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156 Chapter 4 B[gauss] = 104 μo N I, (4.5-18) where μ0 is the permeability of free space, equal to 4 10–7 henries/m; N is the number of turns per meter; and I is the coil current in amperes. For this rf thruster example, a magnetic field of 12.6 G is produced. While this sounds like a low field, it is an axial field induced in the majority of the interior of the thruster depending on the plasma skin depth, which is large in these low density plasmas. The reduction in the ion velocity flowing radially to the wall for the situation of a transverse magnetic field and ambipolar flows was analyzed in Section 4.3.5. Figure 4-33 shows the reduction in the radial Bohm current ( fc ) from evaluating Eq. (4.3-15) for the condition when the diffusion length is now essentially the thruster radius. Fields on the order of 10 G throughout the thruster volume can reduce the ion and electron loss to the discharge chamber wall by over a factor of two. While the rf magnetic field strength decreases with radius due to the finite length of the antenna coil (solenoid end effects), the field strength near the axis is still sufficient to reduce the ion loss rate [51]. The discharge loss calculated by the 0-D model for our 20-cm rf thruster example is shown in Fig. 4-34 as a function of rf magnetic field induced in the plasma. The discharge loss is reduced from the case of no magnetic confinement (B=0) of 450 eV/ion at 90% mass utilization to a value of 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 Fig. 4-33. Ion confinement factor (the fraction of the Bohm current to the wall) as a function of the induced magnetic field in the discharge chamber volume. 0 5 10 15 20 25 30 Axial Magnetic Field (gauss) Fraction of Bohm CurrentPDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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