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Exploring Plasma Sheath Solutions for Planar and Cylindrical Anodes

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Master's thesis,

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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. Eta, a nondimensional ratio of electrical energy to thermal energy in the sheath, allows temperature effects to be studied. The investigation focuses on three disparate plasma families that span a range of 1.1729 to 2,1493, at eta values defined by plasma temperatures of 6000 K, 3000 K, and 3000 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., eta. 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 that only those anodes whose radii are comparable to the plasmas characteristic radius gamma must be treated with the cylindrical formulation non-vacuous plasma 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-eta plasmas.

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  • Plasma Physics and Magnetohydrodynamics

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