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150 Chapter 4 The criteria for the rf plasma generator to provide net heating of the electrons is that a sufficient number of electrons make a collision within the electric field interaction region. If the interaction region is, say, a few centimeters across, the mean free path should be on this order. The probability of an electron making a collision is given by P=1–exp–x/ =1–exp–no x. (4.5-4) Using Eq. (2.7-2) to convert from neutral density to pressure, the minimum pressure at a temperature T in the plasma chamber of an rf thruster for breakdown to occur is Pmin[torr]=–1.04 10–25 Tln(1–P). (4.5-5) x For example, the minimum pressure for starting the rf-generated plasma is plotted in Fig. 4-30, where room temperature (290 K) xenon gas with a xenon atomic radius of 1.24 Å in a 5-cm-long interaction region is assumed. If 10% of the electrons must make an electron-neutral collision within a 5-cm interaction region to provide sufficient heating for sustaining ionization and breakdown to proceed, then the minimum pressure in the thruster is about 1 10–3 torr. Minimum pressures in the range of 10–3 to 10–2 torr are commonly reported in the literature for rf plasma sources to ignite the plasma. Once the plasma source is ignited, the required electron collisions to provide the heating in the rf 10−2 10−3 10−4 10−5 0.0 0.1 0.2 0.3 0.4 0.5 Collision Probability Fig. 4-30. Minimum pressure for starting a xenon rf thruster with a 5-cm interaction zone as a function of the probability of an electron having a collision. Minimum Pressure (torr)PDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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