Abstract
Abstract Using Magnetospheric Multiscale observations at the Earth’s quasi-parallel bow shock we demonstrate that electrons are heated by two different mechanisms: a quasi-adiabatic heating process during magnetic field compression, characterized by the isotropic temperature relation T / B = ( T 0 / B 0 ) ( B 0 / B ) α with α = 2/3 when the electron heating function ∣ χ e ∣ < 1 , and a stochastic heating process when ∣ χ e ∣ > 1 . Both processes are controlled by the value of the stochastic heating function χ j = m j q j − 1 B − 2 div ( E ⊥ ) for particles with mass m j and charge q j in the electric and magnetic fields E and B . Test-particle simulations are used to show that the stochastic electron heating and acceleration in the studied shock are accomplished by waves at frequencies (0.4–5) f ce (electron gyrofrequency) for bulk heating, and waves f > 5 f ce for acceleration of the tail of the distribution function. Stochastic heating can give rise to flat-top electron distribution functions, frequently observed near shocks. It is also shown that obliquely polarized electric fields of electron cyclotron drift and ion acoustic instabilities scatter the electrons into the parallel direction and keep the isotropy of the electron distribution. The results reported in this paper may be relevant to electron heating and acceleration at interplanetary shocks and other astrophysical shocks.
Highlights
The observational advances enabled by multipoint measurements in space like Cluster (Escoubet et al 1997), THEMIS (Sibeck & Angelopoulos 2008), and Magnetospheric Multiscale (MMS) (Burch et al 2016) have stimulated significant progress in space plasma physics
We analyze MMS measurements from 2018 January 6 obtained by the three-axis electric field sensors (Ergun et al 2016; Lindqvist et al 2016; Torbert et al 2016) and magnetic field vectors measured by the Fluxgate Magnetometer (Russell et al 2016), and the number density, velocity, and temperature of both ions and electrons from the Fast Plasma Investigation (FPI) (Pollock et al 2016)
All of these signatures support the suggested heating scenario at shocks, which starts with the compression of N and B, develops lower hybrid drift (LHD)/modified two-stream (MTS)/electron cyclotron drift (ECD) instabilities on the gradients and induced drift velocities, and further lead to either quasi-adiabatic or stochastic heating controlled by the stochastic function χj (Stasiewicz 2020a, 2020b; Stasiewicz & Eliasson 2020)
Summary
The observational advances enabled by multipoint measurements in space like Cluster (Escoubet et al 1997), THEMIS (Sibeck & Angelopoulos 2008), and Magnetospheric Multiscale (MMS) (Burch et al 2016) have stimulated significant progress in space plasma physics. The recent MMS mission comprising four spacecraft flying through the bow shock and the magnetosheath in formation with separation distances of about 20 km has opened unprecedented possibility for testing theoretical models for heating and acceleration mechanisms that operate at collisionless shocks by detailed comparison with observations. Using these state-of-the-art measurements, which will be discussed in Section 2 of the present paper, Stasiewicz (2020a, 2020b) and Stasiewicz & Eliasson (2020) have identified a chain of collective plasma processes that operate at both quasi-parallel and quasiperpendicular bow shocks and lead to the heating of ions and electrons. The aim of this paper is to make a detailed analysis of electron heating at quasi-parallel shocks, which complements the work of Stasiewicz & Eliasson (2020), concerned with ion and electron heating at quasi-perpendicular shocks
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