Magnetic field dependence of RF surface impedance

The surface impedance, Z_s, is calculated for type-II superconductors subjected to a static magnetic field and small-amplitude microwave radiation. A complex penetration depth is calculated by using a model of vortex dynamics including a linear pinning restoring force and a viscous drag force. The static magnetic field dependence of the surface resistance, R_s and the surface reactance, X_s, is found by examining the dependence of the complex penetration depth on the length scales for low-field penetration, pinning penetration, and flux-flow penetration. In turn, from R_s, the static magnetic field dependence of the rate of energy dissipation is found