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110 Chapter 4 Since the primary electron current lost directly to the anode is generally minimized for best efficiency, the discharge current is carried to the anode mainly by the plasma electrons. The plasma electrons are almost exclusively lost at the magnetic cusps, but their motion is affected by the presence of ions that also penetrate the cusp. Therefore, ions and electrons are lost to a hybrid anode area [27] at the cusp given by Aa=4rhLc=4 reriLc, (4.3-6) where rh is the hybrid Larmor radius, re is the electron Larmor radius, and ri is the ion Larmor radius. The flux of plasma electrons, Ia , that overcomes the sheath at the anode is 1 8kTe 1/2 –e /kT Ia=4 m eneAa exp e, (4.3-7) where is the local plasma potential relative to the anode (essentially the anode sheath potential). The plasma in the discharge chamber obeys particle conservation in that the current injected and produced in the discharge must equal the total current that leaves the discharge: (Iinjected +Iproduced)= Iout. (4.3-8) The current injected into the discharge volume is the primary electron current, and the current produced is the ion and electron pairs from each ionization collision. The current lost to the anode is the sum of the direct primary loss, the plasma electron loss, and a fraction of the ion loss. There is also ion current lost to cathode potential surfaces and the accelerator structure from the balance of the ions produced in the discharge. The plasma potential will adjust itself such that the total electron current to the anode is equal to the total ion current out of the discharge. It will be shown in the following sections that changing the anode area via the magnet strength or number of magnet rings will change the plasma potential relative to the anode (essentially the anode sheath voltage), which affects both the energy loss though the sheath and the stability of the discharge. 4.3.4 Ion Confinement at the Anode Wall Ions are typically unmagnetized in ion thruster discharge chambers because the magnetic field is relatively low throughout the bulk of the discharge chamber,PDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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