is expressed in terms of the reflectivity. The spectrum is typically harder than the spectrum predicted by the classical DSA theory.

Electron temperature gradient scale at collisionless shocks

Shock waves are ubiquitous in space and astrophysics. They transform directed flow energy into thermal energy and accelerate energetic particles. The energy repartition is a multiscale process related to the spatial and temporal structure of the electromagnetic fields within the shock layer. While large scale features of ion heating are known, the electron heating and smaller scale fields remain poorly understood. We determine for the first time the scale of the electron temperature gradient via electron distributions measured in situ by the Cluster spacecraft. Half of the electron heating coincides with a narrow layer several electron inertial lengths (c/ω(pe)) thick. Consequently, the nonlinear steepening is limited by wave dispersion. The dc electric field must also vary over these small scales, strongly influencing the efficiency of shocks as cosmic ray accelerators.

A critical Mach number for electron injection in collisionless shocks

Electron acceleration in collisionless shocks with arbitrary magnetic field orientations is discussed. It is shown that the injection of thermal electrons into the diffusive shock acceleration process is achieved by an electron beam with a loss cone in velocity space that is reflected back upstream from the shock through the shock drift acceleration mechanism. The electron beam is able to excite whistler waves which can scatter the energetic electrons themselves when the Alfvén Mach number of the shock is sufficiently high. A critical Mach number for the electron injection is obtained as a function of upstream parameters. The application to supernova remnant shocks is discussed.

Interstellar Shock Waves

An understanding of interstellar shock waves is crucial in determining the structure of the interstellar medium. By causing the gas to radiate, interstellar shocks provide astronomers with valuable diagnostics on both the physical conditions in the interstellar medium and the energy source that produced the shock. The complexity of the interstellar plasma-its degree of ionization, its molecular content, the presence of small dust grains and cosmic rays, and the magnetic field-leads to a rich variety of structures for interstellar shocks, which are being actively investigated both observationally and theoretically.