Modeling and Simulation of Electrical Breakdown in DC for Dielectric-Loaded Systems with Non-Orthogonal Boundaries Including the Effects of Space-Charge and Gaseous Collisions

Improved modeling of angled-dielectric insulation in high-voltage systems is described for use in particle-in-cell (PIC) simulations. Treatment of non-orthogonal boundaries is a significant challenge in modeling angled-dielectric flashover, and conditions on boundaries are developed to maintain uniform truncation error in discretized space across the dielectric angles studied. Extensive effort was expended in isolating particular operating regimes to illustrate fundamental phenomenological surface effects that drive the discharges studied herein; consequently, this document focuses on the phenomenology of two specific dielectric angles at 6.12° for multiplicative breakdown (the so-called single-surface multipactor) and 22.9° for a non-multiplicative discharge that evolves into a dark current at steady state.;Phenomenological results for simulations in vacuum through "ultra-low pressures" on the order of a few hundred mTorr are presented. A multipactor front forms via net emission of electrons from impact on the dielectric surface, where emission leads to saturated field conditions in the wake of the front, producing a well-defined forward-peaked wave. A treatment of the gain and saturation characteristics is presented, isolating the surface electric fields as the driving contributor to both metrics. Physical models include oftenneglected effects such as space-charge, dielectric-surface charging, and particle distributions in energy and space. For the discharges treated in this study, breakdown voltages of the typical Paschen form are not applicable, since multiplicative conditions are driven primarily by surface effects.;Phenomenological results are also presented for simulations at low pressure (~ 1Torr), which is shown to be a transitional limit where volume effects become appreciable compared to surface effects. A coupling between space charge and surface charge is shown to lead to oscillatory effects in otherwise DC discharges. Surface multipactor leads to increased ionization and space charge, and the ensuing space-charge momentum alters what would have been a steady-state saturation as in the case of vacuum-like discharges. Models for diffusive outgassed species are developed and implemented, extending the capabilities of the PIC suite.;The overarching theme of this study is to communicate the dependence of multiplicative discharges dominated by surface effects on near-surface electric field conditions. It is shown through various examples from vacuum through low pressures, and in diffusive gases, that single-surface multipactor conditions can be expressed solely in terms of the dielectric surface field angles. This treatment lays the foundation for a novel extension of RF breakdown susceptibility theory [1] to the DC regime, grounding breakdown susceptibility to the well-established fundamentals on secondary emission [2, 3]. This theory shows that breakdown characteristics can be modeled in an a-priori framework, hence the lack of a Paschen-type curve.;Finally, the effect of the seed source on discharge characteristics is also studied. A comparison between a constant-waveform source, a Fowler-Nordheim source, and an application of a modified source based on theoretical treatment from [4] are presented, showing that the seed is a necessary but insufficient condition for surface flashover, where the dominant contributor is the configuration of the surface fields downstream of the seed source. While the seed can influence upstream conditions to alter the injected current, the gain characteristics of the downstream region are still well described by the framework developed in the remainder of this document.