Field and temperature dependencies of critical current on industrial Nb3Sn strands

ELSEVIER PII: SOOll-2275(97)00151-3

Cryogenics 37 ( 1997) 865-875

0 1998 Elsevier Science Ltd. All rights reserved

Printed in Greal Britain

WI l-2275/98/$19.00

Field and temperature dependencies of critical current on industrial Nb,Sn strands A. Martinez and J.L. Duchateau

Association EURATOM-CEA, Departement de Recherches sur la Fusion Contrblee CEA Cadarache, F-13108 Saint Paul Lez Durance, France

Received 8 September 1997

The increasing need for high field magnetic devices has focused attention on filamentary Nb$n conductors, whose critical data are superior to NbTi conductors. To choose the suitable operating parameters and to determine the stability margin of magnet systems, it is very important to know the effect of temperature and magnetic field on the superconducting properties, especially on the critical current. Up to now, for design calculation, the so-called “Summers model” was assessed theoretically on experimental data obtained by Spencer et al., (The temperature and magnetic field dependence of superconducting critical current densities of multiinflammatory Nb,Sn and NbTi composite wires. /EEE Trans Mag, Mag-15 (1979) 76) and Suenaga et al., Superconducting critical-current densities of commercial multifilamentary Nb,Sn(Ti) wires made by the bronze process. Cryogenics (1985) 25,123). Apart these very useful preliminary experimental data, very little has been done on the very different industrial strands which are now produced in the industry. Industrial Nb,Sn strands are generally tested and checked only at 4.2 K and their operating design temperature is often very different, sometimes around 6 K. It is now urgent to validate the model and to confirm that the data taken up to now in the design calculations are conservative. 0 1998 Elsevier Science Ltd. All rights reserved

Keywords: critical current density; upper critical field; Nb$n

Nomenclature

JC Critical current density T Temperature B Magnetic field B c2 Critical field

B c20 Zero-temperature critical field T CO Zero-field critical temperature B c20m Maximum (strain-free) upper critical field T corn Maximum zero-field critical temperature E Uniaxial strain

In this study are presented the magnetic field and temperature dependencies of the transport current density J, in two Nb,Sn multi-filamentary strands, one manufactured by Eur- opa Metalli and the other manufactured by Vacuum- schmelze, in the frame of the ITER programs. The results of the critical current measurements of these wires, at a temperature between 4.2 K and the critical temperature, Tco, and in magnetic fields, B up to 20 T, are compared with the Summers model’.2.

Experimental procedure

Principle of the cryostat

The variable temperature cryostat has been described in more detail elsewhere3, therefore only a brief description is given here.

The difficulty in measuring the critical current of superconducting strands, in magnetic fields which can reach 20 teslas, is to supply a current of approximately 500 A to the strand to be tested without temperature modification. To solve this problem, we have used a new principle. Two current leads are cooled by helium circulation, their two cold ends are connected by a sample support making up a thermal shunt. The superconducting strand to be tested is wound around this support and thermalized by helium which is at the same temperature. The electrical resistance of the support must be high enough to limit the current circulating in the support to a negligible value, when the strand to be tested is in the superconducting state.

Description

The test cryostat is an insert-cryostat which is placed in an existing 80 K cryostat. The general diagram is shown in

Cryogenics 1997 Volume 37, Number 12 665

Field and temperature dependencies of critical current: A. Martinez and J.L. Duchateau

Figure 1. It essentially includes a helium tank of about 18 1. This annular tank is pressurized up to a maximum pressure of 0.29 Mpa. It therefore allows the performance of measurements in supercritical helium. A pressure/backpressure regulator system regulates the pressure to the desired value. The helium extracted through the lower part is supplied to the two current leads. If liquid helium is used, an evaporator/heater helps to supply the current leads in helium gas at an adjustable temperature. Two control valves, placed at the outlet of the current leads, regulate the temperatures of the two cold ends at the same set point (5 K < r,, < 20 K). The stability of the temperature is then better than 0.1 K. The sample holder is connected to the cold ends of the current lead. During the test, the cryostat is maintained under vacuum by cryopumping.

Sample

The sample (see Figure 2) is connected to the current lead ends by two high-purity copper bus bars (Residual Resis- tivity Ratio (RRR) = 400) which are as symmetrical as possible to minimize the temperature gradient. The reaction mandrel is a Versailles Project on Advanced Materials And Standards (VAMAS) type titanium mandrel which is also kept for the test without any tranfer and possible associated degradation. Two copper ends are soldered ono the titanium mandrel for the sample terminations. A thin copper cylinder is added after reaction to ensure a very uniform temperature of the mandrel. This piece is not in electrical contact with the strand to avoid any low resistance short circuit. Two Cemox temperature sensors are installed at the top and the bottom of the sample. The third one is installed in the very middle of the sample. The insertion of the sensor in front of the central turn of the sample after reaction is possible

cold ends of current leads

0 2 4 6 6cm I I I I ,

Figure 2 The sample.

