Studies of enhanced field emission relevant to high field superconducting radio frequency devices

Surface roughness represents the measure of the irregularities on the surface contributing to the local field enhancement. The traditional Fowler-Nordheim equation established for perfectly planar surfaces is not suitable for describing emission from rough surfaces. Instead, it is more appropriate to use the equation that accounts for the field enhancement factor describing the effect of the surface morphology. In superconducting radio frequency cavities field emission may occur in the irises and the tips on the cavity surface may act as an emitter leading to the high electric field. For this study, calculations for hemispherical, cylindrical, and conical tips have been performed by using a multiphysics software package COMSOL. The focus was put on the dependence of the field enhancement factor on the shape and the radius of the protrusions. The electric field strength and the current density increase with increasing the root mean square average of the profile heights due to field enhancement at the cavity irises. The lowest value of the electric field has been achieved for the hemisphere. The calculated values for the field enhancement factors are consistent with the data from the literature, in which case the protrusion may represent a small local bump on the surface of a superconducting cavity. Based on the fit of the results, presented here, the relation between the enhancement factor and the radius has been suggested. The accurate estimation of the field emission may play a crucial role in the design of accelerators and other technological applications with requirements of very high precision.