Fundamentals of Electric Propulsion: Ion and Hall Thrusters

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Fundamentals of Electric Propulsion: Ion and Hall Thrusters ( fundamentals-electric-propulsion-ion-and-hall-thrusters )

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108 Chapter 4 4.3.3 Electron Confinement The primary electrons are injected into the discharge chamber from the hollow cathode. The discharge chamber can be viewed as a volume with reflecting boundaries and discrete loss areas for the electrons at the cusps where the magnetic fields lines are nearly perpendicular to the surface. The primary electrons then effectively bounce around in the chamber until they are either lost directly to the anode wall by encountering the finite loss area at the cusps, make an ionization or excitation collision, or are thermalized by coulomb interactions with the plasma electrons. The primary current lost directly to the anode cusps is given by IL = npevpAp , (4.3-2) where np is the primary electron density, vp is the primary electron velocity, and Ap is the loss area for the primaries. The loss area for primary electrons at the cusp [27] is given by Ap=2rpLc=2 2mvp Lc, (4.3-3) Be where rp is the primary electron Larmor radius, B is the magnetic field strength at the cusp at the anode wall, vp is the primary electron velocity, e is the electron charge, and Lc is the total length of the magnetic cusps (sum of the length of the cusps). Using a simple probabilistic analysis, the mean primary electron confinement time can be estimated by p= V , (4.3-4) vp Ap where V is the volume of the discharge chamber. The mean primary electron path length prior to finding a cusp and being lost to the wall is L = vp p . Likewise, the ionization mean free path is = 1 / no , where represents the total inelastic collision cross section for the primary electrons. The probability that a primary electron will make a collision and not be directly lost to the anode is then

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