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300 Chapter 6 proportional to the square root of the operating time [51], an equation yielding the insert lifetime due to barium depletion can be derived [47]: y 2 life= 100μm y100μm , (6.8-4) where 100 μ m is the time to deplete to 100 m in depth from Eq. (6.8-3), y is the insert thickness in m, and y100μm is the 100- m reference depth. Using Eq. (6.8-3) in Eq. (6.8-4), the life of a Type S dispenser cathode in hours is = 10 4 y2 exp 2.8244e 15.488 , (6.8-5) life kT where y is the insert thickness in m and T is the insert temperature in kelvins. Figure 6-45 shows the insert life for a 1-mm depletion depth versus the insert temperature. Insert life of over 100,000 hours is readily achievable if the insert is thick enough. At around a nominal 1100 ̊C operating temperature, the life increases a factor of 2 if the temperature decreases 40 ̊C. This model represents a worst-case estimate of the cathode life. In very high- density hollow cathodes, like the NSTAR cathode, the ionization mean free path for the evaporated barium is significantly less than the insert plasma radius. This means that a large fraction of the barium is ionized close to the insert surface. The electric field in this region is primarily radial, which means that some large fraction of the barium is recycled back to the surface. The barium surface coverage is then partially re-supplied by recycling, which can extend the life considerably. Fig. 6-45. Insert life from barium evaporation calculated for a 1-mm depletion depth versus temperature.PDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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