Runge Solution of the Continuum Equations for Spherical Electrostatic Plasma Probes

Abstract

An approximate but convergent method is used to determine the electric potential and charged particle density near non-small spherical probes in a weakly ionized continuum plasma. Quantities determined partly by experiment (e, PP' yp) and partly from continuum theory (J +, J _) are introduced into three continuum differential equations which are then solved using Runge's method. The initial conditions must be estimated iteratively until the sheath solution joins smoothly to the quasi-neutral solution. Two different types of solution curves are discussed.