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Change of a.c. energy losses of Nb-Ti composite superconductors with aging
Change of a.c. energy losses of Nb-Ti composite superconductors with aging N.M. Vladimirova, V . M . Drobin and E.I. Dyachkov Joint Institute for Nuclear Research, 1 4 1 9 8 0 , Dubna, Russia
Received 17 June 1992; revised 4 September 1992 A comparison of the a.c. energy losses of Nb-Ti composite superconductors at various time intervals over several years is carried out. The observed decrease of eddy current losses by a factor of 1 . 4 - 3.4 is probably associated with increasing effective transverse resistivity of the matrix due to diffusion b e t w e e n Nb-Ti and copper. The processes of aging did not result in a decreasing current-carrying capability.
Keywords: energy losses; Nb-Ti; composite superconductors
When applying superconductors in magnetic systems operating in alternating magnetic fields, the level of energy losses is one of the main characteristics of importance. Such energy losses have been studied extensively, both theoretically and experimentally ~-4. In this paper the results of research into the influence of one more factor, time, are presented. The initially determined results were subsequently confirmed by additional measurements. The measurements were carried out with a device described previously 5 using the calorimetric method at 4.2 K without a transport current in a pulsed magnetic field. The pulses were triangular in shape; the maximum amplitude of the magnetic field could change from 0 to 2 T and the velocity of change was between 0 and 6 T s -~. Subsequent measurements on five composite superconducting samples and a copper tube were performed 5 0 - 130 months later. The characteristics of all the samples measured are presented in Table 1. Samples 19, 30 and 31 were clusters of isolated wires, and samples 34 and 34A were pieces of tubular cable with isolated wires and a copper tube, of the type measured in reference 3. The results for the copper tube are shown in Figure 1. The dependence of energy losses on the velocity of change of the magnetic field remained unaltered after 88 months. This result testifies to the reliability of the experimental method. Concerning the results for composite superconductors, the losses changed for all samples except for sample 19 with a relatively small number of superconducting filaments (n = 61). For the samples with filament numbers 1045 and 2970 the energy losses decreased considerably; typical results are presented in
Figure 2. The measured dependences of the value of losses on the velocity of change of the magnetic field B are linear in character (Figure 2) and can be expressed by
W=A+CB where A is the value of hysteresis losses in a composite superconductor and C is a coefficient proportional to eddy current losses. The ratios A2/At and C2/C~ characterize the change of hysteresis and eddy current losses over the period of time between the two measurements. The results of the experiments for all the samples are presented in Table 2. The marked change in hysteresis losses observed in two cases out of ten did not support the above trends and, therefore, one can say only roughly that hysteresis losses did not change significantly with time. The current-carrying capability measured for the two samples also did not change. The dependence of critical current on external magnetic field is shown in Figure 3; a similar result is obtained for sample 34. Let us now consider what the ratio C2/C~ of changing eddy current losses depends on. From Table 2 one can see that a greater change was observed for the samples with the largest number of superconducting filaments. The dependence of decreasing eddy current losses on time for the samples with 2970 superconducting filaments is presented in Figure 4. This decrease is smaller for sample 30 with 1045 filaments, and not observed at all for sample 19 with 61 filaments. One can assume that the decrease in eddy current losses is connected with the increasing effective
0011 2275/93/060629 03 © 1993 Butterworth-Heinemann Ltd Cryogenics 1993 Vol 33, No 6
629
Change of a.c energy losses with aging." N.M. Vladimirova et al. Table 1
Sample characteristics
Sample
19
30
31
34
34A
Wire diameter (mm)
1.25
0.5
0.5
0.05
0.5
Number of filaments
61
1045
2970
2970
2970
Filament diameter (/~m)
110
10
6
6
6
Twist length (mm)
20
7
4
4
4
Sample volume (cm 3)
8.1
2.0
2.0
4.3
4.3
S/V (cm - 1)
172
1670
2850
2850
2850
Period of time between the t w o measurements (months)
128
69
70
65
51
Table 2
Cu tube (5 x 0.7)
12.5
88
Results of experiments for superconducting samples
"3"
~6
..~=I.0ST
Sample
19
30
31
34
34A
28.2 28.2 1.0
4.5 7.0 1.55
7.0 6.5 0.93
2.0 2.0 1.0
4.3 4.0 0.93
7.0 7.0 1.0
9.5 4.0 0.42
5.1 1.5 0.29
8.7 3.13 0.36
7.55 3.4 0.45
103.4 102.0 0.99
11.7 11.2 0.96
10.0 10.0 1 .O
8.0 6.0 0.75
6.5 6.5 1.0
57.9 59.2 1.04
13.4 9.52 0.71
6.75 3.0 0.44
9.9 4.75 0.48
10.75 5.75 0.53
B = 0.42 T
tE /~ t.s
A 1
A2
~2
A2/A1 C 1
1
3
2
C2
t,
C21Cl
E~,Ts-'
B = 1.05 T
Figure 1 Dependence of energy losses on velocity of change of magnetic field for the copper tube: • , • , first measurement; zx, o , second measurement (after 88 months)
A1 A2
A2/A1 C1 C2
C2/C1
30
B= 0.42 T
2o ,-- 10 ~" 0
I
B=I.0ST
I
I
I
•
200
-~ 2o 10 100
Figure 2 Dependence of energy losses on velocity of change of magnetic field for sample31: • , & , f i r s t m e a s u r e m e n t ; O, zx, second measurement (after 70 months)
transverse resistivity of a composite superconductor due to diffusion processes. Table 1 shows the S/V sample parameter, which determines the contact surface area per unit volume. A greater decrease in eddy current losses was observed for samples with a m a x i m u m contact surface between the two metals, in which cases the effects due to diffusion are seen to be greater.
