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Ion Thruster Accelerator Grids 215 Equations (5.4-17) and (5.4-18) show that the electron backstreaming is a function of the accel grid hole diameter. Increases in the accel hole diameter will reduce the penetration of the applied grid bias voltage to the center of the aperture and reduce the minimum potential on axis. This increases either the backstreaming current at a given voltage or the backstreaming limit at a given current. The effect of accel grid hole enlargement due to grid wear is illustrated in Fig. 5-13, where the grid voltage at which backstreaming started is plotted versus accel grid hole diameter for the NSTAR TH15 case measured during the extended life test (ELT) [31]. Larger grid-hole diameters required more negative biasing of the accel grid to avoid the onset of backstreaming. Figure 5-13 also shows an interesting effect in that the shape of the grid hole is important. Early in life, the grid aperture diameter eroded due to sputtering, and the barrel diameter was adequately described by the minimum hole diameter observed optically during running of the test. However, as the test progressed, the erosion of the upstream aperture edge essentially stopped and the aperture was observed to be chamfered on the downstream portion. An effective grid diameter had to be calculated to take into account the non-uniform hole erosion in determining the backstreaming onset, shown on the right-hand side of Fig. 5-13. While the above analytical model accounts for grid diameter and thickness, additional terms would have to be added to account for this conical erosion shape. This situation is best handled by 2-D models that both determine the time-dependent shape of the grid hole and calculate the potential on axis appropriately. −140 −160 −180 −200 −220 −240 −260 Fig. 5-13. Accel grid voltage at which electron backstreaming occurs in the NSTAR thruster at TH15 power level versus the effective accel grid aperture diameter. Minimum Hole Chamfering Hole ELT TH15 Diameter 1.2 1.3 1.4 Effective Accel Grid Hole Diameter (mm) 1.5 1.6 1.7 Electron Backstreaming Voltage (V)PDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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