F. Sumiyoshi

The effect of demagnetization on the eddy‐current loss in a single‐layered multifilamentary superconducting coil

The demagnetization effect of a single‐layered superconducting coil made of a cylindrical multifilamentary wire on its eddy‐current loss is studied for the case of ac magnetic fields parallel to the coil axis. An expression for an effective demagnetization coefficient of the wire is obtained by taking account of the interaction among turns of the coil. It is shown from this expression that the magnitude of the eddy‐current loss increases remarkably with the distance between neighboring turns of the coil. The experimental loss values of the wires wound into various kinds of coils are within 20% of the theoretical values.

ac loss of a multifilamentary superconducting composite in a transverse ac magnetic field with large amplitude

A general study is made of ac losses of a multifilamentary superconducting composite carrying no transport current in a transverse ac magnetic field with large amplitude. In the case of applying a magnetic field below the current‐saturation condition in an outermost layer, an eddy current loss as well as a hysteresis loss is calculated by taking account of the hysteresis effect of a superconducting filament on these losses with an apparent complex permeability of the filament. It is shown that the frequency characteristics of the eddy current loss are considerably different from those calculated from previous theories. In the case above the saturation condition, a loss calculation is made taking account of the phase difference between the applied magnetic field and the internal one. It is shown in this case that the hysteresis loss increases rapidly with frequency around the critical frequency. These calculated results are confirmed by experiments with Nb‐Ti multifilamentary composites. General features o...

Magnetic field dependence of ac losses in multi-filamentary superconducting wires

Abstract The magnetic field dependence of ac losses due to nonlinear flux penetration into superconducting filaments, ie, nonlinearity between an applied magnetic field and a penetrated flux, has been studied experimentally for multi-filamentary superconducting wires with Nb-Tl filaments and Cu matrix. In order to observe this effect, ac loss measurements were extensively carried out for the cases of applied transverse ac magnetic fields ranging from 0.06 to 50 Hz in frequency and from 10 −3 to 0.2 T in amplitude. Shifting of the frequency corresponding to the peak of the eddy current loss with the amplitude of applied magnetic fields was revealed experimentally. The results obtained were explained by taking into account the magnetic field dependence of the effective permeability of the wire originated from nonlinear flux penetration into superconducting filaments. The associated frequency dependence of the hysteresis loss is also discussed.

Effects of tin-diffusion barriers on hysteresis loss and coupling current loss in bronze-processed Nb3Sn multifilamentary composites

Abstract A.c. losses for a practical bronze-processed Nb 3 Sn multifilamentary composite were measured over a wide range of amplitudes (O ⩽ B m ⩽ 14 T,O ⩽ B dc ⩽ 10 T) in transverse magnetic field with trapezoidal wave forms. The composite had a Nb or Ta barrier for ptoecting the Cu stabilizer from Sn diffusion. The observed results were analysed theoretically and a quantitative agreement was obtained over the whole measured range of amplitudes in both types of samples with Nb and Ta barriers. Existing expressions for the hysteresis loss in multifilamentary composites have been known to show deviation by more than a factor of 2 from the observed data. No theoretical discussion has previously been presented for the effects of a Nb barrier.

Eddy-current loss in a fully-stabilized multifilamentary superconducting wire

Abstract A theoretical expression is provided for the ac loss in a fully-stabilized multifilamentary superconducting wire with a thick coating of aluminium or copper. It is shown that for a wire with a large amount of stabilizer, the skin effect in the stabilizer seriously affects the ac loss not only at high frequencies but also at low frequencies. In fact, the loss due to the eddy current along the wire axis induced by the skin effect predominates over the coupling-current loss if the twist pitch of filaments is shorter than the effective perimeter of the whole wire even in the low frequency range. In the middle frequency range, as used for a high-speed pulse magnet, the above feature in the ac loss is retained even if the twist pitch is not so short. The present feature in the ac loss is quite different from the known one for ordinary multifilamentary wires without a large amount of stabilizer. The present theoretical results show quantitative agreements with the results of our experimental measurements.

Increase of coupling-current losses in superconducting cables due to first-stage cabling

Abstract A theoretical discussion is presented on the coupling-current loss in a superconducting sub-cable composed of three or seven multifilamentary wires. Approximate expressions for the induced loss by the application of a changing transverse magnetic field are given as functions of sub-cable parameters such as the thickness of the outer sheath inside the wire and the degree of compaction or solder-filling of the sub-cable. According to the present results, increase of the loss per unit volume of a sub-cable due to first-stage cabling is not as large as predicted by Campbells theory which is applicable only to a special type of sub-cable composed of many strands.

Using magnetic field pulses with a slow sweep rate to produce uniform current distribution in multifilamentary superconducting wire

Abstract A detailed discussion is presented on the change in current distribution which takes place in a twisted multifilamentary superconducting wire induced by successive magnetic field pulses with a slow sweep-rate. The number of the field pulses required for a localized current-distribution to become uniform is estimated. Some modification of existing theories is necessary to describe the phenomenon. The results obtained are confirmed by systematic measurements of the net flux penetration into the wire during each cycle of field pulses.

On the distribution of a transport current inside a multifilamentary superconducting wire in a rapidly changing transverse magnetic field

Abstract For the current distribution inside a multifilamentary superconducting wire carring a dc transport current in a rapidly changing transverse magnetic field, inconsistencies with the existing models are shown by the following experimental evidence: when a transverse magnetic field is applied, the distribution of transport current is not unaltered but is forced to concentrate into the inner circular cross section region during a characteristic time constant τ c , called the coupling time constant. Secondly, the characteristic time constant for the transport current distribution inside the inner region to approach a uniform distribution is not τ c but a new time constant τ 1 called the ‘uniforming time constant’, though the variation in the distribution does not occur unless the external magnetic field changes with time. It is shown that the model of the current distribution based on the above experimental evidence exhibits a remarkable difference from the existing models, especially for the wires containing very fine superconducting filaments.

Coupling-current loss in a multifilamentary superconducting wire with a normal-metal core

Abstract Coupling-current losses in a multifilamentary superconducting wire with a normal metal core were calculated for the case of transverse magnetic fields. The results showed that the dependence of the coupling-current loss of such a wire on the rate of field variation is markedly different from that of a wire without the core, the former being characterized by two time constants while the latter by one. The theoretical result was confirmed experimentally. It was pointed out that in the case when a wire with Cu/CuNi matrices is to be used in a rapidly changing magnet field, Cu for a stabilization should be arranged at the centre of the wire rather than at the surface of the wire in order to reduce the loss.

Losses in a multifilamentary superconducting wire caused by a simultaneous sweep of current and magnetic field

Abstract A theoretical discussion is presented on the energy loss in a multi-filamentary superconducting wire when an applied transport current and an external transverse magnetic field are varied simultaneously with a repeating pulsive wave form. In the present calculation, the effects of the ‘uniforming time constant’ which has been introduced by the authors as a characteristic time constant for the change in the transport-current distribution inside the wire is taken into account, together with the field dependence of the critical current density of superconducting filaments. Thus the present analytic expression for the energy loss of multi-filamentary wire is available to the whole range of the external magnetic field. It is shown that the contribution of the dynamic resistance loss to the total loss is strongly dependent on the position of the wire inside a coil.