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Ion Thruster Plasma Generators 135 Using Eqs. (4.3-7), (4.3-2), and (4.3-17) for each of the three currents, and dividing by the beam current in Eq. (4.3-50), Eq. (4.3-61) becomes 1 8kTe 1/2 1 npvpAp 2nevaAasfc Id 4 m neAa –e /kT e+1 I = 1 b neva AsTs 1 2M 1/2 Aa . (4.3-62) (4.3-63) By inspection of Eq. (4.3-63), it is clear that as the anode area Aa decreases, the plasma potential also decreases. If the anode area is made too small, then the plasma potential will go negative relative to the anode potential. This is called a positive-going (or “electron accelerating”) anode sheath, and is illustrated in Fig. 4-22. In this case, the anode area at the cusps is insufficient to collect the total discharge current by collection of the entire incident random electron flux over the cusp area. The plasma then biases itself to pull in electrons in the Maxwellian distribution that are not initially headed toward the anode, which delivers more current to satisfy the discharge current and charge balance requirements. The plasma electron current collected by the anode then becomes exp 222 neva AsTs Solving for the plasma potential gives kT m AT = eln ss . e Id + Aas fc – 2npvpAp Ib AsTs nevaAsTs neva AsTs Cathode Hollow Cathode φ Vd Anode Fig. 4-22. Transition of the plasma potential to negative relative to the anode due to an anode area decrease, which results in a lower primary electron energy. Vpe Vc Normal New Vpe PotentialPDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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