Cavity Analysis By Reflection A Treatise on Transient Response.pdf

Cavity Analysis By Re ectionA Treatise on Transient ResponseTom HaysLaboratory of Nuclear Studies, Cornell University, Ithaca, NY 14853May 1994 SRF940525-04 AbstractWe present a general method for determining the transientcavity response to an arbitrary driving signal and applyit to some simple situations. The general method is totransform the driving signal to the frequency domain, mul-tiply by a frequency dependent re ection coecient, andthen transform to the time domain. The stored energy inthe cavity can then be computed by conservation of en-ergy. Closed form expressions for the re ected signal andthe cavity stored energy are thus derived. This method candeal with any input signal with amplitude and/or frequencymodulation, but it is restricted to a cavity with constantQ0.1 IntroductionUp until recently most of the cavity testing done in theSRF lab has been using continuous wave (CW) or rectan-gular pulses of RF. The theory describing the cavity energyresponse to such excitations has been worked out [1] in suf-cient detail to yield the re ected power and the storedenergy in the cavity, but the phase of the re ected signalrelative to the drive signal was not considered.In the move to increase the power in peak power process-ing, it has become apparent that more needs to be under-stood about the cavity response to pulsed RF. To protectthe waveguide windows, for instance, we need to know thephase of the re ected signal relative to the incident signalso that one can avoid positioning the windows in regions ofhigh standing wave electric elds.It would also be useful to know the cavity response to anarbitrarily modulated driving signal since, for example, theshape of the 1.3GHz klystron pulse is more closely approx-imated by a smoothed trapezoid than a rectangular pulse.Other modulation approaches might be desired to help in-crease our ability to get high power into the test stand andthus into the cavity.In the following we will explain a procedure of derivinga gen