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176 Chapter 4 4.7.2 Primary Electron Motion and Ionization Model Particle simulation methods have been applied to the modeling of primary electron motion in ion thruster discharge chambers [58,61,62]. In particle simulations, the primary electrons are represented by particles, or macro- particles that represent a large number of primary electrons, that move in discrete time steps based on their initial conditions, applied boundary conditions, and internal electric and magnetic fields. Monte Carlo techniques are used to introduce the particles from the cathode exit into the computational domain at randomized velocities indicative of the cathode emission characteristics. During each time step, the local fields are recalculated based on the new particle position and velocity, and the particles move based on the local forces. Monte Carlo techniques typically are used to handle collisions between the particles. This procedure is repeated through many time steps until the particle is lost, after which the next particle is introduced at a unique initial velocity condition. The primary electron motion between collisions is treated as the motion of a charged particle in the presence of an electromagnetic field, which is described by the Lorentz equation m v =q(E+v B). (4.7-1) t Wirz and Katz [58] developed an improved Boris-type particle-pushing algorithm [63] in which the motion of the particles can be described with an implicit particle-pushing algorithm, where the Lorentz forces on the particle are decomposed into electric and magnetic forces. The primary’s kinetic energy is assumed to be unchanged in an elastic collision, and the particle-scattering angle is estimated by a 3-D probabilistic hard sphere scattering model [58]. In an inelastic collision, some fraction of the primary energy goes into excitation or ionization of the neutrals. Additional energy loss paths exist, as previously discussed, such as coulomb collision thermalization and anomalous processes associated with instabilities. A typical primary trajectory in the NSTAR thruster from the Wirz code [58] is shown in Fig. 4-43, where the primaries are well confined by the strong axial magnetic field component in this thruster, and collisional effects eventually scatter the primary into the cusp loss cone. Arakawa and Yamada’s model for primary electron motion is derived from the Euler–Lagrange equations for the Lagrangian of a charge particle in a magnetic field [61]. However, this technique is computationally more intensive and does not improve the results in comparison with the improved Boris algorithm.PDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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