K.V. Bhagwat

Magnetisation hysteresis and critical current density

Abstract The hysteresis in magnetisation is extensively used to infer the critical current density of high T c superconductors. We use calculated magnetisation curves, obtained analytically for two particular forms of J c ( H ), to examine the validity of the method currently used. We show that this method is valid only at large fields, and that the region of validity depends on the sample size. We compare our results with existing data. We also examine the case of a general form of J c ( H ), and present a method for obtaining a zero field J c from magnetisation curves.

Magnetization curves for a hard superconductor sample in the shape of a general ellipsoid

The critical state model is solved to obtain the virgin and hysteresis magnetization curves for a zero field cooled hard type-II superconductor sample in the shape of general ellipsoid, with the applied magnetic field along one of its principal axes.

Flux penetration in spheroid samples-critical state model with field-dependent critical current density

We present the results of a calculation, within the framework of Beans critical state model, of the magnetization curves for a hard superconductor sample in the shape of a spheroid. The formalism allows a general field dependence of the critical current density Jc. We present numerical results for Jc decaying exponentially with field. Some main experimental features are reproduced and detailed tests can be made with experiments on thin films and platelet-shaped single crystals.

Flux penetration in thin elliptic superconducting cylinders subjected to transverse magnetic fields

We solve for the flux penetration in thin superconducting strips of elliptic cross-section subjected to an external magnetic field. We consider general solutions of current distributions J(r) that allow B to vanish identically within the flux front. From those solutions that violate the requirement J(r) ≤ J c at some r, we reproduce the line current densities that match results being currently presented in the literature for thin strips. We derive new solutions for line current densities with the constraint that the corresponding J(r) macroscopically averages to J c . We present results for the M-H curve, and the magnetic-field distributions. These are then compared with earlier results when J(r) ≤ J c is never transgressed.

Hysteretic loss in hard superconductor samples with non-zero demagnetization factor

Abstract Based on our recent exact solution of Beans critical state model for sample shapes having non-zero demagnetization factor, we present a calculation of AC loss and the related AC susceptibility X″ for samples in the shape of a sphere and a cylinder with its axis perpendicular to the applied field.

Flux penetration in thin superconductor films with field dependent critical current density

The problem of flux penetration in superconductor samples in the form of thin elliptic cylinders and circular discs is considered. When critical current density depends on the local field, the latter satisfies a non-linear integral equation. We obtain a numerical solution for the integral equation and thereby detemine the local field distribution. We present results for the virgin magnetisation and the hysteresis curves for typical parameter values for the exponential model as well as the Kims model for the critical current density.

Mutually perpendicular magnetic fields parallel to a slab a test case for the critical state model

We discuss the response of a hard superconductor sample in the shape of a slab when mutually perpendicular magnetic fields are sequentially applied parallel to its surface. The field profile inside the sample no longer lies in a plane. We present a procedure for calculating the field profiles and the magnetization, and present numerical results for one specific sequence of applying these fields.

Critical state model for general cylinders: unifying scheme for parallel and perpendicular geometries

The critical state model (CSM) is examined for infinite cylindrical samples of a hard type-II superconductor subjected to a magnetic field in an arbitrary direction. The solution is based on a generalization of the result for the surface current density on a cylindrical surface that produces uniform interior magnetic field along an arbitrary direction. In contrast to the case of parallel or perpendicular geometry, in the present case, the direction of shielding current density is not in general perpendicular to the direction of the applied magnetic field. The general result pertaining to the current density has enabled us to get an unified scheme for the treatment of parallel and perpendicular geometries for infinite cylinders of arbitrary cross-section. The numerical scheme followed here is very similar to that followed in Refs. [Phys. Rev. B 65 (2002) 024518; J. Phys. 57 (2001) 763]. Flux contours in the plane transverse to the cylinder-axis are obtained and also hysteresis loops for both the parallel and perpendicular components of magnetization are presented for a typical orientation of the applied field. The variation of the orientations of components of magnetization with that of the applied field is studied.

Metastability and stable vortex state in weakly pinned type-II superconductors

Abstract The peak effect in superconductors like NbSe 2 , V 3 Si, is characterized by the history dependence of the critical current density J c . A phenomenological model was proposed and a numerical solution obtained to account for the history dependence in J c near peak effect. We present an exact solution of the model. Recently, history dependence in J c is reported also in the low field region in V 3 Si system. We present an experimental study, through the measurement of minor magnetization curves, of the history effects across the entire field range encompassing low field and high field order–disorder transitions. We compare the experimental observations with the results of our model calculations.

Time relaxation of magnetization in type-II superconductors

We assume that currents induced by isothermal changes of magnetic field decay logarithmically with time. Incorporating this time dependence into the critical state model, we obtain logarithmic relaxation rate of magnetization as a function of field for the case of an infinite cylinder. We compare these calculations with our earlier calculations on infinite slab geometry.