This chapter deals with the AC loss in a tape carrying a direct or alternating transport current. There is always an alternating magnetic field present and there are no neighbouring tapes. The AC loss consists of a magnetisation and a transport-current loss component. The experimental set-up is extended in order to measure both loss components separately with direct transport current in alternating magnetic field oriented parallel to the tape.
The transport-current loss is described with a dynamic resistance, which occurs at magnetic-field amplitudes higher than the so-called threshold field. The dynamic resistance measured in tapes with non-twisted filaments is compared to predictions from the Critical- State Model. The effect of a lower temperature is examined. In a tape with twisted filaments, the dynamic resistance behaves differently and the threshold field is absent.
Transport current suppresses the magnetisation-loss components caused by large-scale currents in the filaments. The remaining magnetisation loss at high transport current is due to small-scale currents inside the grains. Apart from the grain loss, the influence of a transport current on the magnetisation loss in a tape with non-twisted filaments is well described by the Critical-State Model. The total AC loss in current-carrying tapes with twisted and non-twisted filaments is compared in order to assess the usefulness of filament twist.
In the case of an alternating transport current in a tape exposed to an alternating magnetic field, the losses are measured with the electric and magnetic methods. The limitations and requirements of the measurement technique are described. The calorimetric method is less complex and allows more combinations of current and magnetic field. The sensitivity achieved with the calorimetric method is compared to the sensitivity of electric and magnetic methods. Finally, this chapter describes a new calorimetric measurement technique as well as the reasons why the full functionality is not achieved.
4.1 Direct current in alternating magnetic field
4.1.1 IntroductionWhen a superconducting tape carries a transport current and is exposed to an alternating magnetic field, the total AC loss consists of a magnetisation component and a transport- current component. Both components of the loss are discussed in section 2.5. The magnetisation loss is measured by the magnetic method described in section 3.1. The transport-current loss is measured with an electrical four-probe technique. A similar technique is used to measure the critical current or the transport-current loss due to alternating current in self-field [Ashw94; Cisz95]. However, both methods should be modified when transport current and external magnetic field are combined [Rabb98; Laan99; Ashw99a]. The next section discusses the experimental set-up for measuring both AC-loss components in a tape carrying direct transport current in alternating magnetic field (DC/AF). The case with alternating current and alternating magnetic field (AC/AF) is discussed in section 4.4. Calorimetry is an alternative method for obtaining the total AC loss with both DC/AF and AC/AF (section 4.5).
4.1.2 Experimental set-up
In the DC/AF case, the transport current gives the sample an additional constant magnetic moment. Only the changes in the sample magnetic moment determine the magnetisation loss (see Equation 3.1). The changes in magnetic moment are detected as a voltage over the pickup coils. Therefore the magnetisation part of the measurement remains essentially unchanged. The transport-current loss is obtained from the voltage along the sample. The long-sample pickup coils displayed in Figure 3.2b can contain samples large enough to measure the sample voltage accurately without end effects. Therefore such measurements are made with the magnetic field oriented parallel to the wide side of the tapes.
Current leads with a capacity of about 100 A are added to the pickup coil set. They enter the sample region in the form of thin Ag tapes in order to minimise the extra eddy- current loss detected by the pickup coils. The sample has the form of a double-layer winding: see Figure 4.1a. The transport current spirals upward in the inner layer, which is grey in the figure. The current passes a soldered connection and spirals downward again in the outer layer (white). The + and – signs in the figure indicate the transport-current direction in the cross-section. The tape layers are isolated from each other by thin Tesa film. The transport current is supplied by a DC source. The alternating magnetic field induces a weak alternating current in the transport-current circuit. The alternating current is minimised by reducing the winding area perpendicular to the magnetic field. The double-layer geometry minimises the self-field of the sample, which may be an advantage or a disadvantage. Tapes in a bifilar sample winding (Figure 4.1b) have almost the same self-field as a single tape if the distance between the turns is large enough. However, the winding pitch of the sample then has to be more than twice as large, causing possible degradation and a sample orientation not quite parallel to the magnetic field. Furthermore, the sample length is halved, decreasing the accuracy of the voltage measurement. For simple critical-current measurements (without alternating magnetic field) the sample is wound as a single layer.
The sample voltage is measured with voltage taps connected to the wide side of the sample with low-temperature solder. For measurements of the loss due to direct transport current, the loop formed by the voltage taps should be as small as possible. The AC voltage induced by the magnetic field in the voltage-tap circuit should be minimised because it disturbs the DC-voltage measurement. Due to the small area between the tapes, a pair of voltage taps at both ends of the winding detects only a low induced voltage: see Figure 4.1c. However, it also measures the resistive voltage across the soldered connection between the
layers, which is high compared to the superconductor voltages. An arrangement is attempted with one pair of voltage taps on the inner sample layer and one pair on the outer layer, as in Figure 4.1d. By adding both voltages with a differential amplifier, the DC components remain and the AC components are cancelled. However, the grounded sides of the channels are internally connected in the amplifier. The connection disturbs the measurement even if the amplifier itself is disconnected from ground. Voltages are therefore measured along a single sample layer as shown in Figure 4.1e. The induced voltage is minimised by winding back the voltage taps very closely to the sample. DC voltages down to 1 µV/m are accurately measured by using a low-pass filter.
Figure 4.1 Measurement of transport-current loss in alternating magnetic field.
4.2 Transport-current loss; dynamic resistance
4.2.1 Tape with non-twisted filaments at 77 KThe results of transport-current loss measurements with direct current in alternating parallel magnetic field are presented in terms of the dynamic resistance Rdyn defined as V / It. The resistance is divided by the distance L between the voltage taps. The measured values are compared to predictions from the Critical-State Model for an infinite-slab, derived in section 2.4.3 [Oomen99a]. The model is applied to the filamentary region of a tape with non-twisted, fully coupled filaments.
The dynamic resistance measured in tape A is shown as a function of magnetic-field amplitude in Figure 4.2 and Figure 4.3. Each series of symbols with a different style corresponds to a different transport current. The tape has a critical current of 44 A in zero magnetic field. Other properties of tape A are listed in Table 3.2. The lines in the figures are calculated with the model formed by Equations 2.29, 2.36, 2.41 and 2.42. The magnetic-field frequency f is 48 Hz and the parameter c in the Jc(B) relation is 3.05 T-1. By varying the half- thickness a, width w and critical current Ic0, the model is fitted to the measurement results.
Solder
V
SolderV
SolderDifferential amplifier