We use Magnetospheric Multiscale (MMS) data to study electron kinetic entropy per particle Se across Earth's quasi-perpendicular bow shock. We have selected 22 shock crossings covering a wide range of shock conditions. Measured distribution functions are calibrated and corrected for spacecraft potential, secondary electron contamination, lack of measurements at the lowest energies and electron density measurements based on plasma frequency measurements. All crossings display an increase in electron kinetic entropy across the shock Delta S-e being positive or zero within their error margin. There is a strong dependence of Delta S-e on the change in electron temperature, Delta T-e, and the upstream electron plasma beta, beta(e). Shocks with large Delta T-e have large Delta S-e. Shocks with smaller beta(e) are associated with larger Delta S-e. We use the values of Delta S-e, Delta Te and density change Delta n(e) to determine the effective adiabatic index of electrons for each shock crossing. The average effective adiabatic index is <gamma(e)> = 1.64 +/- 0.07.

We use the Magnetospheric Multiscale mission to study electron kinetic entropy across Earth's quasi-perpendicular bow shock. We perform a statistical study of how the change in electron entropy depends on the different plasma parameters associated with a collisionless shock crossing. The change in electron entropy exhibits strong correlations with upstream electron plasma beta, Alfvén Mach number, and electron thermal Mach number. We investigate the source of entropy generation by correlating the change in electron entropy across the shock to the measured electric and magnetic field wave power strengths for different frequency intervals within different regions in the shock transition layer. The electron entropy change is observed to be greater for higher electric field wave power within the shock ramp and shock foot for frequencies between the lower hybrid frequency and electron cyclotron frequency, suggesting electrostatic waves are important for electron kinetic entropy generation at Earth's quasi-perpendicular bow shock.

We use the Magnetospheric Multiscale mission (MMS) to study electron acceleration at Earth’s quasi-perpendicular bow shock to address the long-standing electron injection problem. The observations are compared to the predictions of the Stochastic Shock Drift Acceleration (SSDA) theory.   Recent studies based on SSDA predict electron distribution being a power law with a cutoff energy that scales with upstream parameters. This scaling law has been successfully tested for a single Earth's bow shock crossing by MMS. Here we extend this study and test the prediction of the scaling law for seven MMS Earth's bow shock crossings with different upstream parameters. A goodness-of-fit test shows good agreement between observations and SSDA theoretical predictions, thus supporting SSDA as one of the most promising candidates for solving the electron injection problem.

We use the Magnetospheric Multiscale mission to observe a bi-directional electron acceleration event in the electron foreshock upstream of Earth's quasi-perpendicular collisionless bow shock. The acceleration region is associated with a decrease in wave activity, inconsistent with common electron acceleration mechanisms such as Diffusive Shock Acceleration and Stochastic Shock Drift Acceleration. We propose a two-step acceleration process where an electron field-aligned beam acts as a seed population further accelerated by a shrinking magnetic bottle process, with the shock acting as the magnetic mirror(s).