Empirical model for low-frequency asymmetry-induced transport

We are currently developing an empirical model of asymmetry-induced transport in our non-neutral plasma trap with an eye toward providing guidance for further theoretical development. Our previous efforts\footnote{D.~L. Eggleston, Phys. Plasmas {\bf 17}, 042304 (2010).} have focused on radii where the asymmetry frequency $f$ matches the local $\bf{E}\times\bf{B}$ plasma rotation frequency $f_R$. We now study the radial particle flux $\Gamma$ produced by frequencies below $f_R$. The flux produced by these frequencies is typically largest at the outer edge of the plasma, $r/R\ge 0.75$, where $R$ is the wall radius. The data support an empirical model $\Gamma(r)\propto\exp{[-(f_0-f)/f_*]}$. Both of the parameters $f_0$ and $f_*$ are proportional to $\phi_{cw}/B$, where $\phi_{cw}$ is the bias of our central wire electrode and $B$ is the axial magnetic field. This scaling suggests a relation with $f_R$ or its derivatives. If we assume the former, then $f_0\approx 1.5f_R$ and $f_*\approx f_R/3$. This model is consistent with empirical constraints obtained\footnote{Eggleston 042304} near the $f=f_R$ points. The physical basis for this model, however, remains to be found.