REGULATING (P .Z 0.29 MPa)

Pa

INSULATING TUBE

HELIUM TANK

CURRENTING LEADS

y \I_/ I‘--- CRYOPUMP

INDIUM SEAL WA HYBRID MAGNET

SAMPLE

Figure 1 Diagram of the variable temperature cryostat.

866 Cryogenics 1997 Volume 37, Number 12


Figure 3 Nb,Sn composite (bronze route process) manufactured by Vacuumschmelze.

by drilling a transverse channel in the mandrel. Two voltage tap couples, one across the central turn and the other across the seven turns monitor the resistive transition of the sample.

Strands

Two strands, representative of the European industry, have been tested. Strand 1 is manufactured by Vacuumschmelze (Figure 3) and strand 2 is manufactured by Europa Metalli (Figure 4). The thermal reaction process and the wire com- position are represented in Table 1.

Results

General principles

The helically wound Nb,Sn wire is placed in a stable magnetic field, at a fixed temperature. In the homogeneous region of the field, two voltage taps are positioned across one turn of the helix. The sample current is then increased through the superconductor. Initially, the sample current does not cause any significant movement of magnetic flux lines from their pinning sites, and the voltage across the one turn is zero. Eventually, at sufficiently high sample currents, flux is depinned and flows across the superconductor.

Figure 4 Nb,Sn composite (bronze route process) manufactured by Europa Metalli.



Table 1 Parameters of the two investigated Nb,Sn strands Measuring conditions

Company Strand 1

Vacuumschmelze

In these tests we were limited by the power supply to a maximum current of 500 A.

Process Wire diameter Cu/non-Cu Twistpitch Ternary Heat treatment

Number of filaments Filament diameter

Bronze route 0.81 mm

1.5 8mm

N bTa 7.5 w/o 57O”C/220 h 65O”C/175 h

4675

4pm

The magnet used for the wire test was the CNRS hybrid magnet (High Field National Laboratory, Grenoble). The quoted field values are within an accuracy of 10m3 tesla over the length of the strand between the voltage contacts.

The sample current was measured using a shunt with an accuracy of 0.5%.

Strand 2

Company Europa Metalti

Process Internal tin Wire diameter 0.81 mm Cu/non-Cu 1.5 Twistpitch 10 mm Ternary NbTa 7.5 w/o Heat treatment* 185”C/120 h

34O”C/72 h 650%/200 h

Number of filaments 5400 Filament diameter 3.5 pm

*This heat treatment does not correspond with the one commonly specified by Europa Metalli.

The greatest source of inaccuracy is the possible temperature gradient between the top and the bottom of the titanium mandrel. In the presence of current the inevitable sources of Joule heat must be minimized. In practice, the temperature can be reduced by careful consideration of the thermal paths intrinsic to the sample support, and can be compensated by an adequate temperature regulation of the cold end of the current leads.

In practical terms this means that the accuracy in the determination of temperature is limited to f 0.025 K (mean square deviation) up to 8 K and & 0.05 K (mean square deviation) up to 17 K.

Analysis

Kramer’s model

The dependence of critical current density Z, on magnetic field B can be inferred from the flux pinning model. The expression for the volume pinning force Fp (B,T) = B x .I,

(BJ’) is most often used in the form of multiplication of two functions; one is temperature-dependent Fpo (Z’), the other magnetic field-dependent. In general, the magnetic field-dependent part can be written as

The curve of the voltage as a function of sample current at this fixed field and temperature is recorded on a data acquisition system.

This characteristic V-Z transition is subsequently measured at different fields (up to 20 7’) and temperatures (up to 17 K) throughout the superconducting phase.

The Laplace force caused by the interaction of the sample current with the applied field acts as a tensile stress to the strand. The helically wound wire generates a central field parallel and with the same direction as the back- ground field.

Critical current definition

A superconductor composite becomes progressively resistive as the current through it is increased, according to the relation

v = h(Z)

where I and V are, respectively, the sample current and the resulting voltage appearing across the composite superconductor and $, n are constant.

