A necessary condition for perpendicular electric field control in magnetized plasmas

The electrostatic model proposed by Poulos [Phys. Plasmas (2019), $\mathbf{26}$, 022104] to describe the electric potential distribution across and along a magnetized plasma column is used to shed light onto the ability to control perpendicular electric fields. The effective electrical connection between facing end-electrodes is shown to be conditioned upon the smallness of a dimensionless parameter $\tau$ function of the plasma column aspect ratio and the square root of the conductivity ratio $\sigma_\perp/\sigma_{\parallel}$. The analysis of a selected set of past end-electrodes biasing experiments confirms that this parameter is small in experiments that have successfully demonstrated perpendicular electric field tailoring. On the other hand, this parameter is $\mathcal{O}(1)$ in experiments that failed to demonstrate control, pointing to an excessively large ion-neutral collision frequency. A better understanding of the various contributions to $\sigma_\perp$ is needed to gain further insights into end-biasing experimental results.