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Ion Thruster Plasma Generators 187 Homework Problems 1. Show the conditions under which the ambipolar velocity of the ions flowing to the wall in a transverse magnetic field reverts to the Bohm velocity. 2. An ion thruster discharge chamber has an internal pressure of 10–4 torr, a plasma density of 2 1017 m–3, gas and ion temperatures of 500 K, electron temperature of 4 eV, and a transverse magnetic field of 40 G near the wall with a diffusion length of 2 cm. What is the average transverse ion velocity and the ion confinement factor (ratio of vi / vBohm )? 3. In Fig. 4-16 it is shown that the reaction rate for ionization exceeds the reaction rate for excitation if the electron temperature exceeds about 9 eV. Why not run discharges with Te 9 eV where ionization is greater thanexcitation? Give a quantitative answer for an idealized thruster producing 1 A with 10-cm-diameter grids on a discharge chamber 10 cm in diameter and 15 cm long with the anode being the full cylindrical and back wall area. Assume an 80% grid transparency and a neutral density of 1018 cm–3, and plot the discharge loss as a function of electron temperature from 3 to 10eV. Explain why. (Hint: examine the various loss terms.) 4. What is the electron temperature in a xenon ion thruster that has an ion loss area of 500 cm2, a plasma volume of 104 cm3, neutral gas density of 1012 cm–3, and a 5% primary electron density at 15 eV? 5. A thruster plasma has a volume of 104 cm3, has a neutral density of 1012 cm–3, is 10% ionized with 15-V primary electrons, has a 5-eV electron temperature, and has a primary loss area of 10 cm2. What are the primary electron confinement time, the primary electron collision time (assume a collision cross section of 2 10–16 cm2), and the primary electron slowing down time? What is the total effective confinement time for a primary electron, and which of the three contributors to the total confinement time is the most important? 6. For a xenon ion thruster with a grid area of 500 cm2 with a screen grid transparency of 70%, what is the discharge current required to produce a 2.5-A ion beam? Assume a discharge voltage of 25 V, a hollow cathode voltage drop of 10 V, a plasma potential of 5 V, and an excitation energy of 10 eV. You can neglect the ion and primary electron loss to the anode, the ion current back to the cathode, and any losses to the back wall of the cylindrical discharge chamber with the same diameter as the grids.PDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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