Sweep-rate dependences of losses in aluminum-stabilized superconducting conductors for the Large Helical Device

Fusion Engineering and Design 20 (1993) 371-376 North-Holland

371

Sweep-rate dependences of losses in aluminum-stabilized superconducting conductors for the Large Helical Device F. S u m i y o s h i a, y . K a n a i a, T. K a w a s h i m a b, M . I w a k u m a c, T. M i t o d, K. T a k a h a t a a n d J. Y a m a m o t o

d, N. Y a n a g i d

d

a Faculty of Engineering, Kagoshima University, Kagoshima 890, Japan h Fukuoka Institute of Technology, Fukuoka 811-02, Japan c Faculty of Engineering, Kyushu University, Fukuoka 812, Japan ,t National Institute for Fusion Science, Nagoya 464-01, Japan

We measured the frequency characteristics of ac losses in the aluminum-stabilized superconducting conductor for the helical coil system of the Large Helical Device (LHD) project, in order to clarify the dependence of the loss on the sweep rate of the poloidal field. In our experiment, a straight and short conductor of about 50 cm long was used as a sample. The sample was subjected to the ac ripple field superposed on the bias field. The data of the ac loss observed in the frequency range from 0.1 to 100 Hz have two peaks just as our analysis predicted. The peak at the lower frequency is the critical frequency related to the inter-strand coupling time constant %. The other peak at the higher frequency is the skin frequency of the normal metal around the strand bundle in the conductor. The lower frequency peak mainly shifts according to the cabling condition of the strand bundle. Under the operating condition of the LHD corresponding to 0.1 Hz, the loss can be decreased as % increases. It is very different from the common design concept. This result suggests that it is necessary to grasp the sweep-rate dependence of the loss in the conductor in order to optimize its structure from the low-loss point of view.

1. Introduction T h e large helical device (LHD), as an e x p e r i m e n t a l device for fusion science in which t h e s u p e r c o n d u c t i n g c o n d u c t o r s are fully used for all the coil systems, is now u n d e r construction [1]. A helical coil system to provide a c o n f i n e m e n t field for the hot ionized plasmas is a main part of the L H D . This coil must have a high stability b e c a u s e it has a big stored energy. A n alum i n u m - s t a b i l i z e d s u p e r c o n d u c t i n g c o n d u c t o r of a pool-cooling type is i n t e n d e d to be used as a winding of the coil [2,3]. W h e n the poloidal coil is energized, the c h a n g i n g m a g n e t i c field s u p e r p o s e d o n the dc field of 8 T is applied to the helical coil c o n d u c t o r carrying dc t r a n s p o r t c u r r e n t of 21 k A in a n o r m a l operation. T h e repetitive wave form of the poloidal coil is of sawteeth, 0.333 T in amplitude, 5 s in rising time and 5 min in falling time. This is the most serious o p e r a t i n g mode. D u r i n g the rising time, a large loss, mainly

Correspondence to: Dr. F. Sumiyoshi, Faculty of Engineering, Kagoshima University, Kagoshima 890, Japan. 0920-3796/93/$06.00

c o m p o s e d of the i n t e r - s t r a n d c o u p l i n g - c u r r e n t loss and the eddy c u r r e n t loss, is p r o d u c e d in the conductor. In o r d e r to keep its stability, the loss must be so small that the heat g e n e r a t e d in the c o n d u c t o r by the loss can be r e m o v e d from it into the coolant during the long falling time. T h e n the h e a t dose not accumulate in the conductor. In the case of the c o m m o n design of the conductor, the inter-strand coupling time c o n s t a n t 7 c is m u c h smaller t h a n the rising time t r [4]. In this case, the external applied field can p e n e t r a t e into the c e n t e r of the conductor, so that the loss does not b e c o m e so large. T h e aluminum-stabilized c o n d u c t o r does not tend to satisfy the condition of % << t r because a lot of a c o p p e r or an a l u m i n u m stabilizer provides a couplingc u r r e n t p a t h with a low resistivity. T h e alternative design c o n c e p t has b e e n r e q u i r e d to get t h e aluminum-stabilized c o n d u c t o r with a low loss which is repeatedly subjected to the c h a n g i n g m a g n e t i c field. In this paper, we elucidate the sweep-rate d e p e n d e n c e of losses in some kinds of the R & D a n d the full-scale conductors [5,6] in o r d e r to get the new design concept of the a l u m i n u m - s t a b i l i z e d conductor.

