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Resolving the Force Term of the Electron Vlasov Equation with MMS
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  • Jason Shuster,
  • Naoki Bessho,
  • Shan Wang,
  • John Dorelli,
  • Daniel Gershman,
  • Vadim Uritsky
Jason Shuster
University of Maryland College Park

Corresponding Author:jason.r.shuster@nasa.gov

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Naoki Bessho
University of New Hampshire
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Shan Wang
Univ of Maryland
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John Dorelli
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Daniel Gershman
NASA Goddard Space Flight Center
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Vadim Uritsky
NASA Goddard Space Flight Center
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Widely employed to model collisionless plasma phenomena occurring naturally in Earth’s magnetic environment, throughout the heliosphere, and in laboratory fusion devices, the Vlasov equation self-consistently describes the fundamental kinetic dynamics of plasma particles as they are accelerated through phase space via electric and magnetic forces. The Fast Plasma Investigation (FPI) onboard NASA’s Magnetospheric Multiscale (MMS) four-spacecraft mission sufficiently resolves the seven spatial, temporal, and velocity-space dimensions of phase space needed to directly observe terms in the Vlasov equation, as recently demonstrated by Shuster et al. [2021] in the context of electron-scale current layers at the reconnecting magnetopause. These results motivate novel exploration of the types of distinct kinetic signatures in ∂fe/∂t, v⋅∇fe, and (F/me)⋅∇vfe which are associated with the magnetic reconnection process, where F = −e(E + v×B) represents the Lorentz force on an electron, and fe specifies the electron phase space density. We apply this approach to characterize the structure of the velocity-space gradient terms in the electron Vlasov equation measured by MMS. Discussion of the uncertainties which arise when computing the velocity-space gradients of the FPI phase space densities is presented, along with initial validation of the (F/me)⋅∇vfe measurements by comparison to the ∂fe/∂t and v⋅∇fe terms. Successful measurement of the force term (F/me)⋅∇vfe in the Vlasov equation suggests a new technique for inferring spatial gradients from single spacecraft measurements which may be applied to improve the spatial resolution of the electron pressure divergence ∇⋅Pe necessary to understand the microphysics of the electron diffusion region of magnetic reconnection. Reference: Shuster, J. R., et al. (2021), Structures in the terms of the Vlasov equation observed at Earth’s magnetosphere, Nature Physics, doi:10.1038/s41567-021-01280-6.