The critical current Z, is defined as the sample current which results in the appearance of an electric field of 0.1 pV/cm along the conductor. The value of the exponent n is representative of the abruptness of the transition from the superconducting to the normal state.

The sample current is increased at a rate of 1 A/s up to a value close to the critical level and then adjusted to 0.1 AZs as the critical level is approached.

The electric field corresponding to the criterion is measured through two voltage taps situated at a distance of 0.08 m from each other.

f(b) = bp( 1 - b)Q

where b is the reduced magnetic field b = BIB,, (Bc2 is the so-called upper-critical field) and p, q are parameters dependent on the specific material.

The commonly accepted and widely used flux pinning model of Kramer predicts P = 0.5 and q = 2, for most Nb,Sn superconductors. In the frame of Kramer’s model it is possible to extrapolate the value of the upper critical magnetic field Bc2 from Z, (B) measurements, at a fixed temperature (for instance T = 4.2 K). The Kramer current, Zk, is decreasing linearly as a function of the field and is crossing the B-axis at Bc2

Zk = c5Bo.25 = A(Bc2 - B)

where A is a function only of temperature for a given superconductor. In Figure 5, Z, is plotted for strands 1 and 2. The Kramer’s fit (solid line), shown in figures, is good, with a linear regression coefficient larger than 0.99.

For both strands, the high Bc2 value, as obtained by this linear extrapolation, is certainly larger than the actual critical field because of the peculiar downward curvature for B > 18 T in the Kramer plot.

n Value determination of strand 1

The n value can be determined by plotting log V vs. log I. The n value is the slope of such a log V vs. log Z fit, calculated through the least squares method. Typically, the elec-



A Kramer plot of the critical current vemus field at ,4.2 K for the strand 1

35

30

A

g 25

k g 20

2? z 15

t E 10 e Y

5

0 Ik = -1.27.8 + 35.36

0 5. 10 15 20 25 30 Ba (4.2 K) 27.74 T =

Magnetic field (T)

A Kramer plot of the critical current versus field at 4.2 K for the strand 2

10 15 20 25 30 Y = -1.791 .B + 44.506

Magnetic field (T) & = 24.05 T

Figure5 A Kramer plot for strands 1 and 2, respectively.

tric field range used to determine the n value is O.l- 1 PVlcm.

The n values generally decrease with increasing magnetic field. But, as is seen in Figure 6, an increase in the magnetic field does not cause an appreciable decrease in n value.

Equation of critical current density

The critical current density .I, strongly depends on the magnetic field, temperature and strain. Summers et ~1.~ obtained the following critical current density formula as a function of field B, temperature T and uniaxial intrinsic strain E, on

the basis of the previous work of Hampshire et al5 for temperature dependence, and Ekin6 for strain dependence.

J,(&T,e) = C,(B,,(T,E))-“~ (1)

(1 - P)W”( 1 - !7)2 (A/m*)

where

&2(T,E) = &20(E)(l - &Cl - r/3) (T) (2)

&20(E) = ~,2rm(1 - 900W7) (r) (3)

b = B/B,,( T,E)



n-value versus magnetic field at 4.2 K for the VAC strand

50

45

40

35

S 30

2 25

= 20

15

10

5

0

0 2 4 6 6 10 12 14 16 16

magnetic field, 1

Figure 6 n-Value vs. magnetic field at 4.2 K for strand 1.

T&(E) = T&J 1 - 9001$.7)‘~ (4) For strand 1, we have finally found:

t = T/T,(E) Bc20 = 31.6 T

B c2om = The maximum (strain-free) upper Kramer critical field (2’)

Tdhn = The maximum (strain-free) zero-field critical temperature (K)

C0 = The coefficient independent of field, temperature and strain (A’P,5m-2)

E = The uniaxial strain

The last four are input parameters for fitting. It has to be clearly pointed out that the Summers model,

through Equation ( 1 ), is that consistent with a Kramer approach of the upper critical field. All the critical fields in reference in the model (Bc2, Bc2,,, BcZOm) are Kramer fields, and not actual critical fields.

Basic consideration of curve fitting

Instead of finding the four parameters through a fit of expression ( 1) to the experimental we have chosen a different approach. Bc2,,,,, and Tcom will be discriminated thanks to a partial check of the Summers model through Equation (2). which does not involve C,. This last parameter will be determined in a second step by fitting Equation ( 1) at 4.2 K.

