Radial drift to diffusion ratio in asymmetry-induced transport

We are using a single-particle code with collisional effects to study asymmetry-induced radial transport in a non-neutral plasma. By following the time variation of the mean change and mean square change in radial position we can obtain the radial drift velocity $v_{\scriptscriptstyle D}$ and the diffusion coefficient $D$ as defined by the flux equation $\Gamma = - D\nabla n +nv_{\scriptscriptstyle D}$. As previously noted,\footnote{D.L. Eggleston, Bull. Am. Phys. Soc. {\bf 55}, 74 (2010).} for asymmetries of the form $\phi_1(r)\cos{(kz)}\cos {(\omega t - l\theta)}$ and low collisionality there are two sources for the observed transport: resonant particle transport and transport produced by axially trapped particles. This latter type, which is often dominant, occurs near radii where $\omega=l\omega_R$, where $\omega_R$ is the azimuthal rotation frequency. For resonant particle transport, we find that $v_ {\scriptscriptstyle D}$ and $D$ satisfy $v_{\scriptscriptstyle D}/D=r\omega_c(l\omega_{\scriptscriptstyle R}-\omega)/l\overline {v}^2$, a generalization of the Einstein relation for $\omega\ne 0$. For the transport produced by axially trapped particles, however, $v_{\scriptscriptstyle D}/D$ is significantly larger than this prediction. In constrast, our experiment\footnote {D.L. Eggleston, Phys. Plasmas {\bf 17}, 042304 (2010).} indicates that $v_{\scriptscriptstyle D}/D$ is significantly {\em smaller} than predicted. We suspect that these discrepancies indicate the need for a non-local determination of $v_{\scriptscriptstyle D}$ and $D$.