Magnetic and mechanical AC loss of the ITER CS1 model coil conductor under transverse cyclic loading

Physica C 310 Ž1998. 253–257

Magnetic and mechanical AC loss of the ITER CS1 model coil conductor under transverse cyclic loading Arend Nijhuis a

a,)

, Niels H.W. Noordman a , Herman H.J. ten Kate a , Neil Mitchell b, Pierluigi Bruzzone c

UniÕersity of Twente, Faculty of Applied Physics, P.O. Box 217, 7500 AE Enschede, The Netherlands b ITER JCT, 801-1 Mukouyama, Naka-machi, Naka-gun, Ibaraki 311-01, Japan c EPFL-CRPP, PSI, Villingen, CH 5232, Switzerland

Abstract The magnetic field in a coil results in a transverse force on the strands pushing the cable towards one side of the jacket. A special cryogenic press has been built to study in a unique way the mechanical and electrical properties of full-size ITER Cable-in-Conduit ŽCIC. samples under a transverse, mechanical load. The press can transmit a variable Žcyclic. force of at least 650 kNrm to a cable section of 400 mm at 4.2 K. The jacket around the cable is partly opened in order to transmit the transverse force directly onto the cable. A superconducting dipole coil provides the AC magnetic field required to perform magnetisation measurements with pick-up coils. In addition the interstrand resistance Ž R c . between various strands selected from topologically different positions inside the cable is measured. The force on the cable as well as the displacement are monitored simultaneously in order to determine the effective cable Young’s modulus and the mechanical heat generation due to friction and deformation as the force is cycled. The mechanical heat generation, the coupling loss time constant nt and R c of a full-size ITER conductor have been studied under load for the first time. An important result is the significant decrease of nt , after cyclic loading. It is also observed that the mechanical heat generation decreases with cycling. q 1998 Elsevier Science B.V. All rights reserved. Keywords: Coupling loss; Transverse loading; Interstrand resistance; Cable-in-conduit; Young’s modulus; Time constant

1. Introduction The electromagnetic AC loss in superconductors consists of hysteresis and coupling loss w1x. When the conductor carries a transport current, the enhanced interstrand conductivity due to the Lorentz force working on the contacts in a cable is a potential reason for higher coupling loss, besides the loss ) Corresponding author. Tel.: q31-53-489-3889 Žoffice., q3153-489-3841 Žsecr. . ; Fax: q 31-53-489-1009; E-mail: [email protected]

increase due to the dynamic resistance Žcurrent saturation at high field rate.. Transverse loading of the ITER conductors due to Lorentz forces is the cause of mechanical effects and variations in the transverse electrical resistivity and contact patterns in the cable. Previous work performed at the University of Twente addressed experimentally the dependence of the cable coupling loss on Lorentz forces in sub-size cables w2x and on cabling parameters such as void fraction, Cr layer thickness and vendor, type of cabling and cabling stage w3,4x. The aim of this study is to measure the

0921-4534r98r$ - see front matter q 1998 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 3 4 Ž 9 8 . 0 0 4 7 1 - 7

A. Nijhuis et al.r Physica C 310 (1998) 253–257

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mechanical Ždeformation, elastic module, frictional heating. and electrical Žtransverse interstrand and -stage R c and nt . properties of full-size cable samples under transverse, mechanical loading. In the case of multistage cables, many different current loops are linked by strand-to-strand crossover contacts everywhere in the cable, all having their characteristic resistance and length sometimes matching with the cable pitches Ž L p .. In fact, this means the loss represented by a particular time constant is created in only a Žsmall. part of the total strand volume, Õ. For that reason, a multiple time constant model ŽMTC. was developed assuming the presence of N dominant time constants all interacting by shielding with a weighted volume fraction Õ w5x.

p

Qcpl s

ž / ½ž Ý ž Ba2

m0

Ny1

v ÕN n N t N 1 q v 2t N2

v Õk n kt k

q

1 q v 2t k2

ks1 N

=

Ł

lskq1

ž

/

/

1 1 q Õ l n l v 2t l2

/5

Jrm3 .

Ž 1.

Qcpl is the coupling loss, Ba is the applied AC field amplitude, v s 2p f and f is frequency of the applied field. Eq. Ž1. can be used to fit N effective time constants Ž k s 1 to N ., Õ k n kt k to the measured coupling loss curve. The shielding effect on the hysteresis loss at higher frequencies can be taken into account using w5,6x: N

Q hys s Qst Ł

ks1

žŽ

1 2

1 q Õ k n k Ž 2p f . t k2 .

for Ba ) Bp , Jrm3 .

