A simplified plasma experiment was designed to provide data for basic validation of computational models for new and existing electric propulsion devices. For this effort, a simple semi-analytical model was developed to provide first-order analysis of the results and guidance for future experimental approaches.The model examines the momentum-exchange and charge-exchange collisions for a 1500 V xenon ion beam guided through a Test Cell populated with xenon neutrals. The model achieves extremely short runtimes by using a semi-analytical approach that assumes a one-dimensional beam, single collisions, and only heavy species interactions. It treats the scattered particles as discrete point sources located along the axis of the cylindrical domain, where particles are deflected with a distribution that is forwardly weighted for momentum-exchange ions and a combination of orthogonally weighted and isotropic for charge-exchange ions. Using this approach, the model provides a rapid analysis capability that yields useful insight into important mechanisms in the experiment. Results from the model agree well with experimental measurements in the single collision regime and illustrate that the heavy species are almost entirely forward scattered at either large or small angles inside the Test Cell. That is, ions from momentum-exchange collisions and fast neutrals from charge-exchange collisions are scattered at small angles, whereas charge-exchange ions are predominantly forward-scattered but at large angles near 90°. Nomenclature Ω= solid angle σ CEX , σ MEX , σ tot = CEX total cross-section, MEX total cross-section, sum of CEX + MEX total cross-sections θ = deflection angle in degrees θ 1 , θ 2 , θ 3 = angles defined per Figure 5 θ CEX , θ MEX = cutoff angles for CEX/MEX differential cross-section A, B = coefficients in differential cross-section equations J beam = beam current J CEX,EP , J MEX,EP = CEX/MEX ion current scattered to the Exit Plate L = domain length defined per Figure 1 λ = mean free path Kn = Knudsen number k = axial position index k B = Boltzmann constant m = number of axial positions considered m Xe= mass of xenon atom n n = neutral particle density P θ,CEX , P θ,MEX = probability of CEX/MEX scattering below θ T n = background neutral temperature v ion , v' ion = pre-collision and post-collision ion speed v' neutral = post-collision neutral speed v therm = mean thermal speed of background neutrals x = axial position
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