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218 Chapter 5 rating” is related to the energy deposition in the electrodes in a simple manner. The power running in the arc is P = IVarc , where I is the discharge current and Varc is the voltage drop in the arc. Assuming that most of the voltage drop is in the cathode sheath, the energy E deposited by the arc on the cathode surface is E= Pdt= IVarc dt. (5.5-2) The voltage drop of refractory metal and graphite arcs is nearly independent of the amount of current running in the arc up to several hundred amperes [39,40]. Therefore the arc voltage can be considered to be essentially a constant, and the energy deposited by the arc on the cathode is E =Varc I dt =Varc Q, (5.5-3) where Q is the total charge transferred in the arc. The arc energy deposited on the cathode surface for a given electrode material is characterized by the total charge transferred by the thruster power supplies during the arc time and not just the stored energy in the power supply. Assuming that the arc remains lit during the entire time required to discharge the filter capacitor in the power supply, the total charge transferred through the arc is Q = CV, where C is the capacitance and V is the capacitor charging voltage. If the arc current falls below the minimum value to sustain the arc, called the “chopping current,” and is prematurely extinguished, then the total charge transferred is reduced. It should be emphasized that the amount of energy delivered to the cathode surface by the arc and the amount of damage to the surface incurred by material removal are independent of any series resistance in the circuit as long as the current is stable for the duration of the event (i.e., the current is above the chopping current). This means that simply adding a series resistor to one leg of the high-voltage power supply circuit or the accel grid circuit will not reduce the surface damage due to an arc unless the arc current drops to less than the chopping current. The only mechanism that reduces surface damage if the current is large compared to the chopping current is to limit the total charge transfer. This requires either reducing the power supply capacitance at a given voltage (which reduces the total stored energy) or actively shunting or opening the circuit to reduce the arc duration. 5.5.2 Molybdenum Electrodes Molybdenum is a standard electrode material used in ion thrusters due to its low sputter erosion rate, ability to be chemically etched to form the aperture array, and good thermal and structural properties. The surface of thePDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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