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Ion Thruster Plasma Generators 129 IL = npevpAp = 2npvpAp . Ib 12 nievaAsTs nevaAsTs The discharge loss can then be written (4.3-59) Ip + I* * 1–T Vd U + U + s(2Vd–Vc+2Vp+2 ) Ib Ib Ts Vd –Vc –2TeV d = Af V V + + as c V +2T +2 d (p ) (p eV ) + AsTs (4.3-60) Vd –Vc –2TeV 2n v A V V –V +V –2T d ppp(d c p eV) + nevaAsTs . Vd –Vc +Vp –2TeV Equation (4.3-60) illuminates some of the design features that improve the discharge efficiency. Since the discharge voltage Vd appears in both the numerator and denominator of Eq. (4.3-60), there is no strong dependence of the discharge loss on voltage shown in this equation. However, increases in the discharge voltage raise the primary energy strongly, which increases the ionization rate and beam current. Therefore, higher discharge voltages always result in lower discharge losses. Higher screen grid transparency Ts , smaller ion confinement factor fc (better ion confinement), smaller primary loss area Ap , and smaller wall surface area Aas all reduce the discharge loss. Lowering the plasma potential also reduces the discharge loss by reducing the energy lost to the anode by the plasma electrons, which is accomplished by reducing the anode loss area at the cusps. The input data required to solve Eq. (4.3-60) are: • Discharge voltage • Discharge chamber surface area and volume • Magnetic field design (magnetic field at the cusp and the closed contour field between the cusps) • Grid area • Grid transparency • Gas temperature • Cathode voltage dropPDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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