The macroscopic theory of force free magnetic fields in the mixed state of type II superconductors is presented. Solutions for cylindrical geometry are compared with experimental data from a Pb-40 at% Tl alloy. In the experiments the sample is subjected to combinations of field and current in a longitudinal configuration and both axial magnetization and axial resistance are simultaneously monitored. The observed paramagnetic moment is in good agreement with the predictions. An unexpected feature of the experimental results is the appearance of flux flow resistance at high currents. Coupled magnetic and resistive oscillations and discontinuities are observed in the flux flow regime. The system is magnetically irreversible in the resistance less state and reversible during flux flow. The results are discussed in the context of force free field theory.

https://iopscience.iop.org/article/10.1088/0305-4608/2/3/020/pdf

Force free magnetic fields in a type II superconducting cylinder

Flux-line cutting (intersection and cross-joining of adjacent nonparallel vortices) has been suggested as a mechanism for steady-state dissipation in current-carrying, type II superconductors in longitudinal magnetic fields. In this paper a specific theoretical flux-line-cutting model is proposed which generates a constant steady-state electric field in a current-carrying, ideal, type II superconducting slab in a longitudinal field. The assumed model consists of parallel vortex planes at different angles which periodically shuttle back and forth between the regions in which flux-line cutting occurs. The resulting macroscopic electric current and magnetic flux density distributions are calculated. The model yields a nonlinear voltage-current characteristic and a longitudinal paramagnetic moment.

Steady-state flux-line cutting in type II superconductors

Hysteresis losses and the behavior of the magnetic flux threading superconducting disks of Nb oscillating slowly over various angular displacements in static magnetic fields H0 directed perpendicular to the axis of rotation have been investigated by continuously monitoring 〈Bz〉 and 〈By〉, the average components of the magnetic induction, in the plane of the disk, parallel and perpendicular to H0. A simple model proposed previously satisfactorily accounts for the initial changes, starting from various initial flux configurations, the subsequent cyclical behavior, and the hysteresis losses. Expulsion of flux from the disk occurs during part of the first oscillation, then the amount of flux threading the disk remains constant during the subsequent oscillations, although the orientation distribution of the flux profile undergoes spectacular periodic variations. The analysis shows that dψ/dx = ±k dB/dx describes the orientation of the sheets of flux lines with respect to H0 with distance from the flat surfaces....

Hysteresis losses and magnetic phenomena in rotating disks of type‐II superconductors

Starting from our general critical‐state theory, which includes the effects of both flux‐line cutting and flux pinning, we develop a numerical method for finding the magnetic response of type‐II superconductors subjected to parallel magnetic fields that change in both magnitude and orientation. We describe model calculations of the time‐evolving magnetic profiles when the direction of an applied magnetic field of fixed magnitude oscillates with large amplitude, and we compare our results with related experiments by Cave and LeBlanc. We also report model calculations for the ac behavior when the sample is subjected to a dc bias field and a large‐amplitude ac field at various angles (0°, 45°, and 90°) relative to this field.

Magnetic response of type‐II superconductors subjected to large‐amplitude parallel magnetic fields varying in both magnitude and direction

A mathematical model of the critical state based on averaged fluxon motion has been implemented to solve for the current and field distributions inside a high temperature superconducting hysteresis machine. The machine consists of a rotor made from a solid cylindrical single domain HTS placed in a perpendicular rotating field. The solution technique uses the finite difference approximation for a two-dimensional domain, discretized in cylindrical polar co-ordinates. The torque generated or equivalently the hysteresis loss in such a machine has been investigated using the model. It was found that to maximize the efficiency, the field needs to penetrate the rotor such that B 0 /?0 Jc R = 0.56, where B 0 is the applied field amplitude, Jc is the critical current density and R is the rotor radius. This corresponds to a penetration that is 27% greater than that which reaches the centre of the rotor. An examination of the torque density distributions across the rotor reveal that for situations where the field is less than optimal, a significant increase in the performance can be achieved by removing an inner cylinder from the rotor.

https://iopscience.iop.org/article/10.1088/0953-2048/13/2/319/pdf

M.A.R. LeBlanc

Papers

Flux expulsion and trapping in rotating discs of type II superconductors

Calculation of the critical current for type II superconducting wires in longitudinal fields

Calculations of the axial and azimuthal fluxes contained in a type II superconducting cylinder in a force-free configuration