# Kinetic theory of the electron strahl in the solar wind

## TL;DR

This paper develops a kinetic model for the electron strahl in the solar wind, analyzing how Coulomb collisions and whistler turbulence influence electron beam broadening at different energies and distances from the Sun.

## Contribution

The paper introduces a kinetic theory that separates the effects of Coulomb collisions and whistler turbulence on the electron strahl, providing a threshold energy and its variation with heliospheric distance.

## Key findings

- Coulomb collisions dominate at energies below ~200 eV near 1 AU.
- Whistler turbulence becomes more significant at higher energies and larger distances.
- The model predicts electron halo formation through energy-dependent broadening mechanisms.

## Abstract

We develop a kinetic theory for {the electron strahl, a beam of energetic electrons which propagate} from the sun along the Parker-spiral-shaped magnetic field lines. By assuming a Maxwellian electron distribution function in the near-sun region where the plasma is collisional, we derive the strahl distribution function at larger heliospheric distances. We consider the two most important mechanisms that broaden the strahl: Coulomb collisions and interactions with oblique ambient whistler turbulence (anomalous diffusion). We propose that the energy regimes where these mechanisms are important are separated by an approximate threshold, ${\cal E}_c$; for the electron kinetic energies ${\cal E}<{\cal E}_c$ the strahl width is mostly governed by Coulomb collisions, while for ${\cal E}>{\cal E}_c$ by interactions with the whistlers. The Coulomb broadening decreases as the electron energy increases; the whistler-dominated broadening, on the contrary, increases with energy and it can lead to efficient isotropization of energetic electrons and to formation of the electron halo. The threshold energy ${\cal E}_c$ is relatively high in the regions closer to the sun, and it gradually decreases with the distance, implying that the anomalous diffusion becomes progressively more important at large heliospheric distances. At $1$ AU, we estimate the energy threshold to be about ${\cal E}_c\sim 200\,{\rm eV}$.