# Inferring source properties of monoenergetic electron precipitation from kappa and Maxwellian moment-voltage relationships

## TL;DR

This study infers magnetospheric source properties of monoenergetic electron precipitation using moment-voltage relationships and compares them with theoretical models, providing new insights into source densities, temperatures, and $ppa$ values.

## Contribution

It introduces two new theoretical number density--voltage relationships and applies a Monte Carlo approach to infer source parameters from measurements.

## Key findings

- Source densities: 0.7-0.8 cm$^{-3}$ and 0.07-0.09 cm$^{-3}$
- Source temperatures: approximately 70 eV and 95 eV
- Source altitudes: 6.4-7.7 R$_E$ and >6 R$_E$

## Abstract

We present two case studies of FAST electrostatic analyzer measurements of both highly nonthermal ($\kappa \lesssim$~2.5) and weakly nonthermal/thermal monoenergetic electron precipitation at $\sim$4000~km, from which we infer the properties of the magnetospheric source distributions via comparison of experimentally determined number density--, current density--, and energy flux--voltage relationships with corresponding theoretical relationships. We also discuss the properties of the two new theoretical number density--voltage relationships that we employ. Moment uncertainties, which are calculated analytically via application of the \citet{Gershman2015} moment uncertainty framework, are used in Monte Carlo simulations to infer ranges of magnetospheric source population densities, temperatures, $\kappa$ values, and altitudes. We identify the most likely ranges of source parameters by requiring that the range of $\kappa$ values inferred from fitting experimental moment-voltage relationships correspond to the range of $\kappa$ values inferred from directly fitting observed electron distributions with two-dimensional kappa distribution functions. Observations in the first case study, which are made over $\sim$78--79$^\circ$ invariant latitude (ILAT) in the Northern Hemisphere and 4.5--5.5 magnetic local time (MLT), are consistent with a magnetospheric source population density $n_m =$~0.7--0.8~cm$^{-3}$, source temperature $T_m \approx$~70~eV, source altitude $h =$~6.4--7.7~$R_E$, and $\kappa =$~2.2--2.8. Observations in the second case study, which are made over 76--79$^\circ$~ILAT in the Southern Hemisphere and $\sim$21~MLT, are consistent with a magnetospheric source population density $n_m =$~0.07--0.09~cm$^{-3}$, source temperature $T_m \approx$~95~eV, source altitude $h \gtrsim$~6~$R_E$, and $\kappa =$~2--6.