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Ion Thruster Plasma Generators 125 where Ip is the total number of ions produced in the discharge, U+ is the ionization potential of the propellant gas, I is the number of excited ions produced in the discharge chamber, U is the excitation energy, Is is the number of ions to the screen plane, Ik is the number of ions flowing back to the cathode, IB is the beam current, Ia is the plasma electron current to the anode, Te is the electron temperature, Iia is the ion current to the anode, and IL is the primary electron fraction lost to the anode. The plasma electron energy lost to the anode wall, e , is 2kTe / e + , which is derived in Appendix C. The ions fall through the pre-sheath potential from the center of the plasma to the sheath edge, such that Vp can be approximated as kTe /2e. The ion energy to the anode, i, is then kTe/2e+ , which was given in Eq. (4.2-10). With the screen grid connected to the cathode potential, the current emitted from the hollow cathode was given in Eq. (4.3-43) in terms of the other currents in the circuit. Likewise, conservation of particles flowing to the anode gives Ia = Id + Iia – IL , (4.3-48) where Id is the discharge current measured in the discharge power supply. Equating the power into the discharge to the power out, using the particle balance equations in Eqs. (4.3-43) and (4.3-48), and solving for the beam current from the thruster gives: Ib=I V–V+V–2T –IU–IU d(d c p eV)p+ ** Vp + –(Is+Ik)(2Vd –Vc+2Vp+2 ) (4.3-49) Vp + I V+2T +2 +I V–V+V–2T ia(p eV )L(d c p eV) – Vp+ , where TeV is in electron volts. The issue in evaluating Eq. (4.3-49) for the beam current produced by a given thruster design is that several of the current terms in the numerator contain the plasma density, which is not known. In addition, the beam current IB is givenPDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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