1.Introduction

Superconducting magnets generating higher magnetic fields than conventional ones are required in Nuclear Magnetic Resonance (NMR) spectrometers and Magnetic Resonance Imaging (MRI) devices. Magnets generating magnetic fields over 30 T have been studied in NMR [1]. In MRI, a 11.7 T-magnet with a large room temperature bore, 900 mm, have been designed [2]. The increases of magnetic fields result in enhancement of nuclide identifications. A lot of superconductors have been discovered, but only a few of them are usable for magnets. Practical superconducting magnets consist of Nb-based low-temperature superconducting (LTS) wires and/or Bi-based high-temperature superconducting (HTS) wires, which are called first generation (1G) HTS wires. One kilometer-long YBa2Cu3O7-x (YBCO) coated conductors (CCs), second generation (2G) HTS wires, with a critical current (Ic) over 200 A/cm-width at 77.3 K and self field have been developed [3]. Nb3Sn superconducting wires, which are one of LTS wires, are used as a material of high field magnets. LTS magnets cannot generate static fields over 25 T due to the upper critical magnetic field (Bc2) of Nb3Sn [4]. Compared with 1G HTS wires, CCs have high Ic under high fields [5] and advantages for high stress applications [6]. The properties of CCs give rise to the possibility of constructing high field magnets with the advent of several kilometers long CCs.

Magnets for NMR spectrometers and MRI devices should generate magnetic fields with high homogeneities and stabilities. In contrast with multi-filamentary LTS wires, HTS wires have tape shape with high aspect ratios. Experiments and calculations [7], [8], [9] have showed that a 1G HTS magnet inserted concentrically into a LTS magnet generates inhomogeneous and unstable fields due to screening currents flowing on the 1G HTS wires. Uglietti et al. [10] have reported that magnetic fields generated by a downsized coil consisting of a CC have inhomogeneities and instabilities as well due to a screening current on the tape-shaped CCs. Magnetic fields component perpendicular to the tape surface induces screening currents. The magnetic fields consist of self field and external fields. It is not known well how the total currents consisting of screening and transport currents flow in CC at 4.2 K under high field. Further investigations regarding relation between the screening and transport currents were carried out in this thesis. The further investigations bring simplification of calculation in electromagnetic design of YBCO magnet and optimization of operating conditions of the magnet.

The purpose of this work is to understand relations between the screening and transport currents at 4.2 K under high field and to suggest a method of electromagnetic design taking screening current into consideration. The following evaluations were performed:

The current distribution flowing in a YBCO CC was estimated from magnetic field distribution.

Magnetic field distributions induced by screening currents flowing in YBCO CCs and the interaction between the screening currents in CCs were evaluated.

Temporal variations of the SCF were measured.

An electromagnetic design method for fabricating a YBCO coil taking the current distribution, temporal variations and the interaction of the screening current between the CCs into consideration was suggested.

2.Current distribution in a single coated conductor

Current distributions were estimated from actual magnetic field distributions generated by transport and screening currents. As shown in Fig. 1, a Hall sensor was scanned in liquid helium under external magnetic field in order to the magnetic field distributions.

Models of total currents consisting of screening and transport currents flowing in a short CC with a short length were examined. Observations of magnetic flux densities above the center of the CC under external magnetic field gave a macroscopic view of the screening current flowing one-dimensionally even in the CC with the short length. Magnetic field dependences of macroscopic critical current estimated from transport measurement expressed external magnetic field dependences of screening-current-induced magnetic field (SCF). This result verifies that the screening current corresponds to the critical current. This may be helpful when considering intensity of magnetic flux density, angular dependence of magnetic field and operation temperature in a magnet design

Assuming that current flows one-dimensionally, a model and a solution using the Tikhonov regularization were described. The distribution of sheet current density was calculated from the distribution of actual magnetic field. Using the distributions of sheet current density, magnetic field distributions at different positions were calculated and then were compared with the actual distributions. The calculation and experimental results agreed well and the validity of the model and solution were confirmed. On condition of low external magnetic field and low transport current, the sheet current density given by actual magnetic field distributions and the Brandt's critical state model [11] agreed well. Therefore, the agreement enhances the validity of the solution of the sheet current density.

It turned out that the transport current relative to critical current depending on external magnetic field determines distribution of the sheet current density under high field shown in Fig. 2. On the other hand, the measurement and analysis reveals that variations of external magnetic field are dominant to the distributions of sheet current density under the low magnetic field, where magnetic flux is not at the center of the CC.

3.Magnetic field distributions generated by multiple YBCO coated conductors

Distributions of SCF generated by arranged and/or superimposed CCs are examined and then the calculation method for estimating the distributions from sheet current densities in a single CC is suggested. The calculation results give the accordance with the experimental values as shown in Fig. 3. As a result, it was verified that distributions of SCF and current density for arranged- and/or superimposed-CCs could estimate current distribution in a single CC.

4.Temporal variations of the SCF

Temporal variations of the SCF generated by arranged- and/or superimposed-CCs were observed. The result shows that the variations are determined by amount of magnetic flux in the multiple CCs and temperature

5.An electromagnetic design method for fabricating a YBCO coil taking the current distribution and the interaction of the screening current between the CCs into consideration

An electromagnetic design method for calculating magnetic field generated by the multi-turn and multi-layer YBCO coil from the sheet current density in a CC was suggested. As an example, Fig. 4 shows distributions of z-component of magnetic flux densities along z-axis generated by a YBCO coil with a diameter of 18 mm. The transport current supplied to the YBCO pancake coil is 200 A. The blue line shows distributions of magnetic flux density along z-axis at instant when background magnetic field goes from 0 T to 1 T. The red line shows distributions of the magnetic flux density at 1 T during a reduction of background magnetic field. The difference between red and blue profile shows that the calculation model takes screening current into considerations.

