| Summary: | Analytically tractable models of thermal-field emission, field enhancement, and heating mechanisms (Nottingham and resistive) are developed and combined to make estimates of the fields and temperatures that accompany the development and growth of asperities. The relation of asperity dimensions to dark current is discussed in two experimentally motivated examples. The hypothetical relation of microscopic sources of dark current and heating to breakdown is discussed in the context of Nottingham and resistive heating. The latter are estimated using a general thermal-field methodology. A point-charge model is used to find field enhancement factors. Last, a thermal model is used to estimate the temperature dependence of the resistivity and thermal conductivity. Together, these models suggest that conditions can arise in which the temperature at the apex of an asperity can experience growth and contribute to melting or fracture (or both), and that Nottingham heating generally dominates the resistive heating term.
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