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Hall Thrusters 335 This expression for the ionization mean free path is different from the usual one, given in Eq. (3.6-6), that applies for the case of fast particles incident on essentially stationary particles. This is because the neutral gas atoms are moving slowly as they traverse the plasma thickness, and the fast electrons can move laterally to produce an ionization collision before the neutral leaves the region. Therefore, the ionization mean-free path depends on the neutral velocity, which determines the time the atom spends in the plasma thickness prior to a collision. The mean-free path also varies inversely with the electron density because a higher number of electrons in the slab will increase the probability of one of them encountering the neutral atom. The percentage of the neutrals exiting the plasma of length L that are ionized is exit =1 e L i . (7.2-15) incident For example, in order to have 95% of the incident neutral flux on the plasma ionized before it leaves the plasma, Eq. (7.2-15) gives L= iln(1 .95)=2.996 i = 3vn , (7.2-16) ne ive or the plasma thickness must be at least three times the ionization mean-free path. Since some of the ions generated in the plasma hit the channel side walls and re-enter the plasma as neutrals instead of exiting as beam ions, the plasma thickness should significantly exceed the ionization mean-free path to obtain high mass utilization efficiency. This leads to one of the Hall thruster scaling rules: i =constant<<1. (7.2-17) L In this example, this ratio should be less than 0.33. The actual channel’s physical depth in dielectric-wall Hall thrusters is given by the sum of the magnetized plasma thickness (L) and the geometric length required to demagnetize the plasma at the anode. This is illustrated schematically in Fig.7-6, where the channel depth is nearly twice the magnetized plasma length. The axial magnetic field gradient has been found to be critical for the thruster performance [12]. A decreasing radial magnetic field strength going toward the anode, as shown in Fig. 7-6, results in higher thruster efficiency [4,12]. At the anode, the plasma is largely unmagnetized, and an anode sheath forms to maintain particle balance, similar to the DC plasmaPDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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