0.5

/

2. Magnetisation measurements The data obtained from the magnetisation measurements can be used to fit a set of time constants Ž N s 2. using the MTC model from Ref. w5x. The values for t k and Õk n k found after fitting are gathered in Table 1. The values found for nt using the initial slope of the loss curve are presented in the right column of Table 1 and the fitted curves are presented in Fig. 1. The nt of the virgin cable for Ba s 200 mT in 0.6 T DC background field amounts to 143 ms. Fig. 1 shows the total loss vs. the frequency of the applied sinusoidal field after loading in comparison with the loss of the virgin sample. The nt determined from the initial slope at f s 0 Hz with the MTC model decreases with the number of cycles to 33 ms after 38 cycles in the case without load Ž F s 0 kN.. If a load is applied of 650 kNrm, then the nt increases to 74 ms. It should be emphasised here that these nt ’s are estimated using the initial slope of the loss vs. f curve. These values are not applicable for a calculation of the coupling loss at higher frequencies because they will clearly result into an over estimation of the loss. A distinction can be made between the coupling loss at very low and higher regimes of the field ramp rate. The nt only from the slope of the loss curve for a cycle time T s lrf F 30 s is 30 ms with full load and 21 ms without load. It is striking that the MTC analysis gives a very high time constant of 4 s for a loaded cable in apparently a very small volume fraction. It contributes for more than an equivalent part Ž Õ 1 n1t 1 s 41 ms. to the total coupling loss in comparison to the

Ž 2.

Qst is the hysteresis loss at zero frequency. The mechanical AC loss is mainly caused by friction and deformation and is indirectly originated by the Lorentz forces on the conductor. The total mechanical loss dissipated in one complete loading cycle is described by Q M s HFd x wJrm3 x in which F is the transverse load on the specimen section and d x represents the transverse displacement. The details of the press, the CS1.1B type of cable and its instrumentation are reported in Ref. w7x.

Table 1 The t and Õn-values found after fitting the measured magnetisation data to the MTC model Condition

k

Õk n k w-x

tk wmsx

Õk n kt k wmsx

ÝÕk n k t k wmsx

Virgin

1 2 1 2 1 2

0.25 0.09 0.077 0.012 0.010 1.36

510 140 380 273 3930 24

130 12.5 29 3.2 41 33

143

0 kNrm 650 kNrm

33 74

A. Nijhuis et al.r Physica C 310 (1998) 253–257

Fig. 1. Results of the magnetisation measurements with pick-up coils on the CS1.1B sample and calculation of the loss. The upper curve is the total loss in the virgin state and the others show the loss with and without load, after 38 full loading cycles of 0–650 kNrm. Ba s 200 mT and the Bdc s 0.6 T.

lower time constant Ž Õ 2 n 2t 2 s 33 ms.. This might be due to the large amount of damage found in the Cr coating of the strand material and the last stage cable wrapping. It is assumed that the hysteresis loss is identical in both cases with and without load. This is not necessarily correct because the critical current and thus the hysteresis loss depends on the strain and thus on the applied pressure Ž F ..

3. Contact resistance measurements The interstrand resistance of selected strand combinations is measured in one of the petals Žintrapetal, petal s last stage cable wrapped with ribbon. and among strands selected from different petals Žinterpetal.. Fig. 2 shows the evolution of the average value of the measured R c ’s for different strand combinations vs. the number of loading cycles. The average interpetal R c without load saturates at 37 mV m. It seems that in the case with load a full saturation has not been reached after 38 cycles and the average value of the interpetal R c has reached a level of 4.2 mV m. After 38 cycles there still seems to be a rise of the intrapetal R c with cycling in the case of an unloaded conductor. The level of 330 nV m seems to be the upper limit of the intrapetal R c for a loaded cable with F s 650 kNrm. Some average R c values are gathered in Table 2.

255

Fig. 2. The average value of the intra- and interpetal contact R c ’s with F s 0 and 650 kNrm vs. the force and the number of loading cycles between brackets.

The R c between superconducting strand and the jacket amounts to approximately 300 mV m. Fig. 3 clearly shows that the intrapetal R c among strands not only decreases when the applied force is raised but also that a hysteresis behaviour of the resistance vs. applied force is noticed. A relaxation of the resistance value after unloading of the force is observed as well. No change of resistance in time Žcreep. under a full load of 650 kNrm is noticed. In the first cycles, hardly any change is observed in the intrapetal R c when load is applied. After 38 cycles the intrapetal R c decreases roughly to 60% when a load of 650 kNrm is applied. A similar behaviour is noticed for the interpetal resistance with a decrease of a factor of nine. The last stage cable pitch of a petal is 147 mm and R c amounts to 330 nV m. The petal pitch is 397 mm and the interpetal R c is 4.2 mV m. For the interpetal loss L2prR c is 38 kmrV and for the intrapetal loss this factor is 65 kmrV. This implies that the contribution of the last cabling stage to the

Table 2 Summary of average R c values State

F R c Intrapetal wkNrmx wnV mx

R c Interpetal wmV mx

Average Min Max Average Min Max Virgin 0 38 cycles 0 38 cycles 650

29 560 330

17 43 320 770 220 440

129 37 4.2

92 154 30 41 3.1 4.8

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A. Nijhuis et al.r Physica C 310 (1998) 253–257

