A reverse-blocking effect of antiparallel magnetic fields on electron transport in gas

In order to analyze fundamental features of electron conduction in a magnetically neutral loop discharge (NLD) plasma, electron transport in CF$_4$ at 0.67~Pa along a magnetically neutral channel (NC) between gradient antiparallel \textbf{\textit{B}} fields were simulated by a Monte Carlo method. The \textbf{\textit{B}} field was set as $(B_x,B_y,B_z)=(0,0,\hat{B}x)$ ($\hat{B}=\mbox{const}>0$) to let the $y$-$z$ plane be the NC as a simplified model of the electron path in the NLD plasma, and the \textbf{\textit{E}} field was applied as $(E_x,E_y,E_z)=(0,E,0)$ ($E=\mbox{const}$). Two modes of electron transport were observed. When $E<0$, the electrons drifted in the -\textbf{\textit{E}} direction. They were confined near the NC and their spatial distribution $f(x)$ was a Gaussian with a standard deviation $\sigma_x\propto\hat{B}^{-1/2}$. The values of the mean electron energy $\bar{\varepsilon}$, the effective ionization frequency $\nu_{\rm i}$, the average velocity $W_{\rm v}$ and the centroid drift velocity $W_{\rm r}$ were close to those in dc $E$ fields without \textbf{\textit{B}} field at the same $E/N$. The diffusion coefficients $D_y$ and $D_z$ were also close to the longitudinal and transverse diffusion coefficients $D_{\rm L}$ and $D_{\rm T}$ in the dc \textbf{\textit{E}} field, respectively, but $D_x\simeq0$. In contrast, when $E>0$, the electrons were led into the regions of stronger \textbf{\textit{B}} field by the \textbf{\textit{E}}$\times$\textbf{\textit{B}} drift away from the NC and they hardly drifted in the $-\textbf{\textit{E}}$ direction because of the gyration. The parameters decreased slowly and their equilibrium values were not available in a trace up to 7.3~$\mu$s, but only $D_x$ had its equilibrium value $E/\hat{B}$.