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Hollow Cathodes 301 To predict cathode life in a thruster application from an insert depletion mechanism, a relationship between the insert temperature and the discharge current at a given gas flow must be obtained. The SSC insert temperature was measured versus discharge current by Polk [50]. These data are well fit in the plasma contact region (the 3 mm closest to the orifice plate) by T =1010.6 Id0.146[K]. (6.8-6) At 12 A of discharge current, this gives an insert temperature of 1453 K. Since the insert in this cathode is about 760- m thick and we assume that the insert is depleted when the depth reaches about two-thirds of the thickness (due to some barium diffusion out the outside diameter of the insert), Eq. (6.8-5) predicts a life of 30,000 hours. This is in good agreement with the SSC life test data where the cathode failed to start after about 28,000 hours at 12 A of discharge current [52]. In this case, barium recycling may not affect the insert life significantly because the plasma is in contact with the insert for only a couple of millimeters, from the orifice plate, and the barium will tend to migrate to regions that are not involved in the emission process. For the NSTAR cathode, the insert temperature data as a function of discharge current measured by Polk [33] are well fit in the plasma contact region by T = 1191.6 Id0.0988[K] . (6.8-7) At the full-power discharge current of 13 A, and using the insert thickness of 760 m, Eq. (6.4-5) predicts an insert life of 20,000 hours. The ELT ran at full power for about 14,000 hours and accumulated an additional 16,352 hours at much lower discharge currents [53]. The barium depletion model indicates that the insert should have been depleted in the emission zone in less than 24,000 hours. Measurements indicate partial depletion in the emission region near the orifice, but that as much as 30% of the original barium was still present [53]. Clearly barium recycling in the plasma reduced the effective evaporation rate and extended the life of the cathode significantly. For the NEXIS hollow cathodes, the operating insert temperature profile has not yet been measured. Estimates of the insert temperature were made using an early version of the combined plasma and thermal model [47]. Since the discharge loss and efficiency performance of the NEXIS thruster are known, the relationships in Chapter 2 can be used to plot thruster life versus engine performance. The NEXIS thruster operates at 75% to 81% efficiency over an Isp of 6000 to 8000 s [54]. Figure 6-46 shows the model-predicted depletion- limited life of this insert versus specific impulse for several thruster power levels. At the nominal operating point of 7000 s Isp and 20 kW, the cathode isPDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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