Theory of ‘‘supercurrents’’ and their influence on field quality and stability of superconducting magnets

Abstract

Unexpected periodic variations of the magnetic field were recently found along the axes of superconducting accelerator magnets. This modulation, which reduces the field quality of the magnets, shows a complex space and time dependence containing very long time constants. We show in this article that the variation of the field rate dB/dt along the length of a superconducting cable induces superposed coupling currents which flow over a long length. The space and time dependence of these ‘‘supercurrents’’ for a two-wire cable model is obtained by the solution of the diffusion equation with the diffusivity given by the cable parameters. The existence of supercurrents explains the observed effects in accelerator magnets. It is furthermore shown that supercurrents can lead to a highly inhomogeneous current distribution over the cable cross section and to additional coupling losses, even in sections of the magnet where dB/dt=0. Both these effects can reduce the stability of magnets, which may explain the ramp rate limitation found in accelerator magnets as well as in large magnets for fusion research.

Analytical solution for the current distribution in multistrand superconducting cables

“…Our general solution reduces to the solution given in [11] when a two-strand cable exposed to a localized external flux change is considered. As we will show, it is however possible to derive directly an analytical solution also in the case of cables made of equal strands, thus enlarging significantly the possibility of fast scoping and parametric studies.…”

“…More recently Krempasky and Schmidt [11] have given the analytical solution of the equation of current diffusion in a two-strand cable and applied it to the study of long range "supercurrents" induced by longitudinal variations of the time derivative of the magnetic field applied to the cable. The evaluation of the strand currents in the presence of a generic current cycle was obtained by considering two different analytical solutions of the equation of current diffusion in the presence of field ramps (forced diffusion), and during constant field phases (free diffusion).…”

“…two-strand cables) [7][8][9][10][11][12]. In particular, Turck [7] analyzed current sharing between two non-insulated coupled superconducting wires, with and without superficial oxides.…”

“…Mitchell [12] used an approximate analytical model of a two-strand cable derived using the same model as the one described in [11] to study the effect of current redistribution from a normal zone on the stability margin of a cable. The approximate model assumes that the strands portion where the current redistribution takes place is in superconducting state.…”

Advances in the Understanding and Operations of Superconducting Colliders

“…This effect, however, had to be relegated to be of secondary importance, when Kuchnir's measurements revealed flux creep rates in Tevatron magnet cables ( [4]) that were ten times smaller than those observed in magnets. The more recent model, first proposed by Krempasky [5], Verweij [6], Bottura [8] and Wolf [9] on the basis of an idea by R. Stiening [10], postulates that the effect is caused by the re-distribution of currents between strands in the cables making up the coils in conjunction with superconductor demagnetization. [6] refers to these currents as BICC, or boundary induced coupling currents, since they originate in the magnet ends or splices.…”