© 1993 - E l s e v i e r S c i e n c e P u b l i s h e r s B . V . A l l r i g h t s r e s e r v e d

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F. Sumiyoshi et al. / Sweep-rate dependences of losses"

Instead of measuring the sweep-rate dependence of the loss, we here measure the frequency dependence of the ac loss by using our original measurement system [6]. Using the obtained results, we discuss the conductor design from the loss and the current distribution point of view.

2. Experiment 2. 1. Measuring system In order to completely clarify the loss feature of aluminum-stabilized conductors, we need a large measuring system which has such a high sensitivity as to measure the small losses in the rigid conductor even when the external magnetic field B e changes as slowly as 1 < t r < 103 s. It is very difficult in all respects to provide such a system, so that we are originally obliged to design and make a loss-measuring system. This system described below is an alternative plan and enables us to estimate the losses in the rigid conductor [6]. Our compact system is mainly composed of a superconducting split magnet of a race-track type, a superconducting transformer and a superconducting heat switch for the persistent current mode. Figure I shows schematics of this system and a wave form of magnetic fields for measuring. At first, the short sample conductor is put in the split magnet. Both this magnet and the secondary coil of the transformer are energized in series from the dc power supply. After shortening them by using the superconducting heat switch, the dc power supply is removed. At this stage, the persistent current is flowing in this series circuit. Subsequently, the primary coil of the transformcr, wound by the ultrafine

multifilamentary wire for ac uses, is energized by means of a resonance capacitor and ac power supply. (A terminal voltage of the primary coil becomes up to a few kilovolts.) As the result, the small ac magnetic field superposed on the dc field Bdc is generated in the split magnet in the transverse direction to the axis of the short sample. This compact system allows us to measure a wide frequency range of 0.1-200 Hz and has a rather large sample space of 30 m m × 30 mm x 55() mm. By using this system, we can get the loss-frequency characteristic curve in the cases of small ac fields with the amplitude of B m = 0.5-9 mT superimposed on dc bias fields of Bdc = 0-3.6 T. The error of this system can be ncglected as long as the normalized losses of our samples, which will be defined in section 2.3, are bigger than 10 3 The characteristics of this system are as follows. This system uses a ripple ac magnetic field superposcd on the bias field as an applied magnetic field. By using this system, the frequency characteristic curvc of the loss in the short conductor can be obtained for the wide frequency range. The measured loss is expected to be composed of both coupling and eddy current losses, because the applied field amplitude Bn, is very small. In such a low-field case, the hysteresis loss can be generally neglected. This can be confirmed by checking whether the measured loss is proportional to

,gm. By our measuring, it is expected to get the lossfrequency characteristic curve except the lower frequency region than 0.1 Hz. The minimum of the measuring frequency is 0.1 Hz, which approximately corresponds to the minimum time of raising the poloidal magnetic field t r = 5 s. We can get both the characteristic curves of losses in the frequency region of 1"> 0.1

42K

Fig. 1. System for measuring ac losses of a large conductor without flexibility. (1) A superconducting magnet of a race-track type, (2) a superconducting transformer, (3) a superconducting heat switch, (4) a short sample conductor, (5) a dump resistor, (6) a resonance capacitor.

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F. Sum&oshi et al. / Sweep-rate dependences of losses Eu

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helical coil. They differ in the location a n d the s h a p e of the a l u m i n u m stabilizer [2,3,5]. T h e cross section of these conductors a n d their p a r a m e t e r s are shown in fig. 2 and table 1, respectively. As shown in fig. 2, in the case of C o n d u c t o r KISO-4B(S), the a l u m i n u m stabilizer is located in the c e n t e r of the b u n d l e of the twisted strands, in D E S I G N - M a r o u n d the bundle. C o n d u c t o r s KISO-4B-S and K I S O - 4 B - R have almost the same cross section as that of KISO-4B(S) except some p a r a m e t e r s related to the c u r r e n t capacity. T h e C o n d u c t o r s KISO-4B-S and K I S O - 4 B - R differ from each o t h e r in the twisting direction of the strand b u n dle, i.e., in the f o r m e r case the twisting directions of the i n n e r layer of the s t r a n d b u n d l e and the o u t e r one are the same. O n the o t h e r hand, in the latter case, opposite. Four straight sample conductors, a b o u t 500 m m in length, are provided for this experiment, in o r d e r to keep the b e n d i n g strain from decreasing the conductivity of a l u m i n u m and copper. As any direct contact of the s u p e r c o n d u c t i n g filaments produces a m e a s u r e m e n t e r r o r of losses, b o t h ends of the short sample are polished to be smooth and flat.

