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72 Chapter 3 ni ~ ne Boundary Fig. 3-2. Generic quasi-neutral plasma enclosed in a boundary. In the absence of an electric field in the plasma volume, conservation of energy for the electrons and ions is given by 1 m v e2 = k T e , 2e 1 Mvi2 = kTi . 2e If it is assumed that the electrons and ions have the same temperature, the ratio of current densities to the boundary is Je=ve= M. (3.7-2) Ji vi m Table 3-1 shows the mass ratio M/m for several gas species. It is clear that the electron current out of the plasma to the boundary under these conditions is orders of magnitude higher than the ion current due to the much higher electron mobility. This would make it impossible to maintain the assumption of quasi- neutrality in the plasma used in Eq. (3.7-1) because the electrons would leave the volume much faster than the ions. If different temperatures between the ions and electrons are allowed, the ratio of the current densities to the boundary is Je=ve= MTe. (3.7-3) Ji vi mTi To balance the fluxes to the wall to satisfy charge continuity (an ionization event makes one ion and one electron), the ion temperature would have to againPDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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