Turing patterns on a plasma-liquid interface

Radially symmetric patterns are observed in pin-to-plane DC plasma systems where a liquid solution is used as a planar resistive anode. The size and structure of these patterns depends on the plasma current and salt concentration of the liquid anode. We propose that these patterns initiate due to the reaction and diffusion of electrons in the anode sheath, where electron impact ionization serves as an autocatalytic reaction. The resulting system of reaction-diffusion equations is amenable to Turing stability analysis, which we use to theoretically predict the transition from a uniform plasma to a ring-shaped pattern state. Expressing the stability criteria in terms of plasma current and solution salt concentration, we derive a theoretical phase boundary for the onset of pattern formation, which is in excellent agreement with experimental results. (paper)