Abstract: We compute terms of the ion and electron Vlasov equations using the unprecedented dataset provided by the Fast Plasma Investigation (FPI) onboard NASA’s Magnetospheric Multiscale
(MMS) spacecraft, and thus compare MMS measurements directly to kinetic theory. The velocity-space structure and relative contributions of the terms ∂f/∂t, v⋅∇f, and (F/m)⋅∇vf
appearing in the ion and electron Vlasov equations are studied in the context of several reported magnetopause reconnection events [e.g., Shuster et al., 2019; Norgren et al., 2016; Phan et al.,
2016]. A pressure gradient force term ∇⋅Ps can be decomposed into contributions from density and temperature gradients, for each species: ∇⋅Ps = ∇⋅(nsTs) = Ts⋅∇ns + ns∇⋅Ts. Often when the
ion Ti⋅∇ni term provides the dominant contribution to the force balance, we find corresponding unipolar velocity-space signatures in the ion spatial gradient ∇fi terms. For electrons, ring
structures in the ∇fe terms are found to be the kinetic signature of a significant temperature gradient term ne∇⋅Te. When the measured bulk velocity Ue varies between spacecraft in addition
to the presence of a temperature gradient ∇⋅Te, bipolar crescent-shaped features in ∇fe can result. We discuss an approach for interpreting these observations using a simplified Maxwellian model
for the distribution functions fi and fe. Considering the 0th moment of the Vlasov equation for each species, we also investigate terms of the ion and electron continuity equations. Balance
between the ∂n/∂t and U⋅∇n terms is typically observed, suggesting that ions and electrons in the vicinity of the magnetopause are mostly incompressible (∇⋅Ui,e ≈ 0). The ability to resolve
gradients of the distribution function motivates comparison of MMS observations to predictions from gyro-kinetic theory and particle-in-cell (PIC) simulations to aid in determining the kinetic
mechanisms responsible for maintaining force balance during the magnetic reconnection process.

References
Shuster, J. R., et al. (2019), MMS measurements of the Vlasov equation: Probing the electron pressure divergence within thin current sheets, Geophys. Res. Lett., 46, 7862–7872,
doi:10.1029/2019GL083549.

Norgren, C., et al. (2016), Finite gyroradius effects in the electron outflow of asymmetric magnetic reconnection, Geophys. Res. Lett., 43, 6724–6733, doi:10.1002/2016GL069205.

Phan, T. D., et al. (2016), MMS observations of electron-scale filamentary currents in the reconnection exhaust and near the X line, Geophys. Res. Lett., 43, 6060–6069,
doi:10.1002/2016GL069212.