Statistical model for field emitter activation on metallic surfaces used in high-gradient accelerating structures

Both super- and normal-conducting high-gradient linear accelerators are limited by enhanced field emission (EFE) in the accelerating structures, e.g. due to power loss or ignition of discharges. We discuss the dependence of the number density of typical emitters, i.e. particulates and surface defects, on the electric field level at which they are activated for naturally oxidized metallic surfaces. This activation is explained by the transition of a metal-insulator interface into geometric features that enhance the EFE process. A statistical model is successfully compared to systematic studies of niobium and copper relevant for recent and future linear accelerators. Our results show that the achievable surface quality of Nb might be sufficient for the suppression of EFE in the superconducting accelerating structures for the actual European XFEL but not for the planned International Linear Collider. Moreover, some effort will be required to reduce EFE and thus the breakdown rate of the normal conducting Cu structures for the Compact Linear Collider.