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Ion Thruster Plasma Generators 143 DB = 1 kTe . (4.4-2) 16 eB The electron current collected by the anode is the flux that diffuses through the magnetic field times the Boltzman factor at the sheath: Ia =(μ nE–D n)eAase–e /kTe, (4.4-3) where Aas is again the anode surface area exposed to the plasma discharge. The actual current distributions and potential distribution in a Kaufman thruster are the same as for the DC discharge thruster shown in Fig. 4-9. However, there are several terms that were analyzed for ring-cusp thrusters that can be neglected in Kaufman thrusters. First, if the axial magnetic field in the discharge chamber is on the order of 100 G, then the Larmor radius for, say, 20-eV primaries is 1.5 mm. Since the magnetic field lines do not intersect the anode and primaries are too energetic to participate in the collective instabilities that drive Bohm diffusion, the primary electrons must make collisions in order to cross the magnetic field to be lost. That means that the fraction of the primary electron current loss directly to the anode in ring-cusp thrusters, IL , can be neglected, which is an advantageous feature of Kaufman thrusters. Second, the plasma flow across the magnetic field is still governed by ambipolar effects. As was shown in Section 4.3.4, if the transverse magnetic field strength is in excess of about 50 G in typical ion thruster discharge chambers, then the radial electric field in the plasma (in the magnetic field region) is near zero and the ion loss rate is on the order of one-tenth the Bohm current toward the wall. This means that the ion current to the anode term, Iia , can also be neglected to first order. Since the discharge current collected through the anode leg of the discharge power supply connection was given in Eq. (4.3-61) as the plasma electron current minus the ion current and plus the primary current, the discharge current is now just Id = Ia = –D neAase–e /kTe . (4.4-4) Third, the ion current flowing back towards the hollow cathode was neglected in our treatment of ring-cusp thrusters because the hollow cathode exit area in contact with the plasma was so small. In Kaufman thrusters, a baffle is placed on axis in front of the cathode to force the primary electrons off axis to flatten the density profile. Since the magnetic field is strongly divergent, the axial plasma density gradient is significant and the plasma density in contact with thePDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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