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Ion Thruster Plasma Generators 159 presence of collisions. The required magnetic field to achieve this resonance is significant, and the pressure required to achieve sufficient collisions to start the discharge can be relatively high. These effects impact the plasma generator design and performance. The propagation of microwaves in a plasma can be understood by examining the dispersion relationship. The behavior of microwaves in the thruster plasma is described by Maxwell’s Equations: E = – B (4.6-1) t B=μ J+ E . (4.6-2) o o t The electromagnetic behavior is analyzed by linearizing these two equations using E = E0 + E1 B = B0 + B1 J = j0 + j1 , (4.6-3) (4.6-4) (4.6-5) where E0 , B0 , and j0 are the equilibrium values of the electric and magnetic fields and currents, and E1, B1 and j1 are the perturbed values in the electromagnetic fields and current. Linearizing Eqs. (4.6-1) and (4.6.2), and realizing that the equilibrium values have no curl or time dependence and that oμo=1/c2 inavacuum,gives c2 B1 = j1 + E1 . o t Taking the curl of Eq. (4.6-6) gives E1= ( E1)– 2E1=– B1 , t and the time derivative of Eq. (4.6-7) gives E1 = – B1 t (4.6-6) (4.6-7) (4.6-8)PDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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