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54 Chapter 3 ionization and/or excitation losses are significant, the inelastic terms in Eq. (3.5-38) must be augmented accordingly. In ion and Hall thrusters, it is common to assume a single temperature or distribution of temperatures for the heavy species without directly solving the energy equation(s). In some cases, however, such as in the plume of a hollow cathode for example, the ratio of Te /Ti is important for determining the extent of Landau damping on possible electrostatic instabilities. The heavy species temperature is also important for determining the total pressure inside the cathode. Thus, separate energy equations must be solved directly. Assuming that the heavy species are slow moving and the inelastic loss terms are negligible, Eq. (3.5-34) for ions takes the form 3 pin+ 5p v + v p =Q , (3.5-39) 2 t 2inin in in in in where the subscript “in” represents ion-neutral collisions. Finally, the total heat generated in partially ionized plasmas as a result of the (elastic) friction between the various species is given by Q sR = Q eR + Q i R + Q nR s = (Rei +Ren) ve (Rie +Rin) vi (Rne +Rni) vn. Since Rsa = Ras , it is possible to write this as Q sR = R e i ( v e v i ) R e n ( v e v n ) R i n ( v i v n ) . s (3.5-40) ( 3 . 5 - 4 1 ) The energy conservation equation(s) can be used with the momentum and continuity equations to provide a closed set of equations for analysis of plasma dynamics within the fluid approximations. 3.6 Diffusion in Partially Ionized Gases Diffusion is often very important in the particle transport in ion and Hall thruster plasmas. The presence of pressure gradients and collisions between different species of charged particles and between the charged particles and the neutrals produces diffusion of the plasma from high density regions to low density regions, both along and across magnetic field lines.PDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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