#### Event Title

Electromagnetic Hysteretic Response Calculation for Superconductors in Demagnetizing Geometries

#### Location

Snowmass Village, CO

#### Start Date

1-1-1995 12:00 AM

#### Description

The electromagnetic response of the new high Tc superconductors is similar to that of eddy currents in normal metals, except that in the superconductor induced currents are established nonlinearly at a single value known as the critical current density, J c . These materials are extreme Type II superconductors where, in the presence of an external magnetic field and/or a transport current, magnetic flux exists in the material in the form of flux lines distributed on a lattice [1]. Individual flux lines become pinned at microstructural inhomogeneities such that only under a sufficient force caused by locally high current flows will they become depinned and flow throughout the material. The value of the local current density that causes depinning is the microscopic critical current density and is directly proportional to the pinning force strength. A phenomenological approach known as the critical state model [2,3] describes the pinned flux line distribution within the material quasistatically, assuming the equilibrium distribution is achieved at each value of the externally applied field on a short time scale compared to experimental times. Operationally, whenever an external field is increased, flux lines enter the material from the surface and penetrate to a flux front boundary, whose position is determined by the value of the external field at the sample surface. An important nondestructive evaluation (NDE) task to aid the fabrication of high Tc superconductors is to develop methods for quantitatively determining the local current density. In the critical state the current density is either the critical value appropriate to the local value of the induction J c , or it is zero. The electromagnetic response of the material is then determined by the extent of this critical state region and its measurement can be used to determine the local J c . Therefore, a method that can predict the flux front profile with high spatial resolution, and also account for demagnetization effects, is essential. An integral equation technique dealing with a nonuniform applied magnetic field having azimuthal symmetry was presented at the last QNDE conference by the present authors [4]. The current paper shows results from the further development of this technique in two ways. Firstly, the superconducting sample is extended from a half-space to an infinite plate. This is an example of a nonuniform applied magnetic field having azimuthal symmetry. The second application is a sphere, that is a demagnetizing geometry, in a uniform applied magnetic field. In the following section, the general methodology of this technique is outlined. Then some results of both the plate and the sphere examples are given to illustrate this proposed approach. Since the study of the plate sample is still in progress, more results will be reported in future publications. For the sphere sample, detailed discussion and presentation of formulations are given in [5].

#### Volume

14B

#### Chapter

Chapter 6: Material Properties

#### Section

Mostly Metals

#### Pages

1669-1674

#### DOI

10.1007/978-1-4615-1987-4_214

#### Copyright Owner

Springer-Verlag US

#### Copyright Date

January 1995

#### Language

en

#### File Format

application/pdf

Electromagnetic Hysteretic Response Calculation for Superconductors in Demagnetizing Geometries

Snowmass Village, CO

The electromagnetic response of the new high Tc superconductors is similar to that of eddy currents in normal metals, except that in the superconductor induced currents are established nonlinearly at a single value known as the critical current density, J c . These materials are extreme Type II superconductors where, in the presence of an external magnetic field and/or a transport current, magnetic flux exists in the material in the form of flux lines distributed on a lattice [1]. Individual flux lines become pinned at microstructural inhomogeneities such that only under a sufficient force caused by locally high current flows will they become depinned and flow throughout the material. The value of the local current density that causes depinning is the microscopic critical current density and is directly proportional to the pinning force strength. A phenomenological approach known as the critical state model [2,3] describes the pinned flux line distribution within the material quasistatically, assuming the equilibrium distribution is achieved at each value of the externally applied field on a short time scale compared to experimental times. Operationally, whenever an external field is increased, flux lines enter the material from the surface and penetrate to a flux front boundary, whose position is determined by the value of the external field at the sample surface. An important nondestructive evaluation (NDE) task to aid the fabrication of high Tc superconductors is to develop methods for quantitatively determining the local current density. In the critical state the current density is either the critical value appropriate to the local value of the induction J c , or it is zero. The electromagnetic response of the material is then determined by the extent of this critical state region and its measurement can be used to determine the local J c . Therefore, a method that can predict the flux front profile with high spatial resolution, and also account for demagnetization effects, is essential. An integral equation technique dealing with a nonuniform applied magnetic field having azimuthal symmetry was presented at the last QNDE conference by the present authors [4]. The current paper shows results from the further development of this technique in two ways. Firstly, the superconducting sample is extended from a half-space to an infinite plate. This is an example of a nonuniform applied magnetic field having azimuthal symmetry. The second application is a sphere, that is a demagnetizing geometry, in a uniform applied magnetic field. In the following section, the general methodology of this technique is outlined. Then some results of both the plate and the sphere examples are given to illustrate this proposed approach. Since the study of the plate sample is still in progress, more results will be reported in future publications. For the sphere sample, detailed discussion and presentation of formulations are given in [5].