Magnetic field dependence of rf surface impedance

In this paper the surface impedance, Zs, 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 Rs and surface reactance Xs 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 Rs, the static magnetic field dependence of the rate of energy dissipation is found