I. Introduction
Thermal breakdown in SRF cavities is one of the major factors that limit the maximum achievable accelerating field. As has been well verified both theoretically and experimentally in steady state, the thermal stability of SRF cavities strongly depends on the operating frequencies, the BCS surface resistances, the cooling schemes, the material properties of niobium such as RRR (residual resistivity ratio) and the presence of material defects on the surface, etc. In many recently initiated or proposed projects for high intensity proton and electron accelerations, the SRF technology has been selected for the main part of the linear accelerator (linac), which uses elliptical shape cavities in a pulsed operation.