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Ion Thruster Plasma Generators 109 P = 1 – e x p – n o L = 1 – e x p ( n o V / A p ) . ( 4 . 3 - 5 ) By providing strong magnetic field strengths at the cusp to minimize the primary loss area, the probability of a primary electron being lost directly to the anode can be made very small. Similarly, ion thrusters with large volumes and/or operated at higher internal gas densities will cause the primary electrons to undergo collisions and thermalization prior to being lost directly to the anode. Minimizing the energy loss associated with primaries being lost before making a collision in this way serves to maximize the efficiency of the thruster. An example of the probability of a primary electron making a collision before finding a cusp is shown in Fig. 4-12 for the case of the NEXIS thruster designed with either 4 or 6 cusps [20]. For the design with 6 cusps, it is necessary to have cusp-field strengths approaching 2000 G at the surface of the anode in order to minimize primary loss. Designs with a smaller number of ring cusps, corresponding to a smaller primary anode collection area from Eq. (4.3-3), require less magnetic field strength to achieve the same benefit. However, it will be shown later that the number of cusps affects efficiency and uniformity, and that maximizing the probability of a primary making a collision before being lost is only one of the trade-offs in designing an ion thruster. 1.20 1.00 0.80 0.60 0.40 0.20 0.00 4 Cusps 6 Cusps 0 500 1000 1500 2000 2500 3000 Cusp Magnetic Field (gauss) Fig. 4-12. Probability of primary electrons making a collision before being lost to the anode as a function of the cusp magnetic field strength for the NEXIS thruster design [20]. Probability of CollisionPDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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