Electron Heating During Magnetic Reconnection: A Simulation Scaling Study

TL;DR

This study uses kinetic PIC simulations to establish a scaling law for electron heating during magnetic reconnection, showing it depends mainly on the inflowing Alfvén speed and is unaffected by plasma beta or total temperature.

Contribution

The paper introduces a quantitative scaling relation for electron heating during magnetic reconnection based on simulation data, emphasizing the role of the inflowing Alfvén speed.

Findings

Electron heating scales as 0.033 times ion mass times Alfvén speed squared.

Guide magnetic fields suppress perpendicular electron heating, favoring parallel heating.

Electron heating shows minimal variation with downstream distance and ion-to-electron mass ratio.

Abstract

Electron bulk heating during magnetic reconnection with symmetric inflow conditions is examined using kinetic particle-in-cell (PIC) simulations. The degree of electron heating is well correlated with the inflowing Alfv\'en speed $c_{Ar}$ based on the reconnecting magnetic field through the relation $\Delta T_e = 0.033 \,m_i\,c_{Ar}^2$, where $\Delta T_{e}$ is the increase in electron temperature. For the range of simulations performed, the heating shows almost no correlation with inflow total temperature $T_{tot} = T_i + T_e$ or plasma $\beta$. An out-of-plane (guide) magnetic field of similar magnitude to the reconnecting field does not affect the total heating, but it does quench perpendicular heating, with almost all heating being in the parallel direction. These results are qualitatively consistent with a recent statistical survey of electron heating in the dayside magnetopause, which also found that $\Delta T_e$ was proportional to the inflowing Alfv\'en speed. The net electron heating varies very little with distance downstream of the x-line. The simulations show at most a very weak dependence of electron heating on the ion to electron mass ratio. In the antiparallel reconnection case, the largely parallel heating is eventually isotropized downstream due a scattering mechanism such as stochastic particle motion or instabilities. The study highlights key properties that must be satisfied by an electron heating mechanism: (1) Preferential heating in the parallel direction; (2) Heating proportional to $m_i\,c_{Ar}^2$; (3) At most a weak dependence on electron mass; and (4) An exhaust electron temperature that varies little with distance from the x-line.