Particle-in-cell simulations of collisional ISR spectra.

Incoherent scatter radars (ISR) reflect radio waves in the MHz range off electrons in the ionosphere and measure the returning power spectra. The returned spectra in the kHz range "ion line" is the result of collective behavior coupling ion and electron dynamics together, and for most cases the spectra is well predicted with existing theories. The measured spectra are inverted to provide altitude profiles of plasma density, electron and ion temperature, and ion drift speed. When the radar beam points nearly perpendicular to the Earth's magnetic field, the motion of the plasma along the field lines contributes less to the returned spectra while diffusion across field lines due to Coulomb collisions between electrons and ions becomes an important component of the ion line, and neglecting collisions leads to non-physical temperature measurements. This paper presents the first fully kinetic, self-consistent, particle-in-cell simulation of ISR spectra with electron-ion Coulomb collisions. We implement a grid-based Coulomb collision algorithm in the Electrostatic Parallel Particle-in-Cell (EPPIC) simulator, and obtain ISR spectra from simulations both with and without collisions. For look directions greater than 5° away from perpendicular, both sets of simulations match collisionless ISR theory well. For look directions between 1° and 5° away from perpendicular, we find both the collisional and collisionless simulations produce the same spectra, and the simulated spectra match well with the collisional ISR theory in Kudeki and Milla [2011] which approximates all collisions as a Brownian motion process. For look directions less than 1° away from perpendicular to B, the spectra from the collisionless simulation narrows to a delta function while the collisional spectra maintains a finite width that differs significantly from the Brownian motion theory. The deviation between kinetic simulation of collisions and the Brownian motion theory is expected when the radar is not looking exactly perpendicular to B, but the convergence of both of our simulations with the collisional theory at angles as small as 1° away from perpendicular shows the Brownian motion approximation is valid for a wider range of look directions than previously expected.