Section 7.8 · Home exercises · 1 of 4
Home exercise 7.8.1: Ring-down of a cavity
Ring-down of a cavity
#A cavity resonating at is driven, then the source is switched off. A fast detector shows that the field envelope falls to half its value in .
- Find the loaded of the cavity.
- Find the time constant of the stored energy and the number of periods it lasts.
- Find the 3-dB bandwidth.
- How long does the energy take to fall by ?
The energy decays as , so the field decays as , Eq. (7.8.19). One measured time of the field envelope gives , and gives everything else.
at :
, which is periods.
.
in energy is a factor : .
The field halves in , so the energy quarters in : . of energy is a field ratio , that is halvings of the field, and .
Ring-down is the time-domain twin of the bandwidth measurement, . It measures the loaded , because the energy also leaves through the couplings. For a of , as in superconducting cavities, the bandwidth is far too narrow to sweep, and ring-down is the method of choice.