Fitting of critical current data of strand 1

In the frame of Kramer’s model it is possible to extrapolate the value of the upper critical field Bc2 (7’) from 1, (B) measurements, at different temperatures, T. The experimental values of the Kramer upper critical field B,, at different temperatures, T, have been fitted to the Summers relation (2) where B,, and Tco are the coefficients determined by the least squares method (see Figure 7). Two different heat treatments have been applied to strand 1, remarkably leading to the same curve B,, (T> and affecting only C,.

T‘,, = 16.2 K

The strain E relates to sample fabrication or handling, and operation conditions (temperature, Laplace force). We assume a precompression of - 0.22%, an assumption con- firmed by recent experiments.

Using the relationships of (3) and (4), we have deduced the value of the maximum (strain-free) zero field critical temperature Tcom and the maximum (strain-free) upper critical field BczO,,,.

B c2,,,,, = 32.5 T

T&, = 16.4 K

Up to now, for the ITER project, the basic design criteria have taken into account in a simplified approach, for all strands:

B c20m = 28 T

T,,= 18K

This is not satisfactory as is pointed in Figure 7. Therefore the best fit to the experimental critical current

data at 4.2 K has been found by using constant parameters of Bczomr T,, and E, and varying C,. So, the experimental values of the critical current Z, at 4.2 K has been fitted to expression (1) where C,, is the coefficient determined by the least-squares method. We finally found:

C, = 7.05 109A P.5m-2.

The agreement of the experimental critical current data at 4.2 K with the curve expressed by Equation (1) is fairly good for the following parameters:


Figure 7

35

0

35


Comparison of Summers fit of Bcz (T) versus data for the strand 1

0 5 10 15 20

Temperature (K)

Comparison of Summers fit of Bc2 (T) vews data for the strand 2

Ot

0 5 10 15

Temperature (K)

Comparison of Summers fit of SC, (7J vs. data for both strands.

20

B czom = 32.5 T

Tco,, = 16.35 K

Co = 7.05 1 09A P-5m-2

E = - 0.22%

(5)

These parameters (Bc2,,,,,, T,,,, C,, and E) are held constant for the calculation of the critical current density J, vs. the magnetic field B at temperatures between 4.2 and 11 K.

It is seen that the fitting of experimental critical current data, using Equation [ 1 ] with the values of the parameters

given in Hampshire et ~1.5, is reasonably appropriate (see Figure 8).

Fitting of critical current data of strand 2

In the same way, the agreement of the experimental critical current data at 4.2 K with the curve expressed by Equation ( 1) is fairly good (see Figure 8) for the following parameters:

B c20m = 29.1 T(B,,, = 28.6 T)

Tcom = 16.9 K(T, = 16.8 K)



Comparjson of calculated values of Jc versus data, at different temperatures for the strand 1 (low temperature region)

2500E+09 -, I

2.000E+09

1500E+09

1 .OOOE+09

5.000E+06

O.OOOE+OO

I 0 Jcmes(4.2 K)

; - Jccal(4.2 K)

j 0 Jcmes(5.2 K) I --- Jccal(5.2 K)

! x Jcmes(6 K)

I____- - Jccal(6 K)

I + Jcmes(7 K)

i_.-- Jccal(7 K)

5 10 15 20

Magnetic field (T)

Comparison of calculated values of Jc versus data, at different temperatures for strand 2 (low temperature region)

0 JCmes(4.2 K)

/ - JCcal(4.2 K)

I O JCmes(5.2 K)

--- JCcal(5.2 K)

x JCmes(6 K)

:-.... 1 - JCcal(6 K)

i + JCmes(7 K)

I- I- - - - JCcal(7 K) I

5 10 15 20

Magnetic field (T)

Figure8 Comparison of calculated values of .I, vs. data, at different temperatures for both strands. (a) High temperature region; (b) Low temperature region.

C, = 1.13 10’0AT0+r-2

E = - 0.16%

Divergence ratio of experimental J, from summers model

In Figure 9, the divergence ratio of experimental J, from the Summers model is presented as a function of fields and temperatures for both strands. It is clearly visible that the experimental values of J, diverge at high fields and high temperatures in comparison with the values given by the Summers model. This divergence cannot be explained by

the temperature measurement accuracy which is situated at a lower level ( C 10%). It points out the limits of the application of the model.

Remark on Kramer upper critical field Bc2 vs. T

In Figure 10 (for both strands 1 and 2), the actual values of Bc2 obtained by zero linear extrapolation of I, (Z’), at a given magnetic field, B, are compared with the fit (expressed by the relation (2)) deduced from the experimental values of the Kramer upper critical field Bc2 at different temperatures, T. This is to point out the large discrep- ancy between the Kramer upper critical field and the actual upper critical field, especially at high field.



