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Ion Thruster Accelerator Grids 213 Substituting Eqs. (5.4-13) and (5.4-14) into Eq. (5.4-12) gives V = Ii n da + 1 . (5.4-15) 2 o v i d b 2 Since scalar potentials can be added, the sum of Eqs. (5.4-15) and (5.4-5) gives the total of the potential minimum in the accel grid aperture. V =V + V+da(Vbp Va) 1 2tatan 1 da e t d. (5.4-16) ma 2 d 2t aa e aa To calculate the backstreaming current as a function of grid voltage, Eq. (5.4-16) must be equated to Eq. (5.4-4) and solved for the current: Ibe e(Va+ V+(Vbp Va)C Vbp) Te I = (V V , (5.4-17) (5.4-18) In practice, the onset of backstreaming is determined by two techniques. One method is to monitor the increase in the screen power supply current as the magnitude of the accel grid voltage is decreased. Increases in the measured current are due to backstreaming electrons, and a 1% increase is defined as the minimum accel grid voltage to avoid backstreaming: the so-called backstreaming limit. For example, the power supply current from Eq. (5.4-17), normalized to the initial beam current, is plotted in Fig. 5-11 as a function of the accel grid voltage for the NSTAR ion optics [29] for the maximum power throttle point TH15 at the beginning of life (BOL). In this figure, the beam potential and electron temperature were assumed to be 12 V and 2 eV, respectively, consistent with measurements made on this thruster. The onset of backstreaming occurs at about –150 V on the accel grid, which is consistent with the data from tests of this engine [30,31]. A second method for determining the backstreaming limit is to monitor the ion production cost, which is the discharge power required to produce the ion beam current divided by the beam current. This is an effective method for use in i 2 mpbp) M Te where the geometric term C is given by C= da 1 2tatan 1 da e t d. 2 d 2t a a e aaPDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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