Abstract. We discuss the microwave energy losses in superconductors in the critical state. The field-induced variations of the surface resistance are determined, in the framework of the Coffey and Clem model, by taking into account the distribution of the vortex magnetic field inside the sample. It is shown that the effects of the critical state cannot generally be disregarded to account for the experimental data. Results obtained in bulk niobium at low temperatures are quantitatively justified.PACS. 74.25.Ha Magnetic properties -74.25.Nf Response to electromagnetic fields (nuclear magnetic resonance, surface impedance, etc.) -74

a b s t r a c tThe magnetic-field-induced variations of the microwave surface resistance have been investigated in a heavily neutron-irradiated MgB 2 sample, in which the irradiation has caused the merging of the two gaps into a single value. The experimental results have been analyzed in the framework of the Coffey and Clem model. By fitting the experimental data, we have determined the field dependence of the depinning frequency, x 0 , at different values of the temperature. Although the pinning is not particularly effective, the value of x 0 obtained at low temperatures is considerably higher than that observed in conventional low-temperature superconductors.

Abstract. We report on the microwave surface resistance of two polycrystalline Mg 11 B2 samples; one consists of pristine material, the other has been irradiated at very high neutron fluence. It has already been reported that in the strongly irradiated sample the two gaps merge into a single value. The mw surface resistance has been measured in the linear regime as a function of the temperature and the DC magnetic field, at increasing and decreasing fields. The results obtained in the strongly irradiated sample are quite well justified in the framework of a generalized Coffey and Clem model, in which we take into account the field distribution inside the sample due to the critical state. The results obtained in the pristine sample show several anomalies, especially at low temperatures, which cannot be justified in the framework of standard models for the fluxon dynamics. Only at temperatures near Tc and for magnetic fields greater than 0.5Hc2(T ) the experimental data can quantitatively be accounted for by the Coffey and Clem model, provided that the upper-critical-field anisotropy is taken into due account. PACS