630
Cryogenics 1993 Vol 33, No 6
B,T Figure 3 Dependence of critical current on magnetic field for sample 30: O, manufacturer's data; • , results observed in June 1991
According to the results of reference 6, in which for the same samples good agreement is shown between the measured and calculated dependences of eddy current losses, we estimate the effective transverse resistivity of
Change of a.c energy losses with aging. N.M. Vladimirova et al. Table 3
1.0~
B=I.0
Effective transverse resistivity calculation results
Sample
19
30
3!
34
34A
Pl ( x 10-1OQm) P2 ( x 10 l ° f ~ m )
3.71 3.63
1.96 2.76
1.27 2.85
0.86 1.80
0.79 1.49
0.5 B= 0.42 T
0
2'0
4'0
6'0
8b
t, m0nth Figure 4 Dependence of change in ratio C2/Cl of eddy current losses on time for samples with 2970 filaments (samples 31, 34 and 34A)
the composite superconductors using the formula
We -- 2gm/~ r ~[ (\271-/] ~L ] ~ 2p
"1-
which is valid for a rate of change of magnetic field equal to several teslas per second (in the case of our
samples). Here We is the eddy current losses per cycle per volume unit, Bm is the magnetic field amplitude, ro is the composite radius, lp is the twist length and P is the effective transverse resistivity. All values are calculated in SI units. The results of the transverse resistivity calculations are presented in Table 3 lbr a magnetic field amplitude of 1.05 T: pt represents the first measurement and P2 the repeated measurement made several years later.
References
1 Brechna, H. Superconducting Magnet Systems Springer Verlag, Germany (1973) 2 Wilson, M. Superconducting Magnets Oxford University Press, Oxford, UK (1983) 3 Chovanec, F. et al. Cryogenics (1981) 21 559-562 4 Agapov, Y.P. et al. IAE preprint-2913 Moscow, (1977) 5 Drobin, V.M. et al. JINR preprint, P-13-12(152 Dubna (1978) 6 Drobin, V.M. et al. Cryogenics (1982) 22 ~15- 119
Cryogenics 1993 Vol 33, No 6
631
Received 17 June 1992; revised 4 September 1992 A comparison of the a.c. energy losses of Nb-Ti composite superconductors at various time intervals over several years is carried out. The observed decrease of eddy current losses by a factor of 1 . 4 - 3.4 is probably associated with increasing effective transverse resistivity of the matrix due to diffusion b e t w e e n Nb-Ti and copper. The processes of aging did not result in a decreasing current-carrying capability.
Keywords: energy losses; Nb-Ti; composite superconductors
When applying superconductors in magnetic systems operating in alternating magnetic fields, the level of energy losses is one of the main characteristics of importance. Such energy losses have been studied extensively, both theoretically and experimentally ~-4. In this paper the results of research into the influence of one more factor, time, are presented. The initially determined results were subsequently confirmed by additional measurements. The measurements were carried out with a device described previously 5 using the calorimetric method at 4.2 K without a transport current in a pulsed magnetic field. The pulses were triangular in shape; the maximum amplitude of the magnetic field could change from 0 to 2 T and the velocity of change was between 0 and 6 T s -~. Subsequent measurements on five composite superconducting samples and a copper tube were performed 5 0 - 130 months later. The characteristics of all the samples measured are presented in Table 1. Samples 19, 30 and 31 were clusters of isolated wires, and samples 34 and 34A were pieces of tubular cable with isolated wires and a copper tube, of the type measured in reference 3. The results for the copper tube are shown in Figure 1. The dependence of energy losses on the velocity of change of the magnetic field remained unaltered after 88 months. This result testifies to the reliability of the experimental method. Concerning the results for composite superconductors, the losses changed for all samples except for sample 19 with a relatively small number of superconducting filaments (n = 61). For the samples with filament numbers 1045 and 2970 the energy losses decreased considerably; typical results are presented in
Figure 2. The measured dependences of the value of losses on the velocity of change of the magnetic field B are linear in character (Figure 2) and can be expressed by
