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166 Chapter 4 the cost of producing the microwave radiation, the power absorbed by the plasma is equal to the power lost: P = I U++I*U*+(I +I +I ) TeV + +I (2T + ), (4.6-26) abs p s w b 2 a eV where Is is the ion current collected by the screen grid, Iw is the ion current collected by the entire wall, and the ion energy loss is, again, Te / 2 + . The amount of energy lost by electrons to the wall assumes that the electrons have a Maxwellian distribution, which may underestimate the energy lost due to the high energy tail in the electron distribution generated by the resonant ECR heating. The discharge loss is the power in (or out) divided by the beam current: d = Pabs Ib (4.6-27) Ip I* I I T I = U + + U * + s + w + 1 e V + + a ( 2 T e V + ) . Ib Ib Ib Ib 2 Ib The first three current fractions in this equation are given by Eqs. (4.3-55), (4.3-56), and (4.3-57), respectively. The fourth current fraction is given by 1 nievaAw Iw= 2 = Aw , (4.6-28) I b 12 n i e v a A s T s A s T s where the wall area Aw is the rear wall area only. The plasma potential is found again from charge conservation by equating the total ion and electron current: nie kTe(Aw+As)=nee 8kTe[Aw+(1–Ts)As]exp–e /kTe. (4.6-29) 2M4 m Solving for the plasma potential gives = kTe ln Aw +(1–Ts)As 2M , (4.6-30) e A w + A s m which is different from that found for rf ion thrusters because there is no ion confinement factor due to the induced magnetic fields from the antenna (thePDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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