Critical state analysis using continuous reading SQUID magnetometer

Abstract

The critical state in type II superconductors determines the maximum current the superconductor can carry without an energy dissipation. The critical state results from a competition between the Lorentz force acting on flux lines (quantized vortices), thermal agitation, pinning force, and repulsive interaction between flux lines. The pinning force localizes the flux lines on crystal lattice defects (dislocations, voids or impurities) and favors glassy state of flux lines, whereas the repulsive interaction between vortices results in a regular flux line lattice. Materials with a strong pinning are called hard superconductors. Such materials are relevant for power application of superconductors: solenoids for high magnetic fields or cables for large transport currents. Recently, high temperature superconductor (HTS) materials with the critical current density jc of the order of 100 GA m−2 at zero temperature and zero applied field were prepared. The second generation of HTS wires (2GHTSC) is constituted from RE-Ba2Cu3O6+x (YBCO) films. The critical current density is one or two orders higher than was achieved in Bi2Sr2CaCu2O8+x (BSCCO) round wires or MgB2, Nb-Ti, Nb3Sn, and Nb3Al wires. Unlike BSCCO wires whose performance is lowered by a flux flow at temperature above 35 K the YBCO wires operate even at liquid nitrogen temperature. Another important field of application of superconductors is superconducting electronics. Most of today’s superconducting electronics like superconducting quantum interferometer devices (SQUIDs), radiation detectors (SIS mixers), etc. are made of Nb, NbN, or HTS films. The flux lines trapped in the superconducting film may deteriorate sensor sensitivity as the moving flux lines generate noise (Wellstood et al., 1987). The above mentioned elucidates an interest in flux dynamics in thin films, particularly models to a disk and stripe. The critical state is affected by material properties, the wire or sensor geometry (shape), applied current, field, and temperature. Conventionally the critical state is studied (judged) using contact measurements (four probe resistive method) or magnetic measurements (local magnetization profile or magnetization loops). The latter method eliminates the need for electrical contacts and allows us to study the response of the critical state to an applied magnetic field. Frequency dependent magnetization loops reveal a flux creep or flux flow while nonlinear magnetization loops reveal surface or bulk pinning. In order to analyze these magnetic measurements we need appropriate models. In general, these model represent solution of 3D+t partial differential equations for a magnetic vector potential or flux density. 12