Authors: Collin R. Brown, Gregory G. Howes, Aaron Tran, James Juno, Anatoly Spitkovsky, Lorenzo Sironi

Determining the processes and proportional energy contributions of the energy exchange between fields, species flow energy, and species thermal energy of supercritical collisionless shock are a key unknown due to the diverse types of kinetic mechanisms that can arise to dissipate the incoming flow energy of the shock and due to the sensitive dependence of such processes in the multidimensional parameter space of such systems. Here, we present methods that generically enable the determination of these energy channels produced by these different mechanisms. By analyzing phase-space to reorganize the plasma energization term, j⋅E, and by choosing an appropriate reorganization of the energy flux term, ∇⋅Qs, that sufficiently captures particle reflection in the system, one can isolate terms that singularly connect two of these energy stores, e.g. electron thermal energy to wave-particle interactions and electron thermal energy to the diamagnetic drift. When studied in the species flow frame and applying these appropriate reorganizations, the advective portion of our expressions is eliminated, enabling the measurement of energy exchange and thus partitioning throughout the system. We focus on the internal energy profile of electrons to understand non-adiabatic electron heating, a process in which neither the magnetic moment of the first adiabatic invariant nor the Rankine-Hugoniot relations (nor some intermediate amount that depends on the effective amount of isotropization of the electrons) can describe the electron temperature across the shock. In our test perpendicular shock simulation, we identify, isolate, and measure the amount of energy exchange by three processes relevant to the thermal energy of electrons, the diamagnetic drift heating which under ideal circumstances acts to conserve the first adiabatic invariant, the wave-particle interactions, which enhances the perpendicular pressure and thus diamagnetic drift heating, and convective compression of the electrons. We show that this isolation is able to accurately reproduce the measured temperature profile as a sum of these processes, demonstrating the capabilities of these methods to isolate energy exchange and energy partitioning in shocks.