Stability limit field in superconductors. Part I single core T. Akachi, R. Gomez* and T. Ogasawarat Instituto de Investigaciones en Materiales, Universidad Nacional Autonoma de Mexico, Ciudad Universitaria, Ap. Post. 70-360, 04510, Mexico, DF, Mexico *Facultad de Ciencias, Universidad Nacional Autonoma de Mexico, Ciudad Universitaria, Ap. Post. 70-542, 04510, Mexico, DF, Mexico tAtomic Energy Research Institute, College of Science and Technology, Nihon University, Kanda-Surugadai, Chiyoda-ku, Tokyo 101, Japan Received 18 May 1985 The stability limit field, Bfj, is determined for single core superconductors, when an external magnetic field changing linearly with time is applied perpendicularly to the axis of a cylindrical sample. Cases are considered when the magnetic diffusivity is greater than the thermal diffusivity and vice versa. The results are applied to a NbTi sample. Keywords: superconductors; stability limit; single core superconductors In the early days of superconducting magnets, the sudden dissipative rearrangement of magnetic flux within the superconducting wire, known as a flux jump or magnetic instability, was one of the major sources of disturbance causing the transport current carried by the supercon- ducting wire to sometimes be much smaller than that measured on short samples 1. Many studies have been done in high field single core superconductors to under- stand this phenomenon 2-9. From these studies came the insight that a cylindrical superconductor exposed to an external magnetic field parallel to its axis does not show flux jumps if its diameter is less than a certain critical value. This result has led to the development of multi- filamentary superconducting composites, consisting of many fine superconducting filaments embedded in a matrix of normal metal'°JL Recently, however, flux jumps have been observe&2'" in composite conductors, with superconducting filaments smaller than the critical value, when they are exposed to time-varying external magnetic fields. Cart t4 and some other authors "-~s have shown that, in a composite, the induced currents due to the changing magnetic field form loops flowing partly along the superconducting filaments and partly across the matrix from filament to filament, screening also the normal conducting part of the com- posite volume from the external magnetic, field. In other words, the time-varying external magnetic field couples the superconducting filaments. When the filaments are fully coupled the conductor behaves as a single core superconductor. It is the collective behaviour of the superconducting filaments that can induce flux jumps. The collective behaviour of the superconducting filaments of the composite causes the magnetic flux profiles, in the screening layer, to have a similar behaviour to those produced in single core superconductors. There- fore, the authors have investigated the occurrence of flux jumps in single core high field superconductors of 0011-2275/86/060352-06 $03.00 © 1986 Butterworthf~ Co (Publishers) Ltd 352 Cryogenics 1986 Vol 26 June cylindrical geometry when a changing external magnetic field is applied perpendicular to its axis. They calculate the maximum field at which the superconductor is still stable, i.e. the stability limit field, Blj .. Results for multi- filamentary superconducting composttes are reported in a second paper (Part 2). Condition for the stability limit field The magnetic instability problem is usually treated as an adiabatic one, based on the assumption that the move- ment of the magnetic flux inside a high field supercon- ductor is faster than the heat transmission. In other words, it is considered that the magnetic diffusivity, Din, is larger than the thermal diffusivity, Dth. However, as was pointed ouP ,2°, the magnetic diffusivity in high field supercon- ductors, for field values in the region where flux jumps take place, is not necessarily larger than the thermal diffusivity. Hence, we consider the magnetic instability problem for the cases when D m > Dth and vice versa. For the case when D m > Dth, we will assume that there is no heat flow out of the region of flux penetration and, furthermore, that the total heat developed in a flux jump is spread evenly throughout the region of flux penetration; i.e., the new temperature is uniform across this region. For the case when Dth > D m we will assume that the heat developed, when a flux jump takes place, spreads throughout the volume of the sample and that the new temperature is uniform across the entire volume. Let us consider a high field superconducting cylindrical sample of length 1 and radius R, with an external magnetic field B e applied perpendicular to the axis of symmetry of the cylinder. This sample can be thought of as a small length, 1, of a tightly wound superconducting coil. We choose as a reference frame a normal cartesian system with its origin at the centre point