New local field quantity describing the high gradient limit of accelerating structures

A new local field quantity is presented which gives the high gradient performance limit of accelerating structures due to vacuum rf breakdown. The new field quantity, a modified Poynting vector S₂, is derived from a model of the breakdown trigger in which field emission currents from potential breakdown sites cause local pulsed heating. The field quantity S₂ takes into account both active and reactive power flow on the structure surface. This new quantity has been evaluated for many X-band and 30 GHz rf tests, both traveling wave and standing wave, and the value of S₂ achieved in the experiments agrees well with analytical estimates.