Fig. 3. Interstrand contact resistance R c vs. load for two different strand combinations of the first two cabling stages inside a petal and between two petals after 21 cycles up to 650 kNrm, Bdc s 0.6 T and I s 50 A.

total coupling loss production is clearly relevant with respect to the intrapetal loss. This behaviour is clearly confirmed by the magnetisation measurements and the MTC analyses. The overall coupling loss for a time period T - 30 s increases by a factor of 1.5 when a load is applied, while the intrapetal R c decreases 1.5 times. The increase after loading of t l from ; 0.4 to 4 s, matches with the decrease of the interpetal R c Ž9 times.. This may lead to the saturation in current in parts of the conductor at already very low field ramp rates.

4. Mechanical behaviour The curves of the transversal displacement or compression Ž d y . of the cable as a function of the applied force Ž Fy . are presented in Fig. 4. It is shown that after 38 full cycles from zero to 650 kNrm the behaviour is still not completely reproducible though a certain saturation is developing. The total mechanical heat production during one cycle as presented in Fig. 5 decreases with the number of load cycles. The loss for a full cycle from zero to 650 kNrm amounts to 28 Jrm after 38 cycles Ž47 mJrcm3 for strand volume.. The coupling loss for a partial cycle from only D B s 13 y 12 T s 1 T, d Brdt s 1 Trs and nt s 30 ms amounts to 50 mJrcm3. The mechanical loss is by far lower than the total coupling loss production.

Fig. 4. Displacement d vs. applied force from the virgin state to cycle no. 38.

The overall elastic modulus E y can be written as E y s DFyrŽ A y d y . where D is the cable diameter and A y is the cable cross section Ž A y f 0.01 m2 .. The E y has a level of nearly 0.4 GPa at a load of 650 kNrm. For the stiffness of the cable at a certain level of stress Žand strain. we can define the dynamic elastic modulus as: EsyrE´ y s Ž DrA.EFyrEd y . In which sy is the transversal stress and ´ y is the transversal strain. The EsyrE´ y stays below a level of 10 GPa up to a load of 400 kNrm and then seems to increase gradually up to the modulus of Nb 3 Sn strand material Ž E f 100 GPa.. The stress inside the cable is calculated for two different configurations. In the case of the press arrangement, a surface force of 650 kNrm is exerted on the jacket and the average stress in the cable is ; 15 MPa. The stress in a conductor in a magnet is caused by a volume force in the cable and the average stress inside the cable amounts to ; 10 MPa.

Fig. 5. The total mechanical loss per cycle vs. the number of loading cycle for closed loops.

A. Nijhuis et al.r Physica C 310 (1998) 253–257

5. Conclusions The coupling loss time constant decreases with the number of cycles from 143 ms Žvirgin state. to values between 33 Žno load. and 74 ms Ž650 kNrm. determined from the initial slope of the loss curve. The nt from the slope of the total loss vs. frequency curve for a cycle time of the applied field Ba , T Ž Ba . - 30 s amounts to 21 ms with zero load and 30 ms with a load of 650 kNrm. Hysteresis and relaxation effects in the R c vs. applied force are observed. The contribution to the total coupling loss of the last cabling stage under full load Žwrapped petal. is in the same order as the intrapetal loss. The coupling loss for a time period T - 30 s increases by a factor of 1.5 when a load is applied, while the intrapetal R c decreases ; 1.5 times. The increase after loading of t 1 from ; 0.4 to 4 s in a small cable volume, matches with the decrease of the interpetal R c Ž9 times..

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The smeared Young’s modulus of the cable is less than 0.3 GPa at the full magnet Lorentz load. The total mechanical heat production during one cycle decreases with the number of loads and is by far smaller than the electromagnetic loss.

References w1x A.M. Campbell, Cryogenics 22 Ž1982. 3. w2x A. Nijhuis, H.H.J. ten Kate, P. Bruzzone, IEEE Trans. Appl. Supercond. 7 Ž2. Ž1997. 262. w3x A. Nijhuis, H.H.J. ten Kate, P. Bruzzone, L. Bottura, IEEE Trans. Mag. 32 Ž4. Ž1996. 2743. w4x P. Bruzzone, A. Nijhuis, H.H.J. ten Kate, Proc. of MT-15, Beijing, China, 1997. w5x A. Nijhuis, H.H.J. ten Kate, J.L. Duchateau, P. Bruzzone, Adv. in Cryog. Eng., Vol. 42, Plenum, New York, 1996, 1281. w6x V.B. Zenkevitch, A.S. Romanyuk, Cryogenics Ž1979. 725. w7x A. Nijhuis, N.H.W. Noordman, H.H.J. ten Kate, N. Mitchell, P. Bruzzone, Proc. of MT-15, Beijing, China, 1997.