Hz a n d the absolute loss value at 0.1 Hz, by our measuring. They e n a b l e us to get the valuable information for the c o n d u c t o r design for the helical coil.

2.3. Measured loss-frequency characteristics M e a s u r e d frequency characteristics of the loss for the short sample c o n d u c t o r are shown in figs. 3 a - d , where the vertical axis, i.e., the ' n o r m a l i z e d loss', is the loss p e r cycle normalized by Bm//Z0, 2 w h e r e B m is the

2.2. Short sample conductors T h e sample conductors used in this e x p e r i m e n t are the R & D a n d the full-scale NbTi conductors of the Table 1 Parameters of the superconducting conductor Conductor name Nominal current at 8 T (kA) Outer size (mm x mm) Volume fraction of aluminum

KISO-4B(S) 10 13.5 x 13.5 0.176

DESIGN-M 21 19 × 19 0.230

KISO-4B-R 21 19 × 19 0.231

KISO-4B-S 21 19 × 19 0.231

Strand parameters Diameter of NbTi filaments (t~m) Number of filaments Diameter of a strand (mm) Twist pitch (mm) a

23 720 0.877 + 20

25 1213 1.215 + 17

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84 2

+ 179 - 194 485

- 127 (for all layers) 508

- 232 + 254 508

+ 232 + 254 508

+ sign represents the direction of twisting.

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F. Sumiyoshi et al. / Sweep-rate dependences of losses

amplitude of the applied ripple field, and /z 0 is the permeability of vacuum. Most of the data of the normalized loss do not depend on the field amplitude B m. This indicates that the loss in these data is mainly composed of the Joule losses in the normal metal such as the inter-strand coupling-current loss or the eddy current loss. For Conductor KISO-4B(S), the lossfrequency characteristic curve has a peak near 20 Hz and a notch near 0.3 Hz as shown in fig. 3a. For Conductor DESIGN-M, the curve shown in fig. 3b has a peak near 1 Hz and not a notch. For the higher frequency region than 1 Hz, the loss is inversely proportional to square of frequency. Figures 3c and 3d respectively show the curve for Conductors KISO-4B-R and KISO-4B-S. The former is almost same as KISO4B(S), in shape. In this curve the peak frequency is about 7 Hz, and the notch one about 0.8 Hz. The latter is quite different from the former at the low frequen-

cies although there are no differences between them at the high frequencies. These curves suggest us that the twisting directions of the strand bundles in the outer and in the inner layer influence the loss feature at the low frequencies.

3. Discussion Figure 4 shows the qualitative frequency characteristics of the normalized loss in the conductor. The frequency characteristic curve has generally two peaks at two frequencies just as so in Conductor KISO-4B(S); the lower frequency is denoted by f~ and the higher one by f~. The f~ is related to the inter-strand coupling time-constant r,,, i.e., J'~ = 1/(2~-r~). On the other hand, f¢ is the so-called skin frequency of the normal metal which is located around the strand bundle in the f

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conductor. In the low-frequency region where a frequency f is smaller than f~, the applied magnetic field can penetrate into the whole cross section of the conductor. It is in this region only that the loss values can be obtained from our previous analysis [3]. In the case of the middle-frequency region where fc < f < re, the applied field does not penetrate into the strand bundle. In this case the shielding current flowing in the strands and crossing the solder or the other normal metal does not decay. It must be noted that the applied field can easily penetrate into each strand because the intrinsic coupling time constant of the strand ~'s is much smaller than r~. In the case of the high-frequency region where fe < f , the applied field cannot penetrate into the conductor because the shielding current flows in the normal metal located outside the strand bundle in the conductor. We can quantitatively calculate the loss-frequency characteristic curve at the low-frequency region only, by using the finite element method (FEM) [3]. As for KISO-4B(S), the twisting directions of the strand bundles in the outer and in the inner layer are opposite. At the low-frequency region, a large loss is generated in the conductor, because a large amount of the coupling current flows between the two layers. In fig. 4 it is shown by a solid line. The broken line in fig. 4 shows the loss assuming that the twisting directions of KISO4B(S) are the same. The loss reduces to 1/10 of the former at this frequency region. Thus the loss varies according to the twisting directions of the strand bundles, because the distribution of the shielding voltage in the conductor, and consequently the path of the shielding current, depends on the twisting directions. In the case of DESIGN-M, the loss again reduces to 1/10 of the broken line. It is generated in the alu-

