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Thruster Principles 35 Homework Problems 1. Assume that the ion charge density in a one-dimensional (1-D) accelerator gap between two grids varies as = ox / d , and that a voltage Vo is applied to the electrodes bounding the gap. a. Find the potential and electric field as a function of position in the gap. b. Find the force on each of the grids. c. Findthetotalelectrostaticforcebetweentheionsandthegrids. 2. A mission under study desires to deliver a 800-kg payload through 8 km/s of v. The spacecraft has 3 kW of electric power available for propulsion. The mission planners want to understand the trade-offs for different thrusters and operating conditions, and they want you to make plots of propellant mass and trip time required versus specific impulse for the following cases. Assume xenon is the propellant. a. Ion thruster case: The ion thruster can run at full power from 1 kV to 2 kV. For all throttle conditions, assume the following parameters are constant: total efficiency of 55%, propellant utilization of 85%, beam divergence angle of 12 deg, and double-to-single ion current ratio of 10%. b. Hall thruster case: The Hall thruster can run at full power from 300 V to 400 V. For all throttle conditions, assume the following parameters are constant: total efficiency of 45%, propellant utilization of 85%, beam divergence angle of 25 deg, and double-to-single ion current ratio of 15%. 3. Derive Eq. (2.4-7) for the mass utilization efficiency correction due to double ions. 4. Derive the thrust correction factor and the resulting thrust equation accounting for the presence of triply ionized atoms. Assuming 10% doubles, what is the error in the calculated thrust if 5% actually present triples have been neglected? 5. Mission planners have two candidate ion and Hall thrusters to place on a spacecraft and want to understand how they compare for thrust-to-power ratio and performance. The xenon ion thruster has a total power of 5 kW, a 1200-V, 3.75-A beam with 10% double ions, a total efficiency of 65%, and a mass utilization efficiency of 86%. The Hall thruster has a total power of 5 kW, a 300-V discharge voltage and a 12.5-A beam with 10% double ions, a total efficiency of 50%, and an input xenon gas flow of 19 mg/s.PDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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