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Ion Thruster Plasma Generators 121 Flow is usually given in standard cubic centimeters per minute (sccm) or mg/s, and conversions from these units to number of particles per second, useful in Eq. (4.3-35), are given in Appendix B. The neutral pressure in the discharge chamber during operation of the thruster can also be found using this expression and the conversion from density to pressure given in Eq. (2.7-2), if the neutral gas temperature is known. In general, the neutral gas atoms collide with the anode wall and grids several times before being lost, and so the neutral gas can be assumed to have the average temperature of the thruster body in contact with the plasma. This temperature typically ranges from 200 to 300 deg C for operating thrusters. The electron temperature in the discharge chamber can be found using particle balance of the ions. The total ion production rate, given by Eq. (4.3-25), must equal the total ion loss rate. The ion loss rate is given by the Bohm current in Eq. (4.3-9) with the area A representing the sum of all the surfaces that collect ions (cathode, anode, and grids), with the appropriate confinement factor fc found in Eq. (4.3-16) multiplied by the anode surface area. Equating Eqs. (4.3-25) and (4.3-9) and using Eq. (4.3-35) for the neutral density gives kTe M =2noV =8V Qin(1– md). (4.3-36) ive V + np ivp V Ai voAgAiTa c ne If the total flow into the discharge chamber and the mass utilization efficiency are specified, and the primary electron density is calculated as described below, then Eq. (4.3-36) can be solved for the electron temperature. This is because the ionization and excitation reaction rate coefficients are functions of the electron temperature. Alternatively, if the beam current is specified, then the right-hand side of Eq. (4.3-35) can be used in Eq. (4.3-36) to find the electron temperature. Typically, curve fits to the ionization and excitation cross section and reaction rate data shown in Figs. 4-15 and 4-16 are used to evaluate the reaction-rate coefficients in a program that iteratively solves Eq. (4.3-36) for the electron temperature. The primary electron density in Eq. (4.3-36) can be evaluated from the total primary electron confinement time in the discharge chamber. The emitted current Ie from the hollow cathode is Ie = np e V , (4.3-37) tPDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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