Exploring plasma sheath solutions for planar and cylindrical anodes

Abstract

Anode sheaths impact the operation of many practical plasma devices. This complex region is explored in detail for collisional, isothermal (identical specie temperatures), low-temperature plasmas, where sheath dimensions are in the micron range. The selected approach involves postulation of a specific electric field distribution with two shape factors. Previous research regarding planar anodes is verified and expanded upon using greater parameter ranges. 'z', a dimensionless quantity specifying plasma composition and condition, groups diverse plasmas into 'families' exhibiting similar sheath characteristics. 'n', a nondimensional ratio of electrical energy to thermal energy in the sheath, allows temperature effects to be studies. The investigation focuses on three disparate families that span a z range of 1.1729 to 2.1493, at n values defines by plasma temperatures of 6000(o) K, 3000(o) K, and 300(o) K. Results indicate that at lower temperatures, charge production in the outer sheath is generic to the electric field distribution, and that the sheaths themselves are nearly unaffected by substantial changes in temperature (i.e., n). Conversely, sheath density and extent are shown to vary significantly for differing z values. Newly derived equations governing cylindrical anodes generate sheaths that are virtually identical to corresponding planar cases. It is shown only those anodes whose radii are comparable to the plasma's 'characteristic radius' (y) must be treated with the cylindrical formulation; non-vacuous plasmas would require micron-width anodes to be thus affected. Finally, an analytical approach yields solutions that confirm the numerical results, and offers an algebraic approximation for high-n plasmas.