Transient heat conduction analysis in superconducting cavities

A vector algorithm has been developed for solving two-dimensional nonlinear transient diffusion equations. An analytical solution of transient heat conduction for the step point heat source is also obtained. The calculations show that the steady-state or thermal breakdown for submillimeter-size defects can be reached in about 1 ms. The quench time decreases rapidly with increasing RF field. Smaller defects grow more rapidly than larger ones. The quench may even occur within several microseconds if the cavity field is nearly doubled, as in the high-power processing technique. A sub-micron size defect can reach a very high temperature in a nanosecond; then, the dynamic effect of the atomic diffusion may also be considered. The calculation is compared with experimental data.<>