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The thrust (newtons) developed by a system which accelerates a space charge limited flow of ions of specific charge q/m (coulombs per kilogram) through a voltage V is given by F = (2Â¿/q) Â¿0V2R2 = Â¿2m/qVP. R is an aspct ratio of ion beam diameter to acceleration distance x0, and P is a diode perveance (amp/volts 3/2 ). Lines of electric force extend from charges in transit across the diode to charged surfaces of the accelerator electrode, on which the thrust is thus purely electrostatic. Alkali metals have favorable characteristics for use as propellants because their ions can be produced for small energy expenditure near 100 electron-volts per ion by surface contact ionization, while porous tungsten with pore size less than one micron is an efficient and convenient emitting surface. For practical values of thrust (F>0.01 lbf 2.25 Ã 10-3 newtons) and specific impulse (Isp> 2000 seconds) alkali metal thrust devices will operate at a few kilovolts and require R<<1. But for R>3, unipolar ion beams will reverse their direction of flow within a few x0. Mathematical solutions to the neutralization problem for the case of one-dimensional flow of mixed ion and electron beams are presented assuming no energy exchanges by collisions or plasma instabilities. These show a periodic spatial potential distribution of wavelengths 0.027 x0 for cesium, corresponding to time fluctuations of the potential at the plasma oscillation frequency in a frame of reference moving with the ions.