Addressing Physics in the Field Marshal EnvironmentOne of the phase I tasks was to examine the theoretical formulations required to simulate the key physical processes in the context of high-voltage radiation sources. These include: (a) Electron emission from cathode surfaces, (b) Scattering of high energy electrons from metals and insulating materials, (c) High-voltage electrical breakdown on insulator surfaces, (d) Intense heat fluxes, and (e) X-ray generation and related effects. Details for each of the above physical processes, the physical models and requisite numerical implementation aspects are discussed in the project paper. Essentially, the physics-based analysis provides quantitative equations for the charge creation magnitude, its rate, expressions for subsequent charge transport, and self-consistent evaluations of the overall system currents in a dynamical fashion. The generation/creation processes (both primary, secondary and tertiary), as well as the transport mechanisms are dictated by the local electromagnetic fields and temperature. Large and uncontrolled rates of charge generation lead to breakdown. For self-consistency, both the electromagnetic fields and temperatures have to be computed. The complete mathematical model for electrical conduction and breakdown needs to include: (a) A numerical scheme for charge transport including generation, recombination, and charge fluxes. This can either be based on a continuum fluid model, or the particle-in-cell (PIC) approach. (b) An electromagnetic solver that continually updates the internal electric fields that drive the charges. The Poisson equation can be used under static and quasi-static conditions when the influence of time-dependent magnetic fields can be ignored. For modeling ultra-short time scales or rapid time-variations, the full Maxwell equations would apply. A coupled scheme using the Monte Carlo transport approach and the Maxwell equations was developed by one of us several years ago with details given in the appendix. This amounts to an electromagnetic-particle-in-cell (EM-PIC) simulation approach. Essentially two separate schemes, the fluid model and the Monte Carlo approach, can be used for simulations of charge transport. The Monte Carlo technique is very accurate and yields detailed information pertaining to the transport coefficients, ionization parameters, energy and angular distributions, and microscopic currents. However, it is computationally intensive and yields somewhat "noisy" data due to finite statistical sampling. More importantly, its application to breakdown dynamics is limited to time scales over which the particle population does not exceed the array upper bounds of the numerical software. By contrast, fluid models yield smooth data, and are computationally manageable. Such fluid schemes have been implemented by our group. They do not suffer from problems associated with rapid increases in density during the breakdown phase. Ideally, therefore, it is best to use the MC technique only for short time scales (e.g., to analyze the breakdown initiation), or over small regions (e.g., close to the insulator interface). However, an optimal choice would be a hybrid scheme involving the MC for microscopic details and calculation of dynamic transport coefficients that feeds into an overall fluid transport model. Electromagnetic solvers would yield the self-consistent electromagnetic fields for each level of complexity. References
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