The Scaling of the Traveling-Wave RF Breakdown Limit

The accelerating gradient limit given by rf breakdown in normal conducting traveling-wave structures has been observed to variously depend on a number of parameters including surface electric field, pulse length, power flow and group velocity. In order to try to empirically determine a general scaling of the breakdown limit, data has been assembled from many types of structures over the frequency range of 3 to 30 GHz. To a compelling precision, the limit appears to be given by the quantity, $P\tau^{1/3}/C$ where P is the power flow through the structure, $\tau$ is the pulse length and C is the minimum circumference of the structure. The possible physical significance of this quantity is discussed.