Electron Heating in 2D Particle-in-Cell Simulations of Quasi-Perpendicular Low-Beta Shocks

Abstract

We measure the thermal electron energization in 1D and 2D particle-in-cell (PIC) simulations of quasi-perpendicular, low-beta (${\beta }_p=0.25$) collisionless ion-electron shocks with mass ratio $m_i/m_e=200$, fast Mach number ${\mathcal{M}}_{ms}=1$-$4$, and upstream magnetic field angle ${\theta }_{Bn}=55$-$85^{\circ }$ from shock normal $\hat{\mathbf{n}}$. It is known that shock electron heating is described by an ambipolar, $\mathbf{B}$-parallel electric potential jump, $\Delta {\varphi }_{\parallel }$, that scales roughly linearly with the electron temperature jump. Our simulations have $\Delta {\varphi }_{\parallel }/(0.5m_i{u_{\mathrm{sh}}}^2)\sim 0.1$-$0.2$ in units of the pre-shock ions' bulk kinetic energy, in agreement with prior measurements and simulations. Different ways to measure ${\varphi }_{\parallel }$, including the use of de Hoffmann-Teller frame fields, agree to tens-of-percent accuracy. Neglecting off-diagonal electron pressure tensor terms can lead to a systematic underestimate of ${\varphi }_{\parallel }$ in our low-${\beta }_p$ shocks. We further focus on two ${\theta }_{Bn}=65^{\circ }$ shocks: a ${\mathcal{M}}_s=4$ (${\mathcal{M}}_A=1.8$) case with a long, $30d_i$ precursor of whistler waves along $\hat{\mathbf{n}}$, and a ${\mathcal{M}}_s=7$ (${\mathcal{M}}_A=3.2$) case with a shorter, $5d_i$ precursor of whistlers oblique to both $\hat{\mathbf{n}}$ and $\mathbf{B}$; $d_i$ is the ion skin depth. Within the precursors, ${\varphi }_{\parallel }$ has a secular rise towards the shock along multiple whistler wavelengths and also has localized spikes within magnetic troughs. In a 1D simulation of the ${\mathcal{M}}_s=4$, ${\theta }_{Bn}=65^{\circ }$ case, ${\varphi }_{\parallel }$ shows a weak dependence on the electron plasma-to-cyclotron frequency ratio ${\omega }_{pe}/{\Omega }_{ce}$, and ${\varphi }_{\parallel }$ decreases by a factor of 2 as $m_i/m_e$ is raised to the true proton-electron value of 1836.

arXiv comment32 pages, 25 figures; accepted to ApJ. Figures 6, 8, 16, 23 updated to fix Liouville mapping procedure normalization (Equation (8))

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Cited by in corpus (1)

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