Elastic Scattering of Ions in Electrostatic Thruster Plumes

Abstract

It is postulated that the ion population and energy in most ion and Hall-Effect thruster plumes, at angles beyond the main beam divergence, is largely determined by the elastic scattering of high-energy ions by neutral atoms. A theoretical model of the scattered ion density and energy is presented. The model accounts for the presence of a main ion beam emanating from the thruster and neutral atoms from the ambient and thruster-induced environment. The treatment of elastic scattering incorporates angle-dependent differential cross sections that are computed classically. Results from the model are compared with ion flux and energy measurements taken by a retarding potential analyzer as a function of angle from the thruster’s axis of symmetry. The good agreement between model results and measurements for ion energy and flux suggests that the determination of the differential cross section using classical formulations is adequate for the high-energy ions associated with electrostatic propulsion plumes. But the comparisons also emphasize the importance of accurate models of the neutral particle densities in these plumes. Nomenclature A = area of thruster acceleration channel, m 2 E = impact energy associated with the scattering event, eV F = ion particle flux, particles/m 2 s Fr = radial component of ion flux vector, particles/m 2 s Fz = axial component of ion flux vector, particles/m 2 s f = multiple ionization flux fraction I = differential cross section, m 2 /sr J = current, A M = reduced mass, kg m = particle mass, kg ˙ mi = ion mass flow rate, kg/s N = number of scattered particles n = ion particle density, particles/m 3 n0 = neutral particle density, particles/m 3 n∞ = reference ion particle density, particles/m 3