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466 Appendix B flow of 3.7 sccm, with an orifice diameter of 1 mm and the length of the cylindrical section of the orifice 0.75 mm. Assuming the gas in the orifice is 4000 K due to charge-exchange heating and P2 = 0 , the upstream pressure is found from Eq. (B-10) to be 6.7 torr. The pressure measured upstream of the cathode tube for this TH15 case is about 8 torr [5]. Correcting for the pressure drop in the insert region (also due to Poiseuille flow), the actual pressure upstream of the orifice plate is about 7.2 torr. The pressure calculated from Eq. (B-10) is low because the downstream pressure is finite (about 2 torr where the barrel section ends) and the bevel region at the output of the orifice has a finite molecular conductance in the collisionless flow regime. In general, it can be assumed that the results of Eq. (B-10) are about 10% low due to these effects. Similar agreement has been found for neutralizer cathodes with straight bore orifices, suggesting that this technique provides reasonable estimates of the pressure in the cathodes. Finally, once the pressure inside the cathode or in the orifice region entrance is estimated, it is straightforward to calculate the local neutral density from Eq. (2.7-2): n =9.65 1024 *P particles , (B-12) o T m3 where P is the pressure in torr and T is the gas temperature in kelvins. References [1] S. Dushman and J. Lafferty, Scientific Foundations of Vacuum Techniques, New York: Wiley and Sons, 1962. [2] K. F. Herzfeld and H. M. Smallwood, Taylor’s Treatise on Physical Chemistry, 2nd edition, vol. 1, New York: D. Van Nostrand Co., p. 175, 1931. [3] A. Roth, Vacuum Technology, New York: North-Holland, 1990. [4] R. C. Reid, The Properties of Gases and Liquids, New York: McGraw- Hill, p. 403, 1977. [5] K. K. Jameson, D. M. Goebel, and R. M. Watkins, “Hollow Cathode and Keeper-Region Plasma Measurements,” AIAA-2005-3667, 41st Joint Propulsion Conference, Tucson, Arizona, July 11–13, 2005.PDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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