Electron Heating Scales in Collisionless Shocks Measured by MMS

Electron heating at collisionless shocks in space is a combination of adiabatic heating due to large-scale electric and magnetic fields and non-adiabatic scattering by high-frequency fluctuations. The scales at which heating happens hints to what physical processes are taking place. In this letter, we study electron heating scales with data from the Magnetospheric Multiscale (MMS) spacecraft at Earth's quasi-perpendicular bow shock. We utilize the tight tetrahedron formation and high-resolution plasma measurements of MMS to directly measure the electron temperature gradient. From this, we reconstruct the electron temperature profile inside the shock ramp and find that the electron temperature increase takes place on ion or sub-ion scales. Further, we use Liouville mapping to investigate the electron distributions through the ramp to estimate the deHoffmann-Teller potential and electric field. We find that electron heating is highly non-adiabatic at the high-Mach number shocks studied here.