2.50E+09

n^ E

a 2.00E+09 - >,

.*

t 150E+09

4

2 t l.OOE+09

3

= .Y 500E+08 .E

0

O.OOE+OO i-

comparison of calculated values of Jc versus data, at different temperatures for the strand 1 (high temperature region)

w Jcmes(8 K)

- Jccal(8 K)

A Jcmes(9 K) --- Jccal(9 K)

0 Jcmes(l0 K _ . - - - - Jccal(l0 K)

A Jcmes(l1 K -.-- Jccal(l1 K)

0 2 4 6 8 IO 12 14 16 18

Magnetic field (T)

Comparison of calculated values of Jc versus data, at different temperatures for the strand 2 (high temperature region)

2.50E+09 \ ‘, \

. \ I I

0 2 4 8 8 10 12 14 16 18

Magnetic field (T)

Figure 8 Continued.

Conclusions

We have analysed the measurements of the critical currents of two Nb,Sn strands manufactured by European compa- nies. The measurements were performed at temperatures between 4.2 and 11 K in magnetic fields up to 20 T. In the frame of the Summers model, we have proposed a method to fit the experimental results, using a fit of experimental Kramer Bc2 (T). For both European strands the method is satisfactory: around 8 K and 13 T, a range of temperature and field which are quite relevant for ITER design, the divergence ratio is around lo%, which is acceptable.

A JCmes(9 K)

--- JCcal(9 K)

0 JCmes(l0 K)

_ _ _ . . -JCcal(lO K) -.____I A JCmes(11 K)

__-. JCcal(l1 K)

Acknowledgements The authors acknowledge essential contributions from the staff of a department especially the cryogenic subdivision, MS Bocquillon, Nicollet, and M Serries for the apparatus thermal adjustment and M Cloez for the preparation of the samples. Part of this work was done within the framework of a collaboration with the Grenoble High Magnetic Field Laboratory (CNRS ).

References 1. Spencer, X., Sanger, P.A. and Young, M., The temperature and mag-

netic field dependence of superconducting critical current densities of



Divergence ratio from Summers model as a function of fields and temperatures for the strand 1

loo% 1 I I j I

c 90% i I I L--l FAi E *

80% (04.2 K

L 70% 05.2 K

m

0” x6K

60% 7 ‘+7K r

z 50% w8K

E 40%

< I 30%

3 i

A9K

010 K

~11 K

g 20%

1 (Y 10%

0%

0 2 4 6 8 IO 12

Magnetic field (T)

14 16 18 20

Divergence ratio from Summers model as a function of fields and temperatures for the strand 2

100%

90%

80%

70%

60%

50%

40%

30% I

20% = I 1

10%

0%

8 IO 12

Magnetic field (T)

Figure9 Divergence ratio of experimental J, from the Summers model as a function of fields and temperatures for both strands.

2.

3.

multifilamentary Nb,Sn and NbTi composites wires. lEEE Tram Mag, 1979, 15, 76.

4.

Suenaga, M., Tsuchiya, K., Higuchi, N. and Tachikawa, K., Supercon- ducting critical-current densities of commercial muhifilamentary Nb,Sn(Ti) wires made by the bronze process. Cryogenics, 1985, 25, 123.

5.

Jager, B., Bocquillon, A., Chaussonnet, P., Martinez, A., Nicollet, S., Serries, J.P. and Vallier, J.C., A variable temperature cryostat to meas-

ure Jnon~v of ITER strands up to 20 teslas, ICEC16BCMC Proceedings May 1996, 435-438

6.

Summers, T., Guinan, M.W., Miller, J.R. and Hahn, P.A., A model for the prediction of Nb,Sn critical current as a function of field, temperature, strain, and radiation damage. IEEE Tram Mag, 1991, 27, 2041. Hampshire, P., Jones, H. and Mitchell, E.W.J., An in-depth charac- terization of (NbTa),Sn filamentary superconductor. IEEE Tram Mag, 1985, 21, 289. Ekin, W., Strain scaling law for flux pinning in practical superconductors. Partl: Basic relationships and application to Nb,Sn conductors. Cryogenics, 1980, 20, 611.



ii p” ‘? 3

5

0

35

30

z u 25 Z

; 20

0

:; 15

t g 10

3

5

0

Strand1

I I I I f 0

, I

4 8 12 16

Temperature (K)

Strand 2

0 4 8 12 16

Temperature (K)

Figure 10 Upper critical fields as a function of temperature.


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Field and temperature dependencies of critical current on industrial Nb3Sn strands