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116 Chapter 4 The dipole strength per unit length is M = BrVm , (4.3-24) 4 w where Br is the residual magnetic field of the magnet, Vm is the volume of the magnet, and w is the width of the magnet. For example, for two rows of magnets that have a residual magnetic field of 10,000 gauss, a volume per width of 0.6 cm2, and a separation of 10 cm, the maximum transverse magnetic field is 24.8 gauss and occurs at a distance of 2.9 cm above the boundary. As an example of the ion loss rate to the anode, the fraction of the Bohm current to the anode ( Iia / IBohm ) is plotted in Fig. 4-14 as a function of the magnetic field at the saddle point for the NSTAR ion thruster [13]. At zero transverse magnetic field, the ion flux to the anode is the Bohm current. As the transverse field increases and reduces the electron mobility, the ions are slowed and the current loss decreases. In the NSTAR design, the last closed magnetic contour is about 20 gauss, and so roughly half of the ions initially headed radially toward the anode are lost. For closed magnetic field contours of at least about 50 gauss, the ion loss to the anode is reduced by nearly a factor of 10 compared to the unmagnetized Bohm current. This can make a significant difference in the efficiency of the plasma generator and the amount of discharge power required to produce the beam ions. Even though the ions are unmagnetized in these thrusters, it is clear that ambipolar effects make the ring- cusp magnetic fields effective in reducing the ion loss to the walls. 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 Fig. 4-14. Fraction of the Bohm current density to the anode wall as a function of the transverse magnetic field strength for the NSTAR ion thruster [13]. 0 10 20 30 40 50 60 Peak Closed Transverse Magnetic Field (gauss) Fraction of Bohm Current (fc)PDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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