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172 Chapter 4 thruster performance parameters such as plasma profile and double-ion content, and to examine the details of different designs. Multi-dimensional modeling of the discharge chamber requires detailed models of discharge chamber walls and magnetic fields as well as of neutral propellant gas, ions, and primary and secondary plasma electrons [56–58]. Because the important physical mechanisms are different, each species (neutral gas, ions, and primary and secondary electrons) is modeled differently. For example, most neutral gas atoms travel in straight lines until they hit a wall or are ionized, so the neutral models can take advantage of simple straight-line trajectories to develop neutral density profiles. On the other hand, primary electron trajectories are dominated by rotation around magnetic field lines, and typically particle-tracking techniques are used to determine the density and spatial distributions. Ion and secondary electron behaviors are obtained using fluid equations due to the relatively collisional behavior of the species. Therefore, ion thruster discharge models that require computer codes that use both fluid and particle-tracking models are known as “hybrid” codes. Figure 4-40 shows a generic flow diagram for an ion thruster hybrid model [58]. From the thruster inputs (geometry), a mesh is generated inside the discharge chamber. A magnetic field solver determines the field everywhere in the chamber. Depending on the type of mesh used, the mesh generator may be iterated with the magnetic field solver to align the mesh points with the magnetic field lines. Aligning the magnetic field line simplifies the plasma diffusion calculations since the equations can be separated into parallel and perpendicular components, which can result in improved code accuracy for a sufficiently fine mesh. A neutral gas model, such as the “view-factor” model described below, determines the neutral density throughout the volume. The “ionization model” uses the magnetic field and electric field to compute the trajectories of primary electrons and their collisions with other plasma components (i.e., neutrals, ions, secondary electrons), which create ions and serve to dissipate the primary electron energy. The ionization model also determines the collisions due to secondary electrons. The ion optics model determines the transparency of the ion optics to neutrals and ions, as described in detail in Chapter 5. The ion diffusion model uses the magnetic field information and plasma properties to determine the motion of the plasma. The electron thermal model determines the energy balance for the electrons to find the distribution of temperatures of the secondary electron population. These processes are iterated until a convergent solution is found. 4.7.1 Neutral Atom Model Accurate knowledge of the neutral gas is required in multi-dimensional plasma codes to predict the beam profiles, details of discharge plasma behavior, andPDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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