MMS Measurements of the Vlasov Equation: Probing the Electron Pressure Divergence Within Thin Current Sheets

We investigate the kinetic structure of electron‐scale current sheets found in the vicinity of the magnetopause and embedded in the magnetosheath within the reconnection exhaust. A new technique for computing terms of the Vlasov equation using Magnetospheric Multiscale (MMS) measurements is presented and applied to study phase space density gradients and the kinetic origins of the electron pressure divergence found within these current sheets. Crescent‐shaped structures in ∇⊥2fegive rise to bipolar and quadrupolar signatures in v·∇femeasured near the maximum ∇·Peinside the current layers. The current density perpendicular to the magnetic field is strong (J⊥∼2 μA/m2), and the thickness of the current layers ranges from 3 to 5 electron inertial lengths. The electron flows supporting the current layers mainly result from the combination of E×Band diamagnetic drifts. We find nonzero J·E′within the current sheets even though they are observed apart from typical diffusion region signatures. We discovered how to use data from outer space to measure what is known as the Vlasov equation, held by many to be the most important equation in plasma physics. Beginning with Ludwig Boltzmann's insights from the late 1800s regarding microscopic motions of ordinary gases, Anatoly Vlasov in 1945 applied Boltzmann's ideas to understand the nature of electrified gases called plasmas. What has prevented researchers from measuring the Vlasov equation for over 100 years since Boltzmann? The difficulty is that Vlasov's equation lives in phase space, which enlists no less than seven dimensions — three for position (x, y, z), three for velocity (vx, vy, vz), and one for time (t) — thus, for over a century, no experiment has been designed to sufficiently and accurately resolve each of these dimensions. Today, instruments comprising the revolutionary Fast Plasma Investigation onboard NASA's four spacecraft Magnetospheric Multiscale mission, flying over 40,000 miles away from Earth through regions where the magnetic fields of the Earth and Sun collide, equip space scientists with data collected at higher resolution than ever before achieved — high enough to at last resolve terms in the Vlasov equation for the first time in history, which we demonstrate here. Bipolar and quadrupolar structures in the spatial gradient term of the electron Vlasov equation were measured for the first time with MMSElectron‐scale current layers exhibit alternating velocity space crescent structures in electron phase space density gradient distributionsEnergy conversion was observed in thin diamagnetic current layers in the magnetopause reconnection exhaust far from the diffusion region