375

minum stabilizer located outside the strand bundles. In fig. 4, fc and the peak value at fc can be easily obtained from the approximate calculation, but fc itself can not. So, we here obtain fc by using both the calculated loss for f < f c and the peak value at fc; wcp, which is assumed as wcp = 7%', where ~" is the volume fraction of the strand bundle including the area surrounded by the strands to the whole conductor [7]. This assumption comes from the similarity of the conductor to a multifilamentary wire. In the case of KISO-4B(S) the frequency characteristic curve, as mentioned above, typically has two peaks. But as the measuring region includes the part of the large frequency only, it has one peak of fe and one notch only (fig. 3a). In the case of DESIGN-M (fig. 3b), as the loss at the region of the low frequency is , as mentioned before, so small that the two peaks are very near. These measured data also agree with our analytical results. As for KISO-4B-R and KISO-4B-S (figs. 3c and 3d), the measured data at the peak of fe and its surrounding region agree with our analytical prediction, i.e.: The position of fc of KISO-4B-R is shifted to the lower frequency than that of KISO-4B-S. The reason is as follows: In the case of KISO-4B-R and KISO-4B(S), the twisting directions of the strand bundles of the two layers are opposite. Then zc is large and consequently f~ is small. On the other hand, in the case of KISO-4B-S as well as the broken line case of KISO-4B(S) in fig. 4, the twisting directions are same. Then zc is small and f~ is large. In order to keep the stability of the coil system, it is necessary to reduce the loss power produced in the conductor. The decrease of the loss per cycle will result it. We. therefore, propose to decrease the loss per cycle near 0.1 Hz. The loss-frequency characteristic curve, as mentioned above, has two peaks and one notch between them. When we take into account that it is impossible to get 0.1 Hz <
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F. Surniyoshi et al. / Sweep-ratedependencesof losses

of the strand. In the frequency region including the notch, fc < f < f ~ , the shielding c u r r e n t is constantly kept at this value i n d e p e n d e n t of f. This shielding c u r r e n t is s u p e r p o s e d on the o p e r a t i n g t r a n s p o r t current of the conductor. This confirms the stability of the coil system. K I S O - 4 B - R is b e t t e r t h a n KISO-4B-S not only for the purpose of adjusting the n o t c h to 0.1 Hz, but also for unifying the c u r r e n t distribution in the c o n d u c t o r because the twisting directions are opposite. This m e a n s that we h a d b e t t e r increase %. This is very different from, or opposite to, the c o m m o n design concept of the c o n d u c t o r in which, in o r d e r to reduce the loss, the c o n d u c t o r is used in the condition of f
References [1] O. Motojima and LHD Design Group, Design status of superconducting large helical device, IEEE Trans. Magn. MAG-27 (1991) 2214-2219.

[2] T. Mito, J. Yamamoto, K. Takahata, N. Yanagi, O. Motojima and LHD Design Group, Development of superconducting conductors for large helical device, IEEE Trans. Magn. MAG-27 (1991) 2224-2227. [3] T. Kawashima, F. Sumiyoshi, N. Oohito, T. Nagase, T. Mito, J. Yamamoto and K. Takahata, Losses of superconducting conductors for large helical device, IEEE Trans. Magn. MAG-27 (1991) 2154-2158. [4] Special issue on the IEA large coil task, eds. D.S. Beard, W. Klose, S. Shimamoto and G. Vecsey, Fusion Engrg. Des. 7 (1988) 191-196. [5] T. Mito, K. Takahata, N. Yanagi, S. Yamada, A. Nishimura, M. Sakamoto and J. Yamamoto, Short sample tests of full-scale superconducting conductors for large helical device, IEEE Trans. Magn. MAG-28 (1992) 214217. [6] F. Sumiyoshi, Y. Kanai, T. Kawashima, M. Iwakuma, T. Mito, K. Takahata, N. Yanagi and J. Yamamoto, Losses of aluminum-stabilized superconducting conductors for large helical device, IEEE Trans. Magn. MAG-28 (1992) 210 213. [7] W.J. Carr Jr, AC loss in a twisted filamentary superconducting wire, J. Appl. Phys. 45 (1974) 929-938.