6.Conclusion

This thesis reveals a relation between screening and transport currents in a coated conductor and then, a coil design taking screening current into consideration became possible. This design method may promote a construction of YBCO magnet.

Fig. 1: Schematic diagram of measurements of magnetic flux densities above a coated conductor under external magnetic field and transport currents.

Fig. 2: Profiles of sheet current density Jy relative to critical sheet current density Jc unified by the transport current relative to critical current It/Ic.

Fig. 3: Distributions of SCF for 3-parallel, 3-layers CCs at external field with magnetic flux of 1 T. The blue circles show experimental values. Green and red lines were calculated using the iteration and the simple sum method, respectively. Distributions of SCF for 3-parallel, 3-layers CCs at external field with magnetic flux of 1 T. The blue circles show experimental values. Green and red lines were calculated using the iteration and the simple sum method, respectively.

Fig. 4: Distribution of z-component of magnetic flux densities along z-axis

本論文は「Study on current distribution in YBa2Cu3O7-x superconducting wire for NMR magnet design(NMR用マグネット設計の指針となるイットリウム系(Y系)超電導線材内の電流分布に関する研究)」と題し、高磁界・コンパクトという特長をもつ次世代NMRマグネットとして期待されているイットリウム系超電導線材利用のマグネットについて、解決すべき重要課題であるイットリウム系超電導線材に誘導される遮蔽電流とそれがNMRマグネット設計に与える影響を検討したものであり、8章から構成される。

第1章は「Introduction」であり、Y系超電導線材とNMRマグネットの開発現状、およびY系超電導線材をNMRマグネットに適用する上での課題、特にY系線材中の電流分布について整理した上で、本研究の目的を述べている。

第2章は「Experimental Setups」と題し、本研究で使用した実験装置と測定システムについて記述している。4.2Kから30Kまでの範囲の極低温、18Tまでの強磁場下で、Y系線材に通電した際の線材内の電流分布を明らかにするために、ホールセンサを用いた磁場分布測定システムを製作した。

第3章は「Determination of Method for Estimating Current Distribution」と題し、Y系超電導線材内の電流分布を測定した磁場分布から求める方法について記述している。線材を幅方向に対して均等に分割し、各区間に一様な電流が一次元的に流れると仮定するモデルに基づき、実測した磁場分布からビオ・サバールの法則の逆問題を解くことで電流分布を算出し、その電流分布の妥当性を検証した。

第4章は「Current Distribution in a Single Coated Conductor in Background Magnetic Field」と題し、通電中の単一のY系超電導線材に対して外部磁場を印加した際の磁場分布と線材内の電流分布について、実験結果に基づいて議論していて、線材全体に磁束が侵入する外部磁場下では、超電導線材の臨界電流に対する通電電流の大きさによって電流分布が決まることを示した。

第5章は「Magnetic Field Distribution Generated by Multiple Coated Conductors」と題し、複数のY系超電導線材に外部磁場を印加した際に線材内に誘導される電流が発生する磁場分布を測定し、遮蔽電流間の相互作用を検討した。その結果、磁束が線材全体に侵入した単一の線材において求めた電流分布から、複数線材の遮蔽電流が発生する磁場分布を求める手法の構築に成功し、本手法を第7章において適用した。

第6章は「Temporal Variations of Magnetic Field Generated by Screening Current」と題し、積層あるいは並列配置の複数のY系線材内に生じた遮蔽電流の減衰過程における線材間の相互作用について検討している。磁束クリープによる遮蔽電流の減衰は、積層あるいは並列の枚数に依存しないが、並列させた線材の常伝導層に流れる遮蔽電流の時間減衰は並列枚数に依存することを示した。

第7章は「Magnetic Field Distribution Generated by YBCO Pancake Coil」と題し、第4章と第5章の成果に基づいて、Y系超電導コイル内に生じる遮蔽電流分布を考慮した発生磁場分布の計算を行う手法を構築し、発生磁場の強度、磁場均一度への遮蔽電流の影響を定量的に評価できることを示している。遮蔽電流の影響を低減するためには、励磁プロセスを工夫して、線材内の電流分布を変えることが有効である。

第8章は「Conclusions」であり、本研究の成果を総括している。

以上これを要するに、本論文は、高い磁界均一度が要求されるNMR用マグネットにイットリウム系線材を利用する上で問題となる、線材に誘導される遮蔽電流に関して、短尺線材を用いて様々な外部印加磁界と輸送電流の条件で実験を行って、遮蔽電流分布とそれが作る磁界分布特性を明らかにし、それらの影響を低減し、実用的なNMRマグネットを設計するための基本的な指針を与えたものであり、先端エネルギー工学、特に超電導工学に貢献するところが少なくない。

なお、本論文第2章から第7章は、大崎博之、関野正樹、木吉司との共同研究であるが、論文提出者が主体となって解析と実験および考察を行ったもので、論文提出者の寄与が十分であると判断する。

したがって、博士(科学)の学位を授与できると認める。