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Basic Plasma Physics 73 Gas Protons (H+) Argon Xenon Mass ratio M/m 1836 73440 241066.8 Square root of the mass ratio M/m 42.8 270.9 490.9 Table 3-1. Ion-to-electron mass ratios for several gas species. be orders of magnitude higher than the electron temperatures. In ion and Hall thrusters, the opposite is true and the electron temperature is normally about an order of magnitude higher than the ion temperature, which compounds the problem of maintaining quasi-neutrality in a plasma. In reality, if the electrons left the plasma volume faster than the ions, a charge imbalance would result due to the large net ion charge left behind. This would produce a positive potential in the plasma, which creates a retarding electric field for the electrons. The electrons would then be slowed down and retained in the plasma. Potential gradients in the plasma and at the plasma boundary are a natural consequence of the different temperatures and mobilities of the ions and electrons. Potential gradients will develop at the wall or next to electrodes inserted into the plasma to maintain quasi-neutrality between the charged species. These regions with potential gradients are called sheaths. 3.7.1 Debye Sheaths To start an analysis of sheaths, assume that the positive and negative charges in the plasma are fixed in space, but have any arbitrary distribution. It is then possible to solve for the potential distribution everywhere using Maxwell’s equations. The integral form of Eq. (3.2-1) is Gauss’s law: sE ds= 1 V dV= Q , (3.7-4) oo where Q is the total enclosed charge in the volume V and s is the surface enclosing that charge. If an arbitrary sphere of radius r is drawn around the enclosed charge, the electric field found from integrating over the sphere is E= Q rˆ. (3.7-5) 4 or2 Since the electric field is minus the gradient of the potential, the integral form of Eq. (3.2-5) can be writtenPDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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