Particle-in-cell simulations of velocity scattering of an anisotropic electron beam by electrostatic and electromagnetic instabilities

The velocity space scattering of an anisotropic electron beam (T⊥b/T∥b>1) flowing along a background magnetic field B0 through a cold plasma is investigated using both linear theory and 2D particle-in-cell simulations. Here, ⊥ and ∥ represent the directions perpendicular and parallel to B0, respectively. In this scenario, we find that two primary instabilities contribute to the scattering in electron pitch angle: an electrostatic electron beam instability and a predominantly parallel-propagating electromagnetic whistler anisotropy instability. Our results show that at relative beam densities nb/ne≤0.05 and beam temperature anisotropies Tb⊥/Tb∥≤25, the electrostatic beam instability grows much faster than the whistler instabilities for a reasonably fast hot beam. The enhanced fluctuating fields from the beam instability scatter the beam electrons, slowing their average speed and increasing their parallel temperature, thereby increasing their pitch angles. In an inhomogeneous magnetic field, such as the geomagnetic field, this could result in beam electrons scattered out of the loss cone. After saturation of the electrostatic instability, the parallel-propagating whistler anisotropy instability shows appreciable growth, provided that the beam density and late-time anisotropy are sufficiently large. Although the whistler anisotropy instability acts to pitch-angle scatter the electrons, reducing perpendicular energy in favor of parallel energy, these changes are weak compared to the pitch-angle increases resulting from the deceleration of the beam due to the electrostatic instability.