Electron Heating in 2D Particle-in-cell Simulations of Quasi-perpendicular Low-beta Shocks

Journal Article · 01 April 2024 · The Astrophysical Journal

DOI: https://doi.org/10.3847/1538-4357/ad1f69 · OSTI ID:2332919

Tran, Aaron ; Sironi, Lorenzo

Abstract We measure the thermal electron energization in 1D and 2D particle-in-cell simulations of quasi-perpendicular, low-beta ( β _p = 0.25) collisionless ion–electron shocks with mass ratio m _i / m _e = 200, fast Mach number ${\mathcal{M}}_{\mathrm{ms}}=1$ –4, and upstream magnetic field angle θ _Bn = 55°–85° from the shock normal $\hat{\mathit{n}}$ . It is known that shock electron heating is described by an ambipolar, B -parallel electric potential jump, Δ ϕ _∥ , that scales roughly linearly with the electron temperature jump. Our simulations have $\mathrm{\Delta }{\varphi }_{\parallel }/\left(0.5m_{\mathrm{i}}{u_{\mathrm{sh}}}^2\right)\sim 0.1$ –0.2 in units of the pre-shock ions’ bulk kinetic energy, in agreement with prior measurements and simulations. Different ways to measure ϕ _∥ , 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 ϕ _∥ in our low- β _p shocks. We further focus on two θ _Bn = 65° shocks: a ${\mathcal{M}}_{\mathrm{s}}=4$ ( ${\mathcal{M}}_{\mathrm{A}}=1.8$ ) case with a long, 30 d _i precursor of whistler waves along $\hat{\mathit{n}}$ , and a ${\mathcal{M}}_{\mathrm{s}}=7$ ( ${\mathcal{M}}_{\mathrm{A}}=3.2$ ) case with a shorter, 5 d _i precursor of whistlers oblique to both $\hat{\mathit{n}}$ and B ; d _i is the ion skin depth. Within the precursors, ϕ _∥ has a secular rise toward the shock along multiple whistler wavelengths and also has localized spikes within magnetic troughs. In a 1D simulation of the ${\mathcal{M}}_{\mathrm{s}}=4$ , θ _Bn = 65° case, ϕ _∥ shows a weak dependence on the electron plasma-to-cyclotron frequency ratio ω _pe /Ω _ce , and ϕ _∥ decreases by a factor of 2 as m _i / m _e is raised to the true proton–electron value of 1836.

• Sponsoring Organization: USDOE
• Grant/Contract Number: SC0023015
• OSTI ID: 2332919
• Journal Information: The Astrophysical Journal, Journal Name: The Astrophysical Journal Journal Issue: 1 Vol. 965; ISSN 0004-637X
• Publisher: American Astronomical SocietyCopyright Statement
• Country of Publication: United States
• Language: English