Cahill, A.D. Dolgashev, V.A. Rosenzweig, J.B. Tantawi, S.G. Weathersby, S.P. JACoW Geneva, Switzerland 978-3-95450-182-3 10.18429/JACoW-IPAC2017-THPIK125 English 4395-4398 THPIK125 Contribution to a conference proceedings 2017 2017-05 http://dx.doi.org/10.18429/JACoW-IPAC2017-THPIK125 http://jacow.org/ipac2017/papers/thpik125.pdf RF breakdown is one of the major factors limiting the operating accelerating gradient in rf particle accelerators. We conjecture that the breakdown rate is linked to the movements of crystal defects induced by periodic mechanical stress. Pulsed surface heating possibly creates a major part of this stress. By decreasing crystal mobility and increasing yield strength we hope to reduce the breakdown rate for the same accelerating gradient. We can achieve these properties by cooling a copper accelerating cavity to cryogenic temperatures. We tested an 11.4 GHz cryogenic copper accelerating cavity at high power and observed that the rf and dark current signals are consistent with Q₀ changing during rf pulses. To take this change in Q₀ into account, we created a non-linear circuit model in which the Q₀ is allowed to vary inside the pulse. We used this model to process the data obtained from the high power test of the cryogenic accelerating structure. We present the results of measurements with low rf breakdown rates for surface electric fields near 500 MV/m for a shaped rf pulse with 150 ns of flat gradient.