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Ion and Hall Thruster Plumes 425 Kapton-Coated Spacecraft Surface r Ion Thruster Fig. 8-19. Flat panel positioned over an ion thruster plume. a. Use the equations in your textbook to express the ion beam density, n, as a function of spatial coordinates (r,z). Produce contour plots of the beam density within a radius of r = 0.5 m from the center of the thruster exit(r=0,z=0).Assumethattheiondensityn0 at(r=0,z=0)is 4 1015 m–3 and that the ion beam velocity V0 is 40 km/s. Also, assume that uBohm / V0 = 0.03 . b. Derive an expression for the radial component of the ion beam flux, r = r , as a function of spatial coordinates (r,z). Plot the radial ion beam flux as a function of z for r = 0.3, 0.4, and 0.5 m. c. Perform a literature search to find the sputtering yield Y of Kapton as a function of ion energy/ion charge, E, and incidence angle, , and then plot Y for 300-V and 1000-V ions between 0 and 90 deg of incidence angle. (Hint: The sputtering yield for many materials is usually expressed as Y(E, ) = (a + bE)f( ), where f( ) is a polynomial function and a,b are constants.) d. Compute the erosion rate in (Å/s) caused by the main ion beam along the Kapton plate (in the r-z plane), as a function of z, for r = 0.3, 0.4, and 0.5 m. Assume that the molecular weight of Kapton is 382 g/mol and that its mass density is 1.42 g/cm3 (1Å = 10–10 m). e. If the panel was placed at r = 0.5 m from the thruster, how long would it take for the main ion beam to erode completely the Kapton layer? f. For partial credit, choose one answer to the following question: how would you advise your boss based on your results? i. The Kapton coating will be just fine. There’s no need to perform a test. Build the spacecraft as is (panel radial location = 0.5 m). ii. The Kapton coating will not survive. We must consider changing the location of the panel relative to the thruster. Ion Beam zPDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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