On a Mixed–Boundary Value Problem Related to the Electrostatics of Plasma Jet Reactors

A semi-analytical model is presented for the determination of the electric field in Cold Atmospheric-Pressure Plasma jet systems (CAPP jets) in applications associated with plasma science and contemporary engineering. We consider a simplified system configuration of a single charged electrode, surrounding a dielectric tube of minor contribution to the field. Introducing the cylindrical geometry, we separate our domain in three distinct areas, as dictated from the external conditions. Based on the electrostatic limit of Maxwell's equations, we use cylindrical harmonic potential field expansions that produce the corresponding electric fields in each subdomain. Due to the imposed mixed-type boundary value problem, additional linear terms are incorporated, leading to three possible solutions of the physical problem. The efficiency of our method is demonstrated by comparing the final formulae with a numerical solution, followed by the necessary discussion.