Structures in the terms of the Vlasov equation observed at Earth’s magnetopause

The Vlasov equation describes collisionless plasmas in the continuum limit and applies to many fundamental plasma energization phenomena. Because this equation governs the evolution of plasma in six-dimensional phase space, studies of its structure have mostly been limited to numerical or analytical methods. Here terms of the Vlasov equation are determined from observations of electron phase-space density gradients measured by the four Magnetospheric Multiscale spacecraft in the vicinity of magnetic reconnection at Earth’s magnetopause. We identify which electrons in velocity space substantially support the electron pressure divergence within electron-scale current layers. Furthermore, we isolate and characterize the effects of density, velocity and temperature gradients on the velocity-space structure and dynamics of these electrons. Unipolar, bipolar and ring structures in the electron phase-space density gradients are compared to a simplified Maxwellian model and correspond to localized gradients in density, velocity and temperature, respectively. These structures have implications for the ability of collisionless plasmas to maintain kinetic Vlasov equilibrium. The results provide a kinetic perspective relevant to how the electron pressure divergence may develop to violate the electron frozen-in condition and sustain electron-scale energy conversion processes, such as the reconnection electric field, in collisionless space plasma environments. Insights into the structure of the Vlasov equation that governs the evolution of collisionless plasmas from observations have been limited. Now the spatial gradient term for electrons is analysed with recent data from the MMS mission.