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164 Chapter 4 2 r fL 2 22L2 L T = L g + L = v | | + L . ( 4 . 6 - 2 5 ) Using this value for the path length x of the electron in Eq. (4.6-21) gives the probability of a collision with the neutral gas. Figure 4-35 shows this probability calculated for xenon gas at room temperature for electrons with a temperature of 2 eV in two different interaction lengths. To achieve the order of 10% of the electrons colliding with neutral gas atoms in a 5- to 10-cm-long resonance region requires an internal pressure of at least 10–3 torr. In reality the electrons must make multiple collisions within the interaction region because the energy gain in a single gyration is small. However, this pressure is similar to that found for rf thrusters to achieve sufficient collisions to start or sustain a discharge, for essentially the same reasons. Again, once the plasma is started, coulomb collisions will aid in transferring the electron motion in the microwave fields into heating, which reduces the pressure required to operate the plasma generator and permits higher mass utilization efficiencies to be achieved. As was shown in Tables 4-1 and 4-2, a high magnetic field (>1 kG) and a high microwave frequency (>2.8 GHz) are required to produce sufficient plasma density to deliver reasonable current densities (>1mA/cm2 in xenon) to the grids in microwave thrusters. Due to the difficulty in producing these high magnetic fields throughout the discharge chamber volume, the resonance region is often localized to a small zone inside the thruster volume, and the plasma is allowed 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 L = 10 cm L = 5 cm 10−4 10−3 10−2 10−1 Pressure (torr) Fig. 4-35. Probability of an electron-neutral collision before leaving the resonance zone length indicated as a function of neutral pressure for 2-eV electrons. Probability of CollisionPDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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