Magnetic Field Dependence of the Diffusion Coefficient in Asymmetry-Induced Transport

The dependence of the asymmetry-induced radial particle flux $\Gamma$ on axial magnetic field $B$ is complicated by the fact that the field enters the physics in at least two places: in the asymmetry-induced first order radial drift velocity $v_r=E_ {\theta}/B$ and in the zeroth order azimuthal drift velocity $v_ {\theta}=E_{r}/B$. To separate these, we assume the latter always enters the physics in the combination $\omega -l\omega_R$ where $\omega_R(r)=v_{\theta}/r$ is the column rotation frequency and $\omega$ and $l$ are the asymmetry frequency and azimuthal mode number, respectively. We then select from a $\Gamma$ vs $r$ vs $\omega$ data set those points where $\omega- l\omega_R=0$, thus insuring that any function of this combination is constant. When the selected flux is plotted versus the density gradient $\nabla n$, a roughly linear dependence is observed, showing that our assumption is valid and that we have isolated the diffusive contribution to the transport. The slope of a least-squares fitted line then gives the diffusion coefficient $D$. Varying the magnetic field, we find $D\propto B^{-1.33\pm 0.12}$. This does not match the scaling predicted by resonant particle transport theory\footnote {D.L. Eggleston and T.M. O'Neil, Phys. Plasmas 6, 2699 (1999).}.