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Ion Thruster Plasma Generators 163 Otherwise, the energy received by an electron during acceleration on each half- cycle of its cyclotron motion is taken back by deceleration of the electron in the field on the next half-cycle. Therefore, there is a minimum pressure at which sufficient collisions occur to ignite the plasma and sustain the discharge. The probability of a collision occurring is P = 1– exp–no x = 1– exp( x/ en ) , (4.6-21) where x is the path length of the electron in the neutral gas with a density of no , and en is the electron-neutral collision mean-free-path. An electron entering the interaction region gyrates around the magnetic field lines due to its perpendicular velocity and travels along the magnetic field line due to its parallel velocity. While the electron cyclotron heating tends to spin-up the electron motion around the field lines, collisions tend to scatter the motion along the direction of the field lines and thermalize the electrons into a Maxwellian distribution, sometimes with a high-energy bump or tail driven by the resonance. The collisionality requirements to achieve heating can be found from examining the path length of an electron at a temperature Te spiraling along a field line. The distance that the electron travels when gyrating around the field lines is given by the Larmor radius, which was derived in Chapter 3: rL=v =mv =1 2mv . (4.6-22) c qB B e The time for an electron to leave the microwave interaction region of length L is t = vL , (4.6-23) || where v|| is the parallel electron velocity along the field line. The number N of gyrations that an electron makes in the interaction region is the microwave frequency f multiplied by the time in the resonant region. The path length of the perpendicular gyration of the electron is then L g = 2 r L N = 2 r L f vL . ( 4 . 6 - 2 4 ) || The total path length of the helical motion of the electron isPDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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