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84 Chapter 3 significantly greater than the electron temperature, the sheath thickness is several times this value and the sheath transitions to a Child–Langmuir sheath. 3.7.5 Double Sheaths So far, only plasma boundaries where particles from the plasma are flowing toward a wall have been considered. At other locations in ion and Hall thrusters, such as in some cathode and accelerator structures, a situation may exist where two plasmas are in contact but at different potentials, and ion and electron currents flow between the plasmas in opposite directions. This situation is called a double sheath, or double layer, and is illustrated in Fig. 3-5. In this case, electrons flow from the zero-potential boundary on the left, and ions flow from the boundary at a potential s on the right. Since the particle velocities are relatively slow near the plasma boundaries before the sheath acceleration takes place, the local space-charge effects are significant and the local electric field is reduced at both boundaries. The gradient of the potential inside the double layer is therefore much higher than in the vacuum case where the potential varies linearly in between the boundaries. Referring to Fig. 3-5, assume that the boundary on the left is at zero potential and that the particles arrive at the sheath edge on both sides of the double layer with zero initial velocity. The potential difference between the surfaces accelerates the particles in the opposite direction across the double layer. The electron conservation of energy gives 12 m v e2 = e 2 e 1 / 2 ve= m , (3.7-43) φ 0 e− i φs x Double-Layer Solution Vacuum Solution Fig. 3-5. Schematic of the double-layer potential distribution.PDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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