Correlation between voltage current relation and current distribution in superconducting cables

Transcription

1 Physica C 401 (2004) Correlation between voltage current relation and current distribution in superconducting cables A. Kuijper a, *, A.P. Verweij a, H.H.J. ten Kate b a AT Division, CERN, CH 1211 Geneva 23, Switzerland b University of Twente, TNW, P.O. Box 217, 7500 AE Enschede, The Netherlands Abstract For many years it has been known that the properties and operating margins of superconducting magnets are influenced by the distribution of transport and induced currents among the strands in the cables with which the magnet is wound. In FRESCA, CERNÕs test station for measuring electrical cable properties at 1.9 and 4.3 K, the voltage current curve of Rutherford type cables and the homogeneity of the current distribution can be measured simultaneously. The longitudinal variation of the cable self-field is measured along one twist pitch, and taken as a measure for the variation of the strand currents. A change in the background field, which is applied non-uniformly along the length of the cable, will induce boundary induced coupling currents. These coupling currents decay very slowly and cause a variation in the strand currents, resulting in a different electro-magnetic behaviour of the cable, even long after the field sweep has finished. In this paper the experimental results on about 40 cables for large hadron collider magnets are presented in terms of quench current and apparent critical current and n-value. The measurements will be sustained by calculations. Ó 2003 Elsevier B.V. All rights reserved. PACS: Keywords: Superconducting cables; Current distribution; UI characteristic 1. Introduction The large hadron collider (LHC) is currently under construction at CERN. This new, circular particle accelerator is constructed with superconducting magnets to keep the particles in their trajectory. About 6400 km of superconducting, Rutherford type NbTi cable is used for the main dipole and quadrapole magnets. To assure all cables comply with the specifications, reception tests * Corresponding author. Tel.: ; fax: address: anton.kuijper@cern.ch (A. Kuijper). are performed. Most of these tests are performed at Brookhaven National Laboratory (BNL), at a temperature of 4.3 K [1]. For more elaborate testing, particularly at 1.9 K, CERN has its own cable test station, FRESCA. In FRESCA, the electromagnetic properties of cable samples can be tested at both 1.9 and 4.3 K. An external magnetic field of up to 10 T can be applied to a section of the cable in four different directions. The transport current through the samples can reach 32 ka [2]. Instrumentation is present to allow the monitoring of the distribution of the current among the strands during any measurement. The voltage current (UI) curves measured with FRESCA are altered if a large change in applied /$ - see front matter Ó 2003 Elsevier B.V. All rights reserved. doi: /j.physc

2 130 A. Kuijper et al. / Physica C 401 (2004) field precedes a measurement. It will be shown that these alterations are caused by an inhomogeneous distribution of the current in the cable, in this case induced by the field change. In Section 2, the essential parts of the experimental set-up will be discussed further. After this, some measurement results that show the described phenomena will be presented. Section 3 will give the theoretical explanation. The explanation is verified by data measured during the last year. Finally the matter is discussed in Section Experimental set-up 2.1. FRESCA The most important use of FRESCA is to perform reception tests on superconducting cables that will be used for the new LHC. The cable transport current is ramped up until the cable quenches. During this ramp, the voltage is measured across a section of the cable, typically 600 mm long. The UI curve measured in this way is used to determine an apparent cable critical current I c;a and an apparent n-value n a. Two samples, connected in series, are measured simultaneously. Fig. 1 gives a schematic view of the samples in the set-up. Additional to the voltage taps, an array with 26 Hall probes is placed alongside each of the cables, as in Fig. 2. The Hall probes are used to monitor the local self-field of the cable along one cable twist pitch. When the current varies from strand to strand, the cable self field will vary as well. This variation is measured by the array of Hall probes. Since there are generally more than 26 strands in a cable, it is not possible to derive exactly the distribution of the current among the strands from the 26 Hall probe signals. Instead, the standard deviation of the HP signals is taken as a measure for the inhomogeneity of the current distribution. For special cases, more information can be deduced about the strand currents. If the distribution is sinusoidal, then the HP signals will be sinusoidal as well. In this particular case the strand currents can be deduced from the HP signals case as follows: Fig. 1. Schematic view of the cable samples in FRESCA. Two samples are soldered together at the bottom. The field is applied along approximately 1 m length. An array of Hall Probes is placed alongside each cable. Fig. 2. Position of the Hall Probe Array. The self-field of the black strand is seen mainly by the black probe. A s ¼ C SA S HP ; ð1þ where A s is the amplitude of the sinus in the strand current in [A], S HP is the standard deviation of the HP signals in [T] and C SA is a constant, depending on the cable geometry and the exact position of the HP array. For the current set-up, C SA is approximately 4 A/mT BICCs For standard measurements the applied field, B a, is usually ramped up to 8 or 9.4 T, after which

