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138 Chapter 4 leads to a lower impedance discharge and a lower discharge voltage. These two effects will be shown next to cause a reduction in the plasma potential, and thrusters designed for low discharge loss with a minimum plasma potential at the nominal operating point can encounter negative plasma potentials and discharge instability during recycling. The time-dependent behavior of the pressure in the discharge chamber from the high-voltage-off event can be calculated using molecular dynamics, and the subsequent time-dependent plasma potential for stability can be evaluated using the 0-D model. The time-dependent pressure [42] in the thruster is given by V dP = Qin C P , (4.3-65) dt where V is the discharge chamber volume, P is the pressure in the thruster discharge chamber, C is the conductance of the grids, and P is the pressure drop across the grids. The initial pressure just before the start of the recycle, when the thruster is operating normally, is found from Eq. (4.3-35) and the conversion of neutral density to pressure in Eq. (2.7-2): Po =4.1 10–25 ToQin(1– m). (4.3-66) voeAgTa c With the high voltage off, the ions and neutrals flow to the grid region, where a small fraction exits through the accel aperture to escape, and the majority strike the upstream side of the grids or the grid aperture barrel wall and flow back into the thruster. Since the grid conductance is defined as the flow divided by the pressure drop [42], the final pressure after steady state has been achieved is Pf =(1 Ta)Qin , (4.3-67) C where C is the conductance of the grids and the downstream pressure from the grids has been neglected as small. The conductance of the grids can be estimated from the molecular conductance of a thin aperture [42] times the Clausing factor for the finite thickness grids. The conductance is then T 1/2 C=3.64 Ma TaAg c [liters/s], (4.3-68) where Ma is the ion mass in atomic mass units (AMU), and the effective open area of the grids is the optical transparency of the accel grid, Ta , times the gridPDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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