A necessary condition for perpendicular electric field control in magnetized plasmas

The electrostatic model proposed by Poulos [Phys. Plasmas 26, 022104 (2019)] to describe the electric potential distribution across and along a magnetized plasma column is used to shed light on 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 τ function of the plasma column aspect ratio and the square root of the conductivity ratio σ ⊥ / σ ∥. The analysis of a selected set of past end-electrode 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 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 σ ⊥ is needed to gain further insights into end-biasing experimental results.