Superconducting Cavities and Modulated RF

If a cavity has an infinite Qo, 81.5% of the energy contained in a pulse incident upon the cavity is transferred into the cavity by the end of the pulse if the cavity Qe is chosen so that the cavity time constant is 0.796 pulse width (Ta). As Qo decreases, the energy in the cavity at the end of the pulse decreases very slowly as long as Ta is much less than the unloaded cavity time constant, Tco. SC cavities with very high Qo enable us to obtain very high gradients with a low power cw source. At high gradients, however, we often do not attain the high Qo predicted by theory. Therefore, if we are interested in attaining maximum energy in the cavity, as is the case for RF processing and diagnostics, for a given available source energy there is no point in keeping the power on for longer than 0.1 Tco because the energy expended after 0.1 Tco is wasted. Therefore, to attain high fields at moderate Qo, pulsed operation is indicated. This note will derive the fields and energy stored and dissipated in the cavity when Qe is optimized for a given Ta. It will show how to use this data to measure Qo of an SC cavity as a function of field level, how to process the cavity with high RF fields, how to operate SC cavities in the pulsed mode to obtain higher efficiencies and gradients. Experimental results will also be reported.