Effect of lower temperature 1 Increase of critical current

The temperature of 77 K in a liquid-nitrogen bath is rather close to the critical temperature of 110 K for Bi-2223. Operating at a lower temperature significantly increases the critical current of a Bi-2223 tape. Temperatures below 77 K are reached with a cryocooler or by pumping off the N2-vapour. A smaller amount of expensive superconducting tape is then

required to carry the total current in a device. It is necessary to know the AC-loss behaviour of Bi-2223 tapes in the temperature range between 65 K and 77 K where N2 is a liquid. At full

coupling the AC loss is determined by the average critical-current density of the multi- filamentary core, which is directly related to Ic. When the filaments are decoupled, the loss depends on the magnetic critical-current density in the filaments, which is expected to be proportional to Ic. Twisted filaments in a tape in parallel magnetic field are partially coupled as demonstrated in section 3.3. Then the AC loss is affected also by changes in matrix resistivity or in the critical-current density of intergrowths between the filaments.

In the experimental set-up the vapour pressure above the N2 bath may be reduced to a

set value. After a certain cooling-down time, the lower pressure results in a lower temperature. The temperature can be decreased from 77 K to about 65.5 K where the N2

becomes a solid. The decrease in temperature causes an increase in the transport Ic by about a factor 1.7: see Table 3.5. The critical currents are lower than in Table 3.2 due to degradation of the samples.

Table 3.5 Transport and magnetic critical currents of tapes A and Dt at various temperatures.

Tape A with non-twisted filaments Tape Dt with 6.4 mm twist pitch Temperature

T [K] _{Ic [A] Ic,m [A] Ic,m / Ic Ic [A] Ic,m [A] Ic,m / Ic}

77.3 37.8 46.4 1.23 19.4 19.4 1.00

73.3 48.4 57.1 1.18 23.0 25.0 1.09

69.4 57.2 74.2 1.30 26.7 32.0 1.20

65.6 66.2 85.9 1.30 30.9 40.0 1.30

3.4.2 Tape with non-twisted filaments

The AC loss measured in tape A in parallel magnetic field is compared to the CS model for an infinite slab, assuming full coupling in the filamentary core as in section 3.2. The core dimensions wc and dc are fixed at the values listed in Table 3.2. The critical current Ic is used as a fit parameter. The result is a ‘magnetisation critical current’ Ic,m which gives information about the magnitude of the coupling currents in the filaments. The values for Ic,m found at four different temperatures are listed in Table 3.5. The value of 46.4 A at 77 K is about 20 % higher than the measured Ic. It is close to the original critical current of 44 A in tape A. Apparently the new lower Ic is caused by local damage. Large parts of the tape still carry coupling currents equivalent to the original Ic. Both critical currents increase by approximately the same amount if the temperature is decreased. The ratio Ic,m / Ic varies by 10% over the measured temperature range.

In Figure 3.10 the AC-loss function measured at various temperatures is shown as a function of β which is defined as Ba / Bp,c. Here Bp,c is the core penetration field calculated

with the magnetic critical current Ic,m. The scaling with Bp,c cancels the direct effect on the AC loss of the changes in Ic.m. For parallel magnetic field the scaled AC loss is independent of temperature. There are no significant temperature-dependent effects on the AC loss, apart from the change in critical current. Also in perpendicular magnetic field the AC loss scales with the same parameter Ic,m. At high magnetic-field amplitudes the AC-loss density Qmagn and power loss P are proportional to Ic,m, which is apparently proportional to the transport critical current. Then at high magnetic field the normalised power loss P / Ic of a tape with non-twisted filaments is independent of temperature. However, the cooling penalty factor is higher at lower temperatures. Therefore the total power consumption of a device operating at temperatures below 77 K is expected to be higher than at 77 K.

Figure 3.10 Scaled loss function measured in tape A at various temperatures.

3.4.3 Tape with twisted filaments

Twisted filaments are partially coupled in parallel magnetic field. The AC loss then depends on several critical-current densities: Jc,core in the core, Jc,fil,m in the filaments and possibly an effective Jc of the intergrowths. Two cases are possible:

β = Magnetic-field amplitude / core penetration field [ ]

0.1 1 10 Loss function Γ [ ] 0.01 0.1 1 77.3 K; I_c = 37.8 A 73.3 K; I_c = 48.4 A 69.4 K; I_c = 57.2 A 65.8 K; I_c = 66.2 A CS model, full coupling

f = 48 Hz

Perpendicular

magnetic field

Parallel

magnetic field

1) The critical-current densities s have a different temperature-dependence. For instance, the AC loss at low magnetic-field amplitude may be determined by Bi-2212 intergrowths. At 77 K the Jc(T) dependence of Bi-2212 is stronger than that of Bi-2223. If the temperature is decreased, the critical-current density of the intergrowths increases faster than Jc,fil,m. Then the AC loss at low magnetic-field amplitudes increases more than at high amplitudes.

2) All relevant critical-current densities have a similar temperature-dependence. Then the changes in AC loss can be described with changes in a single parameter, e.g. the magnetic critical current.

It is investigated whether tape Dt is described by case 1 or by case 2.

The AC loss measured in tape Dt is treated similarly to the loss of tape A in the previous section. The measured loss function is shown in Figure 3.11 as a function of β, defined as Ba / Bp,c. The core penetration field is calculated with the magnetic critical current

Ic,m. At 77 K a magnetic critical current equal to Ic is assumed. At lower temperatures,

Ic,m-values are sought which make the measured loss functions coincide as well as possible. The scaled loss functions for different temperature are very similar: see Figure 3.11. Tape Dt is described by case 2. The temperature-dependence of the AC loss is governed by the single parameter Ic,m. When the temperature is decreased, Ic,m obtained from the fit increases faster than the transport current. At 65.6 K the magnetic critical current is 30 % higher than Ic: see Table 3.5. Possibly the damage in the filaments due to twisting plays a larger role at lower temperature. Similar results are obtained in other tapes with twisted filaments. However, the 30% increase in Ic,m / Ic is found only in tape Dt. The measured ratio Ic,m / Ic is usually a constant in the temperature range between 65 and 77 K.

Figure 3.11 Scaled loss function measured in tape Dt at various temperatures.

β = Magnetic-field amplitude / core penetration field [ ]

1 10 100 Loss function Γ [ ] 0.01 0.1 77.3 K; I_c = 19.4 A 73.2 K; I_c = 23.0 A 69.4 K; I_c = 26.7 A 65.4 K; I_c = 30.9 A

Parallel magnetic field