3 A. Kuijper et al. / Physica C 401 (2004) the cable current is ramped up to a quench for the first time. Since B a is not applied uniformly over the entire length of the cable, so-called boundary induced coupling currents (BICCs) are induced in the cable [3]. These BICCs flow along the entire length of the cable sample. They affect the distribution of the current among the strands and can be measured with the Hall Probe Arrays. BICCs have typical decay times in the order of 1000 s in our set-up. This means they are still present in the sample when the cable is quenched for the first time after a field ramp. Calculations with the network model developed in [3] show that the current distribution resulting from BICCs will be sinusoidal in our setup. The standard deviation of the HP signals after a ramp in the applied field is typically 5 mt. This corresponds to an amplitude in the strand currents of roughly 20 A. Fig. 3 shows a measurement of the BICCs and their decay. Here the externally applied field B a is ramped up from 0 to 8 T, after which it is held constant for 30 min. In the same figure the standard deviation of the Hall probes is shown. During the ramp in B a the signal will increase. Once the applied field remains constant, the Hall probe signals slowly decay. The spatial distribution of the HP signals just after the ramp in B a is shown in the insert plot. Summarising, a ramp in the magnetic field will introduce in the cable a slow decaying nonhomogeneous current distribution, of which the shape and amplitude is known. This knowledge will be used later for the calculation UI curve The presence of a non-uniform current distribution has an effect on the measured characteristics of the cable. In Fig. 4, two measured UI curves are shown. One of the curves is measured immediately after a change in the applied field B a, in the presence of BICCs. After the first quench, the cable has been resistive so all currents are erased. During the second measurement therefore, no BICCs are present. For any subsequent measurements under the same conditions, the UI curve remains the same. Each measured curve is fitted with the power law (U ¼ U 0 ði=i c Þ n ), with which two parameters are found, the apparent critical current, or I c;a, and the apparent n-value n a. They are called apparent to avoid discussion whether or not they are physical cable parameters. n a and I c;a are cable parameters specific for the measurement method chosen here. I c;a is the current where the UI curve crosses the straight line in Fig. 4. This line corresponds to a resistivity criterion of X m. A third parameter deduced from the measurement is the quench current: the highest transport current reached before the samples quench, known as I q.it Fig. 3. Measurement of BICCs. Applied magnetic field (1) and standard deviation of the 26 Hall Probe signals (2) versus time. BICCs are induced by the field change. During a constant background field, they decay slowly. The insert shows the separate HP signals just after the field sweep. Fig. 4. Two measured UI curves and the X m criterion. The 1st run after a field sweep is affected by the BICCs in the cable.

4 132 A. Kuijper et al. / Physica C 401 (2004) Fig. 5. Changes in cable parameters due to the presence of BICCs: (1) I q1 =I q2 ; (2) I c;a1 =I c;a2 ; (3) n a1 =n a2 versus the standard deviation of the Hall probe signals. For each parameter, a linear fit through the data points is shown. can be seen that I c;a and n a of the first run, I c;a1 and n a1 are reduced by the presence of BICCs. Fig. 5 shows the changes in the three parameters due to the presence of BICCs. For this plot all samples measured with the current set-up have been taken into account. The values of the parameters affected by the BICCs, I q1, I c;a1 and n a1, have been normalised to I q2, I c;a2 and n a2, the parameters deduced from the second run. The normalised parameters are shown versus the value of the standard deviation of the Hall probes just after the magnet ramp. 3. Theory When the transport current in a cable is increased, the distribution of the current among the strands is governed by two mechanisms, both affecting the strand voltages. First there is the selfinduction L s of each strand. Because of this, it is necessary to apply a certain voltage to the strand to increase its current. In a Rutherford type cable, the strands are fully transposed, i.e. they each have the same self-induction. An increase in transport current will therefore distribute itself evenly among all strands. The second mechanism is the strand resistance R s. This includes the contact resistance between the cable and its current source. The resistive voltage is small for superconducting cables, and during a ramp it is negligible compared to the inductive voltage. During an extended period of constant transport current, the cable current will distribute itself according to each strands resistance. Without BICCs, all strands will carry comparable currents, and, if similar I cs values are assumed for each strand, will become resistive simultaneously. In first approximation, the cable can be thought to consist of a number of identical strands, with values for the n-value and critical current: n s ¼ n a and I cs ¼ I c;a =N s ; ð2þ where N s is the number of strands in the cable. With BICCs present in the cable, the strands still have the same physical characteristics, so n s and I cs are assumed to be as before. The only change is that the strands carry different currents, and they will therefore become resistive consecutively. If A s is the amplitude of the BICCs in the cable, and the transport current is still evenly divided among all strands, a voltage drop over the cable will be measured when the first strand becomes resistive. It will be shown later that once some strands start to become resistive, the current distribution will slowly become more uniform. For high ramp rate of the transport current, however, the current distribution will not change before the cable I c;a has been reached, so that I c;a ¼ðI cs A s ÞN s ¼ I c;a A s N s : ð3þ This means that the degradation in I c;a is A s N s, roughly one order of magnitude larger than the amplitude of the BICCs themselves. A s can be deduced from the HP measurement, following equation (1). In Fig. 6 the absolute decay of I c;a is shown versus A s N s. A linear trend through the plotted points shows a slope of approximately 1, as expected. During the transition, the voltage developed by some strands will alter the distribution of current among the strands, making it more uniform. This can be seen in Fig. 4, where the shift in the UI curve that is seen at the beginning of the transition slowly vanishes. This will result in a decreased n a value. As the transport current rises beyond I c;a, the resistance of the strands with elevated current becomes important. The current in these strands will

