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336 Chapter 7 generator case discussed in Chapter 4. The anode sheath polarity and magnitude depend on the local magnetic field strength and direction, which affects the axial electron mobility, and on the presence of any insulating layers on the anode that affects the particle balance [14–16]. Maintaining the local plasma near the anode close to the anode potential is important in applying the maximum amount of the discharge voltage across the plasma for the acceleration of ions. In addition, the magnetic field profile near the thruster exit strongly affects both the ability to achieve closed electron drifts in the azimuthal direction [8] and the focusing of the ions in the axial direction as they are accelerated by the electric field [9]. Optimal magnetic field design in the exit region reduces the ion bombardment of the walls and improves the ion trajectories leaving the thruster [17]. Additional information on the thruster operation can be obtained by examining the ionization criteria. Properly designed Hall thrusters tend to ionize essentially all of the propellant gas incident on the plasma from the anode, so that nnne ive AeL nnvnAe. (7.2-18) Using Eq. (7.2-6) for the Hall current, Eq. (7.2-18) becomes L= vnVdw . (7.2-19) IH ive B The length of the ionization region naturally must increase with neutral velocity and can decrease with the ionization reaction rate coefficient, as seen in Eq. (7.2-16). This is important in order to achieve high mass utilization when propellants with a lower mass than xenon, such as krypton, are used to increase the Isp of the thruster [18,19]. Studies of optimized Hall thrusters of different sizes [20–25] have resulted in some scaling laws. A detailed comparison of the scaling laws in the literature, with experimental results from the family of empirically optimized stationary plasma thrusters (SPTs), was performed by Daren, et al. [20]. Assuming that the thruster channel inner-to-outer diameter ratio and the ionization mean-free path-to-plasma length ratio are constants, they foundPDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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