#### Title of the Presentation

Observational Verification of the Electron Vlasov Equation with MMS

#### Presentation Type

Talk

#### Presenter Format

Virtual Meeting Talk

#### Topic

Fundamental Processes in Comparative Magnetospheres

#### Start Date

13-5-2022 2:45 PM

#### Abstract

The Fast Plasma Investigation (FPI) onboard NASA’s Magnetospheric Multiscale (MMS) four-spacecraft mission constitutes an historic advance in plasma physics particle detection capabilities. As a result of the unprecedented temporal, spatial, and velocity-space resolution offered by the suite of dual electron spectrometers (DES), MMS is capable of directly measuring the velocity-space structure of terms in the electron Vlasov equation as demonstrated by *Shuster et al.* [2021] for electron-scale current layers observed near Earth’s dayside reconnecting magnetopause. In this work, we present MMS observations of all three terms in the electron Vlasov equation: the temporal derivative term ∂*f** _{e}*/∂

*t*, the spatial gradient term

**v**⋅∇

*f*

*, and the velocity-space gradient term (*

_{e}**F**/

*m*

*)⋅∇*

_{e}

_{v}*f*

*. We discuss various applications, implications, and limitations of our methodology. The immediate advantage of multipoint measurements is the ability to distinguish between temporal and spatial variations in the plasma; both a thin, slow-moving structure and a thick, fast-moving one would produce the same measured time series of a quantity when sampled at only a single spatial location. FPI offers a novel way to infer spatiotemporal variations of the plasma from a single spacecraft: careful measurement of how the*

_{e}*shape*of the plasma’s distribution function

*f*

_{e}(

**v**) changes via the velocity-space gradient term ∇

_{v}*f*

*yields qualitatively similar velocity-space structures as those captured by ∂*

_{e}*f*

*/∂*

_{e}*t*and the four-spacecraft measurement of

**v**⋅∇

*f*

*. Making use of ∂*

_{e}*f*

*/∂*

_{e}*t*for steady-state structures, we obtain a higher spatially-resolved (~1 to 3 km) single-spacecraft version of the parallel component of the electron pressure divergence (∇⋅

**P**

_{e})

_{//}that exhibits agreement with the parallel electric field measured by the electric field double probes (EDP), whereas the standard four-spacecraft method for computing ∇⋅

**P**

_{e}cannot capture spatial variations smaller than the spacecraft separation (~10 km). Just as

**v**⋅∇

*f*

*offers a kinetic perspective into the origins of ∇⋅*

_{e}**P**

_{e}, the (

**F**/

*m*

*)⋅∇*

_{e}

_{v}*f*

*term offers an analogous velocity-space perspective into the energy conversion term*

_{e}**J**⋅

**E**’ whenever

**J**can be approximated by

**J**

*= −*

_{e}*en*

_{e}**U**

*, which is often the case for electron-scale structures. Thus, these results are immediately relevant to the study of fundamentally kinetic energy conversion processes, including electron diffusion regions (EDRs) fueling magnetic reconnection, kinetic-scale turbulence, and wave-particle interactions such as those believed to be consistent with Landau damping as inferred from recently reported velocity-space signatures using MMS data from the turbulent magnetosheath.*

_{e}Observational Verification of the Electron Vlasov Equation with MMS

The Fast Plasma Investigation (FPI) onboard NASA’s Magnetospheric Multiscale (MMS) four-spacecraft mission constitutes an historic advance in plasma physics particle detection capabilities. As a result of the unprecedented temporal, spatial, and velocity-space resolution offered by the suite of dual electron spectrometers (DES), MMS is capable of directly measuring the velocity-space structure of terms in the electron Vlasov equation as demonstrated by *Shuster et al.* [2021] for electron-scale current layers observed near Earth’s dayside reconnecting magnetopause. In this work, we present MMS observations of all three terms in the electron Vlasov equation: the temporal derivative term ∂*f** _{e}*/∂

*t*, the spatial gradient term

**v**⋅∇

*f*

*, and the velocity-space gradient term (*

_{e}**F**/

*m*

*)⋅∇*

_{e}

_{v}*f*

*. We discuss various applications, implications, and limitations of our methodology. The immediate advantage of multipoint measurements is the ability to distinguish between temporal and spatial variations in the plasma; both a thin, slow-moving structure and a thick, fast-moving one would produce the same measured time series of a quantity when sampled at only a single spatial location. FPI offers a novel way to infer spatiotemporal variations of the plasma from a single spacecraft: careful measurement of how the*

_{e}*shape*of the plasma’s distribution function

*f*

_{e}(

**v**) changes via the velocity-space gradient term ∇

_{v}*f*

*yields qualitatively similar velocity-space structures as those captured by ∂*

_{e}*f*

*/∂*

_{e}*t*and the four-spacecraft measurement of

**v**⋅∇

*f*

*. Making use of ∂*

_{e}*f*

*/∂*

_{e}*t*for steady-state structures, we obtain a higher spatially-resolved (~1 to 3 km) single-spacecraft version of the parallel component of the electron pressure divergence (∇⋅

**P**

_{e})

_{//}that exhibits agreement with the parallel electric field measured by the electric field double probes (EDP), whereas the standard four-spacecraft method for computing ∇⋅

**P**

_{e}cannot capture spatial variations smaller than the spacecraft separation (~10 km). Just as

**v**⋅∇

*f*

*offers a kinetic perspective into the origins of ∇⋅*

_{e}**P**

_{e}, the (

**F**/

*m*

*)⋅∇*

_{e}

_{v}*f*

*term offers an analogous velocity-space perspective into the energy conversion term*

_{e}**J**⋅

**E**’ whenever

**J**can be approximated by

**J**

*= −*

_{e}*en*

_{e}**U**

*, which is often the case for electron-scale structures. Thus, these results are immediately relevant to the study of fundamentally kinetic energy conversion processes, including electron diffusion regions (EDRs) fueling magnetic reconnection, kinetic-scale turbulence, and wave-particle interactions such as those believed to be consistent with Landau damping as inferred from recently reported velocity-space signatures using MMS data from the turbulent magnetosheath.*

_{e}