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334 Chapter 7 7.2.2 Ionization Length and Scaling It is clear from the description of the Hall thruster operation above that the electrons must be magnetized to reduce their axial mobility to the anode, but the ions cannot be significantly magnetized so that the axial electric field can efficiently accelerate them to form the thrust beam. In addition, a large majority of the ions must be generated in the channel to permit acceleration by the field in that region and to produce high mass utilization efficiency [13]. This provides some simple scaling rules to be established. The neutral gas injected from the anode region will be ionized by entering the plasma discharge in the crossed-field “ionization” region. Consider a neutral gas atom at a velocity vn incident on plasma of a density ne, electron temperature Te , and thickness L. The density of the neutral gas will decrease with time due to ionization: dnn = nnne ive , (7.2-10) dt where ive is the ionization reaction rate coefficient for Maxwellian electrons, described in Appendix E. The flux of neutrals incident on the plasma is n =nnvn, and the neutral velocity is vn = dz / dt , where Equation (7.2-10) then becomes d n = ne ive dz. n vn This equation has a solution of n(z)= (0)e z i, z is the axial (7.2-11) length. (7.2-12) (7.2-13) where (0) is the incident flux on the ionization region and the ionization mean free path i is given by i = vn . (7.2-14) ne ivePDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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