5 A. Kuijper et al. / Physica C 401 (2004) Fig. 6. The degradation of I c;a versus A s N s. The slope of the linear fit is 1.07 [ ]. then be limited because of two reasons. First, the resistive voltage will limit the transport current to rise any further. Instead, the other strands will take the added current. Secondly, because the voltage of these strands is higher than that of neighbouring strands, current will be transferred to these neighbouring strands through their contact resistance R c. The current distribution will therefore go towards a homogeneous distribution once the strands become resistive. This homogenising of the strand currents will take some time, depending on the contact resistance between the strands. Fig. 7 shows the degradation of I c;a and n a as a function of the current ramp rate for two different samples: one with high R c values and one with low R c values. It can be seen that for slower ramps, the degradation diminishes, and finally even disappears. For the cable with high contact resistance the homogenisation is expected to take longer. Indeed it is seen that the degradation of I c;a disappears only for very low ramp rates, whereas for the low R c cable medium ramp rates suffice. 4. Discussion It has been demonstrated that the presence of BICCs has a clear influence on the UI characteristic of a superconducting cable in the used test set-up. It has also been shown, that the inhomogeneous distribution of the current can explain this effect, not the specific nature of BICCs. Measurements Fig. 7. Degradation of cable parameters as a function of the transport current ramp rate. The first figure shows the degradation of I c;a, the second figure the degradation of n a. For cables with high R c, the degradation shows up at lower ramp rates. have shown that the same effect appears for inhomogeneous distributions obtained in other ways. Since the distributions are then no longer necessarily sinusoidal, the respective calculations to prove that the degradation can be explained fully by the current imbalances are not so easily made. In a real magnet, the field applied to the cables changes with the transport current. Under these circumstances, BICCs are still induced, and can therefore have a negative effect on the magnet performance. A sufficiently low ramp rate has shown to limit or even extinguish the I c;a degradation in the used set-up. Care must be taken however in interpreting the values shown here. In a real magnet, decay times of BICCs are generally orders of magnitude larger than the 1000 s mentioned before for short samples. As a result, the ramp rate needed to limit

6 134 A. Kuijper et al. / Physica C 401 (2004) the degradation in such a magnet will need to be several times smaller than the values shown here. 5. Conclusions The voltage current curve of a cable is different when the transport current is not uniformly divided among the strands. In this paper BICCs have been used to examine this effect. BICCs are induced during a ramp in the applied magnetic field. During the measurement of the cable voltage current characteristic, the distribution of the current in the cable has been monitored. Calculations show that for relatively high ramp rates of the transport current, the measured degradation of the cableõs apparent critical current value, I c;a, can be fully explained by the inhomogeneity of the current distribution. It has been demonstrated that for lower ramp rates, the voltage current characteristic is less, or even not affected at all by the current distribution. In real magnets, the quench current (and thus cable stability) can be severely limited by a nonuniform current distribution. Because of the larger time constants, it would require extremely low ramp rates to prevent the degradation. Acknowledgements The authors would like to thank S.Geminian, R. Monod, R. Rota and O. Vincent-Viry for their help with the set-up and performing measurements. References [1] R. Thomas et al., Testing and evaluation of superconducting cables for the LHC, in: 18th Biennial Particle Accelerator Conference, New York City, NY, USA, Mar Apr 1999, pages e-proc [2] A.P. Verweij et al., 1.9 K Test facility for the reception of the superconducting cables for the LHC, IEEE Trans. Appl. Supercond. 9 (1999) 153. [3] A.P.Verweij, Electrodynamics of superconducting cables in accelerator magnets, PhD thesis, University of Twente, The Netherlands, 1995.