Elliptic Vector Loci of Average Electron Velocity in Real Gases Under AC Electric and DC Magnetic Fields

Monte Carlo simulations (MCSs) of electron swarms in F2, Ar, and CF4 under ac (radio frequency) electric and dc magnetic fields ( $\mathbf {E}(t)$ and $\mathbf {B}$ fields) crossed at a right angle are performed, and the periodic response of the electron drift velocity vector $\mathbf {W}(t)$ is depicted as an elliptic vector locus (EVL). The vector head of $\mathbf {W}(t)$ draws an ellipse synchronously to the alternation of the ac $\mathbf {E}(t)$ field. The tilt of the major axis of the EVL, which represents the Hall deflection, increases with $|\mathbf {B}|$ , and the ellipse drawn by $\mathbf {W}(t)$ takes its maximum around the $|\mathbf {B}|$ value resonant to the ac $\mathbf {E}(t)$ field. It is demonstrated that a theoretical approximation derived from a constant-collision-frequency (CCF) model predicts well the fundamental tendency of the $|\mathbf {B}|$ -dependent variation of the EVL of $\mathbf {W}(t)$ in the three real gases. The $\mathbf {W}(t)$ in F2 agrees well with the CCF model at low electric fields for its nature that the total collision frequency does not change significantly. On the other hand, those in Ar and CF4 deviate from the CCF model. This visual depiction using the EVL of $\mathbf {W}(t)$ is expected to be applicable to the estimation of the directional electron drift in inductively coupled magnetized plasmas and to the characterization of the $\mathbf {W}(t)$ response in real gases.