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Ion Thruster Plasma Generators 145 and the electron temperature is found from the solution to ion particle balance in Eq. (4.3-36) in a similar manner as for ring-cusp thrusters. The negative sign in Eq. (4.4-9) appears problematic in the natural log function, but the density gradient n is negative going outward from the plasma. The primary electron density is calculated from Eq. (4.3-45), with the ballistic loss term neglected as described above since primaries are not lost directly to the anode. Finally, the plasma volume term in the ion and excited neutral production rates can be assumed to be the volume of a cone from the baffle to the grids because the plasma is well confined by the strongly diverging magnetic field. Since the 0-D model assumes relatively uniform plasma, estimates for the radial gradient of the plasma density in the magnetic field region near the anode and the additional cathode voltage drop due to the baffle must be made for Eq. (4.4-8) to be accurate. As an example, take a conceptual Kaufman thruster with a 20-cm-diameter screen grid with 80% transparency and a 25-cm-diameter anode with 25 cm between the grids and the baffle. Assuming that the average magnetic field strength in the thruster is about 50 G, the discharge loss from Eq. (4.4-8) is plotted in Fig. 4-27 for two values of the cathode voltage drop. In this case, the cathode voltage drop is higher than in a ring-cusp thruster because it includes the potential drop in the baffle region. The discharge loss is strongly dependent on this value because it directly affects the primary electron energy. Discharge losses in this range at mass utilization efficiencies of about 90% have been reported in the literature for Kaufman thrusters through the years [46–48], 400 350 300 250 200 150 100 Vc = 15 V Vc = 14 V 0.76 0.78 0.80 0.82 0.84 0.86 Mass Utilization Efficiency 0.94 0.96 Fig. 4-27. Discharge loss calculated for Kaufman thruster example. 0.88 0.90 0.92 Discharge Loss (eV/ion)PDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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