Electron heating mechanisms at quasi-perpendicular shocks - revisited with magnetospheric multiscale measurements

We demonstrate that measurements obtained from NASA's Magnetospheric Multiscale (MMS) mission support quasi-adiabatic electron heating in quasi-perpendicular shocks with temperature 𝑇𝑒⊥ ∝ 𝐵^(1+𝛼), where 𝐵 is the magnetic field strength and 𝛼 represents departure from adiabaticity. Adiabatic heating (𝛼 = 0) results from the conservation of magnetic moment on spatially
increasing magnetic field inside the shock ramp. Negative 𝛼 < 0 is observed in most situations, where perpendicular energy gain from adiabatic heating is redistributed by interactions with waves to the parallel direction leading to a lower isotropic temperature increase. Positive 𝛼 is observed when the stochastic heating of electrons is activated by the 𝐸 × 𝐵 wave acceleration mechanism by electrostatic waves leading to a higher temperature increase. By using test-particle simulations in a realistic shock model we have elucidated the process of stochastic wave acceleration. We have also shown the equivalence of adiabatic heating and acceleration by gradient 𝐵 drift at shocks with low Mach numbers and demonstrated that the cross-shock potential does not contribute to the electron heating. Signatures of quasi-adiabatic heating, and/or stochastic heating of electrons are observed in all shocks analysed with measurements by the MMS.