Abstract
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.
Highlights
Dark current, or the unwanted emission of electrons from the surface of both photocathodes and metal surfaces within an rf photoinjector as a consequence of thermalfield emission, has long been observed in the development of free-electron lasers [1,2]and accelerators
Though much is known about the relationship between dark current, local heating of asperities, field enhancement, and their failure mechanisms, good theoretical models are hampered by a lack of emission models that are correct in the parameter regime of both high fields and temperatures, flexible field enhancement models, and the relationship of temperature and field enhancement to resistive and Nottingham heating for conditions that occur
VI) involve time scales so rapid that little is compromised by assuming ‘‘static’’ conditions in the emission and heating equations to be developed. Such would not be the case if the focus were on surface melting and cone formation, as in other studies [36,37,38], but it is so if the focus is on the applicability of the emission equations and their relationship to Nottingham heating at the emission sites plus methods to estimate field enhancement effects from structures whose relevant dimensions can be orders of magnitude removed from the dimensions of melted regions that follow in the wake of a breakdown event
Summary
The unwanted emission of electrons from the surface of both photocathodes and metal surfaces within an rf photoinjector as a consequence of thermalfield emission, has long been observed (generally, with dismay) in the development of free-electron lasers [1,2]. (see the Appendices) coupled with models of field enhancement that are numerically inferred Such approaches are appropriate to the phases of dark current modeling [9,15,16,20,21]) prior to large temperature excursions, 1098-4402=08=11(8)=081001(17). Nordheim equation are needed; (ii) a model of field enhancement that evolves as conditions evolve is required; and (iii) models describing ‘‘run-away’’ mechanisms leading to failure calculate resistive and Nottingham heating contributions correctly. To meet these demands, a framework that couples the disparate phenomena and which favors analytical rather than numerical methods to address thermal-field emission from evolving protrusions subject to heating mechanisms related to electron emission, in particular, is developed
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