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322 Chapter 6 d. Assume that the plasma density falls exponentially from the orifice entrance to 1018 m–3 in 1 cm. What is the total electron current that can be emitted into the plasma? 3. A 2.5-cm-long BaO-impregnated insert with a 2-cm inside diameter has xenon gas injected to create an internal pressure of 2 torr at 1500 K in the hollow cathode. Assuming the insert plasma is infinitely long, what is the electron temperature in the insert plasma and the radial ion drift velocity at the wall? 4. For the cathode geometry in Chapter 6, Problem 2, what is the internal plasma density for an emission current of 30 A and a heating power of 35 W, assuming a uniform plasma density with an electron temperature of 2 eV? (Hint: estimate the resistivity for the sheath voltage, find the plasma density, then iterate.) 5. A lanthanum hexaboride hollow cathode with a 2-cm inside diameter and 2.5-cm long emits 20 A of electrons into a uniform 2 1019 m–3 plasma with an electron temperature of 1.5 eV. For a heating power of 40 W and an internal xenon pressure of 1.2 torr at 1500 K, find the ion and electron heating powers to the insert. Why is one larger than the other? 6. If a cylindrical discharge cathode orifice is 2 mm in diameter and has an internal pressure of 3 torr at a temperature of 2000 K, what is the electron temperature? (Neglect end losses.) 7. A neutralizer cathode produces 3 A of electron current through a 0.6-mm- diameter orifice that is 1.5-mm long. Assuming that the electron temperature in the orifice is 1.5 eV, the electron temperature in the insert region is 1.2 eV, the pressure is 50 torr at 2000 K, and the sheath voltage at the wall is 12 V, what is the plasma density, the ion heating of the orifice plate, and the axial voltage drop in the orifice plasma? 8. A hollow cathode has an orifice diameter of 2.5 mm and a xenon gas flow of 4 sccm with an effective temperature of 2000 K. Assume that the neutral gas density falls exponentially from the orifice exit with a characteristic length of 0.5 mm (i.e., one e-folding for every 0.5 mm of distance from the cathode). Assuming 15-V primary electrons in the cathode plume and that all of the ions generated fall back through the sheath, find the location downstream of the orifice exit where a double layer might occur.PDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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