Electrostatic Propulsion

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 = (2π/q) <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ϵ</sub> V <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> R <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> = √2m/qV <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> P. R is an aspct ratio of ion beam diameter to acceleration distance x <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> , and P is a diode perveance (amp/volts <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3/2</sup> ). 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 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> newtons) and specific impulse (I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sp</sub> > 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 x <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.</sub> 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 x <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0for cesium, corresponding to time fluctuations of the potential at the plasma oscillation frequency in a frame of reference moving with the ions.</sub>