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332 Chapter 7 magnetic field region causes the axial electric field also to be maximized near the exit plane, as illustrated in Fig. 7-6. Since the neutral gas is injected from the anode region and the mass utilization is very high (nearly every neutral is ionized before reaching the channel exit), it is common to describe an “ionization region” that is located upstream of the electric field peak. Of course, the ions are accelerated directly by the electric field that peaks near the exit plane, which is sometimes called the “acceleration region.” The characteristic scaling length L then spans these regions and is a significant fraction of the total channel depth. The ionization and acceleration regions overlap, which leads to dispersion in the ion velocity and some angular divergence in the resultant beam. This is in contrast to ion thrusters, which have a distinct ionization region in the plasma chamber and a finite acceleration region in the grids that produces nearly monoenergetic beams with low angular divergence determined by the optics and curvature of the grids. In the crossed electric and magnetic field region of the channel, the electrons move in the azimuthal direction due to the E B force with a velocity given by Eq. (3.3-16). The magnitude of the azimuthal electron velocity was found in Chapter 3 to be vE=E B Er [m/s]. (7.2-4) B2 Bz The current in the azimuthal direction, called the Hall current, is then the integral of the electron plasma density and this velocity over the characteristic thickness L [3,4]: 12 10 8 6 4 2 0 Fig. 7-6. Typical Hall thruster radial magnetic field and axial electric field along the channel length. Br Ez Exit Plane 0 10 20 30 40 50 z (mm) Arbitrary UnitsPDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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