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

We measure the thermal electron energization in 1D and 2D particle-in-cell 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 M ms = 1 -4, and upstream magnetic field angle theta Bn = 55 degrees-85 degrees from the shock normal n . It is known that shock electron heating is described by an ambipolar, B -parallel electric potential jump, Delta phi parallel to, that scales roughly linearly with the electron temperature jump. Our simulations have Delta phi parallel to / ( 0.5 m i u sh 2 ) similar to 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 to, 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 to in our low-beta p shocks. We further focus on two theta Bn = 65 degrees shocks: a M s = 4 ( M A = 1.8 ) case with a long, 30d i precursor of whistler waves along n , and a M s = 7 ( M A = 3.2 ) case with a shorter, 5d i precursor of whistlers oblique to both n and B ; d i is the ion skin depth. Within the precursors, phi parallel to 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 M s = 4 , theta Bn = 65 degrees case, phi parallel to shows a weak dependence on the electron plasma-to-cyclotron frequency ratio omega pe/omega ce, and phi parallel to decreases by a factor of 2 as m i/m e is raised to the true proton-electron value of 1836.