W=A+CB where A is the value of hysteresis losses in a composite superconductor and C is a coefficient proportional to eddy current losses. The ratios A2/At and C2/C~ characterize the change of hysteresis and eddy current losses over the period of time between the two measurements. The results of the experiments for all the samples are presented in Table 2. The marked change in hysteresis losses observed in two cases out of ten did not support the above trends and, therefore, one can say only roughly that hysteresis losses did not change significantly with time. The current-carrying capability measured for the two samples also did not change. The dependence of critical current on external magnetic field is shown in Figure 3; a similar result is obtained for sample 34. Let us now consider what the ratio C2/C~ of changing eddy current losses depends on. From Table 2 one can see that a greater change was observed for the samples with the largest number of superconducting filaments. The dependence of decreasing eddy current losses on time for the samples with 2970 superconducting filaments is presented in Figure 4. This decrease is smaller for sample 30 with 1045 filaments, and not observed at all for sample 19 with 61 filaments. One can assume that the decrease in eddy current losses is connected with the increasing effective
0011 2275/93/060629 03 © 1993 Butterworth-Heinemann Ltd Cryogenics 1993 Vol 33, No 6
629
Change of a.c energy losses with aging." N.M. Vladimirova et al. Table 1
Sample characteristics
Sample
19
30
31
34
34A
Wire diameter (mm)
1.25
0.5
0.5
0.05
0.5
Number of filaments
61
1045
2970
2970
2970
Filament diameter (/~m)
110
10
6
6
6
Twist length (mm)
20
7
4
4
4
Sample volume (cm 3)
8.1
2.0
2.0
4.3
4.3
S/V (cm - 1)
172
1670
2850
2850
2850
Period of time between the t w o measurements (months)
128
69
70
65
51
Table 2
Cu tube (5 x 0.7)
12.5
88
Results of experiments for superconducting samples
"3"
~6
..~=I.0ST
Sample
19
30
31
34
34A
28.2 28.2 1.0
4.5 7.0 1.55
7.0 6.5 0.93
2.0 2.0 1.0
4.3 4.0 0.93
7.0 7.0 1.0
9.5 4.0 0.42
5.1 1.5 0.29
8.7 3.13 0.36
7.55 3.4 0.45
103.4 102.0 0.99
11.7 11.2 0.96
10.0 10.0 1 .O
8.0 6.0 0.75
6.5 6.5 1.0
57.9 59.2 1.04
13.4 9.52 0.71
6.75 3.0 0.44
9.9 4.75 0.48
10.75 5.75 0.53
B = 0.42 T
tE /~ t.s
A 1
A2
~2
A2/A1 C 1
1
3
2
C2
t,
C21Cl
E~,Ts-'
B = 1.05 T
Figure 1 Dependence of energy losses on velocity of change of magnetic field for the copper tube: • , • , first measurement; zx, o , second measurement (after 88 months)
A1 A2
A2/A1 C1 C2
C2/C1
30
B= 0.42 T
2o ,-- 10 ~" 0
I
B=I.0ST
I
I
I
•
200
-~ 2o 10 100
Figure 2 Dependence of energy losses on velocity of change of magnetic field for sample31: • , & , f i r s t m e a s u r e m e n t ; O, zx, second measurement (after 70 months)
transverse resistivity of a composite superconductor due to diffusion processes. Table 1 shows the S/V sample parameter, which determines the contact surface area per unit volume. A greater decrease in eddy current losses was observed for samples with a m a x i m u m contact surface between the two metals, in which cases the effects due to diffusion are seen to be greater.
630
Cryogenics 1993 Vol 33, No 6
B,T Figure 3 Dependence of critical current on magnetic field for sample 30: O, manufacturer's data; • , results observed in June 1991
According to the results of reference 6, in which for the same samples good agreement is shown between the measured and calculated dependences of eddy current losses, we estimate the effective transverse resistivity of
Change of a.c energy losses with aging. N.M. Vladimirova et al. Table 3
1.0~
B=I.0
Effective transverse resistivity calculation results
Sample
19
30
3!
34
34A
Pl ( x 10-1OQm) P2 ( x 10 l ° f ~ m )
3.71 3.63
1.96 2.76
1.27 2.85
0.86 1.80
0.79 1.49
0.5 B= 0.42 T
0
2'0
4'0
6'0
8b
t, m0nth Figure 4 Dependence of change in ratio C2/Cl of eddy current losses on time for samples with 2970 filaments (samples 31, 34 and 34A)
the composite superconductors using the formula
We -- 2gm/~ r ~[ (\271-/] ~L ] ~ 2p
"1-
which is valid for a rate of change of magnetic field equal to several teslas per second (in the case of our
samples). Here We is the eddy current losses per cycle per volume unit, Bm is the magnetic field amplitude, ro is the composite radius, lp is the twist length and P is the effective transverse resistivity. All values are calculated in SI units. The results of the transverse resistivity calculations are presented in Table 3 lbr a magnetic field amplitude of 1.05 T: pt represents the first measurement and P2 the repeated measurement made several years later.
References
1 Brechna, H. Superconducting Magnet Systems Springer Verlag, Germany (1973) 2 Wilson, M. Superconducting Magnets Oxford University Press, Oxford, UK (1983) 3 Chovanec, F. et al. Cryogenics (1981) 21 559-562 4 Agapov, Y.P. et al. IAE preprint-2913 Moscow, (1977) 5 Drobin, V.M. et al. JINR preprint, P-13-12(152 Dubna (1978) 6 Drobin, V.M. et al. Cryogenics (1982) 22 ~15- 119
Cryogenics 1993 Vol 33, No 6
631