Spatially-resolved measurement on time-dependent electromagnetic behavior in alternating current carrying coated conductor

Establishment of processing technology for multifilamentary coated conductors (CCs) is a key issue for superconducting electric power applications from the viewpoint of AC loss reduction. On the other hand, CCs sometimes have local inhomogeneity in the superconducting layers. In such case, that will cause a current blocking in a filament or inhomogeneity of critical current among filaments in a multifilamentary CC. Therefore, we need an assessment method for local electromagnetic behavior on AC loss properties of CCs. In this study, we developed a method for visualizing time-dependent AC loss distribution in CCs by using scanning Hall probe microscopy. We succeeded in visualizing local current density, electric field and loss density simultaneously with a spatial resolution of a few hundred micrometers. The measurement system has possible scanning area of 150 x 50 mm 2 and current capacity of 500 A. This enables us to discuss the local electromagnetic behavior on a practical scale of CCs. We believe that this visualization method will be a very powerful tool to estimate the feasibility of processing technology for multifilamentary CCs.

loss properties of CCs. In this study, we developed a method for visualizing time-dependent AC loss distribution in CCs by using scanning Hall probe microscopy.
We succeeded in visualizing local current density, electric field and loss density simultaneously with a spatial resolution of a few hundred micrometers. The measurement system has possible scanning area of 150 x 50 mm 2 and current capacity of 500 A. This enables us to discuss the local electromagnetic behavior on a practical scale of CCs. We believe that this visualization method will be a very powerful tool to estimate the feasibility of processing technology for multifilamentary CCs.

Introduction
Fabricating processes of REBa 2 Cu 3 O 7 - (REBCO, RE: rare earth) coated conductors (CCs) such as YBa 2 Cu 3 O 7 - (YBCO) and GdBa 2 Cu 3 O 7 - (GdBCO) CCs have been developed steadily in recent years [1][2][3][4]. For example, SuperPower Inc. has achieved a 1065 m long CC with the minimum critical current of 282 A/cm [4]. Such a progress leads us to the next stage of the development of practical applications using CCs.
For electric power applications, on the other hand, forming multifilamentary configuration on CCs will also be a key technology from the point of view of AC loss reduction. For example, it has been reported that AC losses in CCs can be reduced by increasing the number of filaments [5][6][7][8]. This demonstrates the high applicability of CCs to electric power applications such as power transmission cables, transformers and superconducting magnetic energy storage.
However, it has also been reported that CCs sometimes have local defects and inhomogeneity in the superconducting layers [9,10]. In case of monofilamentary CCs, e.g., 10-mm-wide CCs, that does not largely influence the total performance because current can flow around such defects. In case of multifilamentary CCs, on the other hand, that will cause a significant current blocking in a filament or inhomogeneity of critical current among filaments. In such cases, we cannot discuss the electromagnetic behavior only from a general AC loss estimation such as the four-probe method and pick-up coil method because we can only detect global loss integrating whole period.
Therefore, for the establishment of the processing technology for multifilamentary CCs, we need an assessment method to understand the local electromagnetic behaviors on AC loss properties of CCs.
In this study, we developed a visualization method of time-dependent AC loss distribution in CCs by using scanning Hall probe microscopy. We tried to visualize local current density, electric field and loss density in a multifilamentary model sample of a YBCO CC under alternating transport current. Fig. 1 shows an optical micrograph of the sample. The sample was prepared from a 10-mm-wide YBCO CC, and was processed by photolithography and wet etching. 10 filaments were patterned on a 5-mm-wide and 8-mm-long area, and the width of each filament was 340 m. Furthermore, some failures such as bridges, disconnections and defects were purposely simulated on the sample. We used this sample as an example for the visualization method. A sinusoidal transport current was applied to the sample from a bipolar current source controlled by a function generator. For noise reduction, also the Hall sensor was biased by another channel of the function generator, and then the signal from the sensor was acquired through a lock-in amplifier. At a measurement point, B z was measured during one cycle of the alternating transport current by synchronizing the transport current. Then, the Hall probe was moved to the next measurement point. These procedures were repeated for a whole measurement area, and eventually we could obtain in-plane distributions of B z as a function of time.

Data analysis
If we assume in-plane 2D current distribution in the sample, i.e., sheet current density in xy-plane, J, the distribution of J can be derived analytically from that of measured B z based on the inverse problem of Biot-Savart law. Roth et al. have already reported a method for that, and x and y components of J, J x and J y , are expressed in Fourier space as follows [11]: that [12], and x and y components of E, E x and E y , are expressed in Fourier space as follows: where x Ẽ and y Ẽ are the Fourier transformations of E x and E y , respectively. However, Eqs. (3) and (4) are valid only when the curl-free electrostatic portion, E p , is negligible compared with the divergence-free inductive E i [12]. In this study, the transport current applied to the sample was 88% of the critical current of the sample at the maximum. In case of a typical CC, the corresponding electric field in steady state, i.e., the magnitude of E p , becomes two orders smaller than the electric field criterion. On the other hand, as a result of the measurement, the magnitude of E i became the same order as the electric field criterion. Therefore, we did not consider E p , and used Eqs. (3) and (4) for the estimation of the distribution of E.
In this way, we can estimate the distributions of J and E from the measurement of B z . That means that we can finally obtain loss density, q, by considering the inner product of J and E: Such superconducting properties are also well shown in the distributions of the absolute value of sheet current density, J. When the transport current increases at t < 125 ms, the current flows from the uppermost and the lowermost filaments. On the other hand, when the transport current decreases at t > 125 ms, the current disappears from such filaments. This can also be interpreted from the coupling of the filaments.
Furthermore, it should be noted that circling current is induced in disconnected or defected filaments. In other words, although such filaments cannot transport enough current, they might generate additional AC losses. That will be discussed in the distributions of q.
From the distributions of the absolute value of electric field, E, it is found that large electric field is induced around t = 70 ms. However, time variation of the transport current is maximum at t = 0 ms (and t = 250 ms). As stated above, magnetic flux are trapped for a while inside the sample. Then, the time variation of magnetic field delays from that of transport current. This is the reason of the difference between them.
Furthermore, comparing the distributions of E between t = 6 ms and t = 30 ms, it is found that electric field invades by skipping the disconnected filaments. Such filaments can contribute neither to trap magnetic field in the sample nor to shield magnetic field from outside. Then, magnetic field cannot keep the same value around such filaments.
This is the reason of the abovementioned time variation. On the other hand, electric field is very small at t > 120 ms, and this can also be interpreted from the field trap.
Finally, we could obtain the distributions of q. The time variation of the distribution has the same tendency as that of E; Large loss is generated around t = 70 ms, and small loss at t > 120 ms. Furthermore, it is also found that the abovementioned circling current does not generate significant AC losses. In this way, this visualization method enables us to discuss the local electromagnetic behavior in a CC on the AC loss.

Conclusion
We developed a visualization method of local electromagnetic behavior in an alternating current carrying CC by using scanning Hall probe microscopy. We succeeded in visualizing sheet current density, electric field and loss density simultaneously with a spatial resolution of a few hundred micrometers as a function of time. Furthermore, we discussed the electromagnetic behavior in detail for a multifilamentary model sample of a YBCO CC. The measurement system had large scanning area and current capacity, and thus we could discuss such local electromagnetic behaviors on a practical scale of the CC. Therefore, we believe that this visualization method will be a powerful assessment technique for the establishment of processing technology for multifilamentary CCs.