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.
Field enhancement factor and field emission from a hemi-ellipsoidal metallic needle
