ISR Spectra Simulations With Electron-Ion Coulomb Collisions

Incoherent scatter radars (ISR) rely on Thomson scattering of very high frequency or ultrahigh frequency radio waves off electrons in the ionosphere and measure the backscattered power spectra in order to estimate altitude profiles of plasma density, electron temperature, ion temperature, and ion drift speed. These spectra result from the collective behavior of coupled ion and electron dynamics, and, for most cases, existing theories predict these well. However, when the radar points nearly perpendicular to the Earth's magnetic field, the motion of the plasma across the field lines becomes complex and Coulomb collisions between electrons and ions become important in interpreting ISR measurements. This paper presents the first fully kinetic, self-consistent, particle-in-cell simulations of ISR spectra with electron-ion Coulomb collisions. We implement a grid-based Coulomb collision algorithm in the Electrostatic Parallel Particle-in-Cell simulator and obtain ISR spectra from simulations both with and without collisions. For radar directions greater than 5 degrees away from perpendicular to the magnetic field, both sets of simulations match collisionless ISR theory well. For angles between 3 degrees and 5 degrees, the collisional simulation is well described by a simplified Brownian motion collision process. At angles less than 3 degrees away from perpendicular the Brownian motion model fails, and the collisional simulation qualitatively agrees with previous single particle simulations. For radar directions exactly perpendicular to the magnetic field the simulated collisional spectra match those from the Brownian motion collision theory, in agreement with previous single particle simulations.