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The 3D finite-element gun and collector modeling code, MICHELLE, has been under development at SAIC in collaboration with industrial partners and national laboratories. This development program has been designed to address the shortcomings of current beam optics simulation and modeling tools for vacuum electron devices. The program specifically targets problem classes including gridded-guns, sheet-beam guns, multi-beam devices, and anisotropic collectors, with a focus on improved physics models. The code includes both structured and unstructured grid systems for meshing flexibility. Advances have been made in the areas of accurate particle tracking through the mesh and beam emission methods, including new models for thermionic, temperature-limited, Child's law and secondary emission.
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Petillo et al. (2002) studied this question.