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90 Chapter 3 5. Answer the following question that might be brought up by a student working in the lab: “In a plasma discharge set up in my vacuum chamber the other day, I measured an increase in the plasma potential with an electrostatic probe. How do I know if it’s a double layer or just a potential gradient within which the ionized gas is quasi-neutral?” 6. Derive Eq. (3.6-9) for the penetration distance of neutral particles in a plasma. 7. Derive the expression for Ohm’s law for partially ionized plasmas, Eq. (3.6-20). 8. Derive Eq.(3.6-81) for the transverse ambipolar ion velocity across magnetic field lines. 9. Derive the Bohm sheath criteria including the presence of double ions. 10. Derive an expression equivalent to the Child–Langmuir law for the condition where the initial ion velocity entering the sheath is not neglected (ions have an initial velocity vo at the sheath edge at z = 0 ). 11. A 2-mm by 2-mm square probe is immersed in a 3 eV xenon plasma. a. If the probe collects 1 mA of ion current, what is the plasma density? (Hint: the probe has two sides and is considered infinitely thin.) b. What is the floating potential? c. What is the probe current collected at the plasma potential? 12. A 2-mm-diameter cylindrical probe 5 mm long in a xenon plasma with Te = 3 eV collects 1 mA of ion saturation current. a. Whatistheaverageplasmadensity? b. How much electron current is collected if the probe is biased to the plasma potential? c. Why is this electron current the same as the solution to Problem 11.c when the plasma densities are so different? 13. An electron emitter capable of emitting up to 10 A/cm2 is in contact with an Xe+ plasma with an electron temperature of 2 eV. Plot the emission current density versus plasma density over the range from 1010 to 1013 cm–3. At what density does the emission become thermally limited (the maximum current density that the electron emitter can emit)?PDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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