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

TL;DR

This study uses 1D and 2D particle-in-cell simulations to analyze electron heating mechanisms in low-beta quasi-perpendicular shocks, revealing the role of electric potential jumps and whistler wave precursors in electron energization.

Contribution

It provides detailed measurements of the ambipolar electric potential jump and its dependence on shock parameters, including the effects of ion-to-electron mass ratio and magnetic field orientation.

Findings

Electric potential jump scales with electron temperature increase.

Whistler wave precursors influence the potential structure ahead of shocks.

Electron potential decreases significantly when increasing ion-electron mass ratio.

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 $\hat{\boldsymbol{n}}$. It is known that shock electron heating is described by an ambipolar, $\boldsymbol{B}$-parallel electric potential jump, $\Delta\phi_\parallel$, that scales roughly linearly with the electron temperature jump. Our simulations have $\Delta\phi_\parallel/(0.5 m_i {u_\mathrm{sh}}^2) \sim 0.1$-$0.2$ in units of the pre-shock ions' bulk kinetic energy, in agreement with prior measurements and simulations. Different ways to measure $\phi_\parallel$, 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 $\phi_\parallel$ 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, $30 d_i$ precursor of whistler waves along $\hat{\boldsymbol{n}}$, and a $\mathcal{M}_s=7$ ($\mathcal{M}_A=3.2$) case with a shorter, $5d_i$ precursor of whistlers oblique to both $\hat{\boldsymbol{n}}$ and $\boldsymbol{B}$; $d_i$ is the ion skin depth. Within the precursors, $\phi_\parallel$ 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, $\phi_\parallel$ shows a weak dependence on the electron plasma-to-cyclotron frequency ratio $\omega_{pe}/\Omega_{ce}$, and $\phi_\parallel$ decreases by a factor of 2 as $m_i/m_e$ is raised to the true proton-electron value of 1836.