Critical State Flux Penetration and Linear Microwave Vortex Response in   YBa_2Cu_3O_{7-x} Films
  The vortex contribution to the dc field (H) dependent microwave surface impedance Z_s = R_s+iX_s of YBa_2Cu_3O_{7-x} thin films was measured using suspended patterned resonators. Z_s(H) is shown to be a direct measure of the flux density B(H) enabling a very precise test of models of flux penetration. Three regimes of field-dependent behavior were observed: (1) Initial flux penetration occurs on very low field scales H_i(4.2K) 100Oe, (2) At moderate fields the flux penetration into the virgin state is in excellent agreement with calculations based upon the field-induced Bean critical state for thin film geometry, parametrized by a field scale H_s(4.2K) J_c*d 0.5T, (3) for very high fields H >>H_s, the flux density is uniform and the measurements enable direct determination of vortex parameters such as pinning force constants \alpha_p and vortex viscosity \eta. However hysteresis loops are in disagreement with the thin film Bean model, and instead are governed by the low field scale H_i, rather than by H_s. Geometric barriers are insufficient to account for the observed results. 
Balam A. Willemsen, J. S. Derov and S.Sridhar (Physics Department,   Northeastern University and Rome Laboratory, Hanscom AFB)