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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Hollow Cathodes 299 are found from the models discussed above, the insert life will be limited by evaporation in the same manner as in vacuum devices. Published measurements by Palleul and Shroff [51] of the depth of barium depletion in dispenser cathodes as a function of time and temperature show that barium depletion obeys a simple diffusion law with an Arrhenius dependence on temperature. This is shown in Fig. 6-44 (from [51]), where the impregnate surface layer in the pore recedes with time. The “activation energy” in the diffusion coefficient that determines the slope of the curves in Fig. 6-44 appears to be relatively independent of the cathode type. From data presented in Fig. 6-44, the operating time to deplete impregnate from the insert material to a depth of 100 m is ln100μm =eVa +C1=2.8244e15.488, (6.8-3) kT kT where the operating time 100 μ m is in hours, e is the elementary charge, Va is the activation energy, k is Boltzmann’s constant, C1 is a fit coefficient, and T is the insert temperature in kelvins. The activation energy was found from Fig.6-44. Using this relationship and the fact that the depletion depth is 103 102 101 S-Type Cathode S-Type Cathode B-Type Cathode B-Type Cathode 1035 CB 1230 CB 1050 CB 1250 CB 102 103 104 105 Time (hr) Fig. 6-44. Depletion depth of a porous tungsten insert as a function of time for cathodes at different temperatures (redrawn from [51]). Depleted Depth ( m) Square-Root Slope

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