Kinetic theory of the electron strahl in the solar wind

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. 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, E_ c; for the electron kinetic energies E\,<\, E_ c the strahl width is mostly governed by Coulomb collisions, while for E\,>\, 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 the formation of the electron halo. The threshold energy 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 E_ c\,~\, 200\, eV.