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276 Chapter 6 orifice plate is usually chamfered on the downstream side, which must be included in the analysis because the rapidly expanding gas plume in this region often transitions to the collisionlesss regime in which the flow is not dominated by diffusion. In the orifice, continuity dictates that the ions that hit the orifice wall are re- emitted as neutrals and re-enter the plasma. The continuity equations for the three species (neutrals, ions, and electrons) in the cylindrically symmetric orifice region are r2 n + vono + 2 rv n = 0 t z w a l l r2 n + vino 2 rv n = 0 t z wall r2 e n+ Je =0, t z (6.5-5) (6.5-6) (6.5-7) where v is the ion or neutral velocity and vwall is the particle velocity at the radial boundary. The average neutral velocity is found from Poiseuille flow: vo= r2 dP, (6.5-8) 8 dz where is the temperature-dependent neutral gas viscosity. For xenon, the viscosity is [26] =2.3 10 5Tr0.965 for Tr <1 = 2.3 10 5T(0.71+0.29/Tr ) for T >1, with units of Ns/m2 or Pa-s and a relative temperature given by Tr = T / 289.7 K. Since a large fraction of the ions undergoes charge exchange within the orifice, the neutral gas is heated and the viscosity is increased. This is incorporated into the model [35] by assuming that the gas temperature varies as T =T + M (fv )2 +v2 , (6.5-10) wallk r o where the fraction of the neutrals that receives the ion radial velocity via charge exchange is given by rr (6.5-9)PDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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