A comparison between kinetic theory and particle-in-cell simulations of anomalous electron transport in $E×B$ plasma discharges

Understanding anomalous electron transport in $E×B$ discharges remains a key challenge in the development of self-consistent models of these systems. It has been shown that short-wavelength, high-frequency instabilities in the azimuthal $E×B$ direction may be responsible for increased electron transport due to an enhanced electron-ion friction force. Although a theoretical model based on quasi-linear kinetic theory has previously been proposed to describe this friction force, it has so far only undergone limited validation testing. Here, we rigorously assess this theoretical model by comparison with the friction force self-consistently obtained from 2D axial-azimuthal particle-in-cell simulations. The simulation geometry is based on a recently established benchmark configuration for $E×B$ discharges, and a broad parametric study is performed by varying the magnetic field strength, the discharge current density, and the presence of different neutral collisional processes. Overall, the theory is found to be in very good agreement with the simulation results for all cases studied, verifying the underlying physical mechanisms leading to enhanced electron transport. We demonstrate, however, that the friction force depends sensitively on the shape of the electron velocity distribution function, thus posing significant challenges to fully self-consistent, first principles modeling of anomalous transport in fluid simulations.