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Ion Thruster Accelerator Grids 209 example, which is due to the beam’s space charge. The actual value of this minimum potential determines the margin to backstreaming, which should be set well above the value at which excessive backstreaming occurs. Examining electron backstreaming in more detail shows that the minimum potential in the accel grid is determined by three factors: the electrostatic potential from the bias voltages applied to the different grids, the beamlet space charge in the accel grid aperture, and the required potential difference between the beam plasma and minimum voltage to reduce the backstreaming electron current to insignificant levels. Each of these factors can be evaluated analytically using simplifying approximations to help in understanding backstreaming physics. As stated above, the backstreaming electron current results from the tail of the beam Maxwellian electron distribution overcoming the potential barrier established in the accel grid aperture. The current of electrons backstreaming into the thruster plasma is just the beam plasma random electron flux times the Boltzman factor for the potential difference between the beam plasma and the minimum potential in the accel grid region [26]: Ii = nievi Aa , and the ion velocity through the system is vi=2eV V , (p bp) M (5.4-2) (5.4-3) 1 8kT 1/2 (Vbp Vm) ne e e Te Aa , (5.4-1) Ieb = where Ieb is the electron backstreaming current, Vbp is the beam plasma 4 m potential, Vm is the minimum potential in the grid aperture, and Aa is the beamlet area in the grid aperture. The current of ions in the beamlet flowing through the grid aperture is where Vp is the plasma generator plasma potential at the sheath edge. Combining Eqs. (5.4-1) through (5.4-3), the minimum potential is 2I m Vp Vbp Vm = Vbp + Te ln eb . (5.4-4) IM T iePDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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