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340 Chapter 7 electron distribution can produce the ionization. Since it is assumed that the discharge current is essentially the total electron current collected by the anode (the ion current is small), the discharge current can be written as Id = Iei + Iec. (7.2-27) The discharge current is also essentially the electron current emitted by the cathode: Using the fact that one electron and one ion are made in each ionization event such that Iei = Iib , Eq. (7.2-27) becomes Id =Iib +Iec. (7.2-29) This relationship describes the net current crossing the exit plane, and so it is commonly stated in the literature that the discharge current is the ion beam current plus the backstreaming electron current crossing the exit plane [4,9]. Depending on the plasma conditions, it is possible for some fraction of the secondary electrons produced near the channel exit to diffuse into the beam. Equation (7.2-29) is still valid in this case because for every secondary electron that diffuses into the beam, another electron from the cathode plasma must cross the exit plane in the opposite direction to maintain the net discharge current. The discharge current is still the net ion beam current plus the backstreaming electron current across the exit plane. Finally, the ion beam current is equal to the current of electrons entering the beam: Id =Ie =Iec+Ieb. (7.2-28) Ionization Event Discharge Supply +ā Fig. 7-8. Electrical schematic for the currents flowing through the discharge plasma and power supply. Id eā i+ Iei Iec Iib Ieb IePDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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