Study of boltzmann relation in collisionless magnetized plasma with finite length scale ratios

The issue of use of Boltzmann relation in magnetized plasmas has been recently again brought to attention by [1, 2]. Boltzmann relation for electrons is a usual assumption in fluid plasma modeling used also in fusion device modeling and it is in general a very good approximation, even though it strictly holds only for massless electrons. But when oblique or wall parallel magnetic field is considered, cross-field diffusion is impeded and even finite Larmor radius effects can influence potential formation in front of the wall. Our task was to study the validity of the Boltzmann factor via a fully-kinetic particle-in-cell code. We did so for finite ratios of three different length scales based on three characteristic dimensions, namely the Debye length, the Larmor radius and the ionization length. We considered a collisionless case, since effects of magnetization can be studied isolated, without side effects of a competing mechanism of collisions. In the simulations particle trajectories are fully resolved and artificial heating is used to maintain the assigned temperature in the volume source region. We qualitatively estimated the deviation of the results obtained from the simulations from the theoretical value calculated via Boltzmann relation in the logarithmic scale and made a simple integral method for the comparison too.