考虑非均匀临界电流密度效应的高温超导体磁通跳跃与交流损耗的理论研究
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摘要
高温超导体在极低温度环境下的磁通跳跃不稳定性现象和在交变条件作用下的能量损耗直接关系到超导装置和系统的安全性和稳定性，是超导体应用中关注的基础性课题，其研究一直受到高度重视。由于高温超导材料在制备过程中不可避免地存在大量各种类型的点阵缺陷造成超导体内钉扎势以及临界电流密度分布的不均匀性，那么与之相关的磁通跳跃和交流损耗就成为超导装置和系统安全设计和优化的关键科学问题。本文采用局部绝热假定从磁热相互作用的角度考虑临界电流密度非均匀分布效应对磁通跳跃和交流损耗的影响并对高温超导薄膜的磁场和电流密度的分布及其损耗情况进行了深入研究，得到了一些有意义的结果。
首先，针对高温超导体磁通跳跃的临界电流密度非均匀分布效应，从磁热相互作用角度考虑环境初始温度和外加磁场变化速度的影响，通过求解初次磁通跳跃预测方程建立了磁通跳跃临界电流密度非均匀分布效应的理论模型，同时在临界态理论框架内考虑热量分布和温度响应给出了高温超导体磁通跳跃的解析表述。本文建立的理论模型能很好地预测已有的实验数据和数值结果，并且理论计算发现：临界电流密度非均匀分布效应严重影响磁通跳跃现象，对磁通跳跃的产生有抑制作用，并且随着表征不同临界电流密度区域强度差异的参数γ=J_(cw)／J_(cs)的增大，抑制作用变得越来越显著。
其次，基于Norris方程考虑自场作用，分析了临界电流密度非均匀分布效应对高温超导圆柱体线材传输交流损耗的影响。理论计算发现：临界电流密度沿着超导圆柱体线材径向由内及外递增的非均匀分布方式能够有效减小传输损耗。当规一化传输电流较大或接近临界电流时，临界电流密度的非均匀分布效应对传输损耗的影响比较显著；当规一化传输电流较小时，其影响一般情况下可以忽略不计。临界电流密度沿横截面径向由内及外以线性和平方的方式对损耗行为的改变与以阶梯状方式有所不同。特别指出，超导圆柱体横截面上边界处的临界电流密度分布对减小传输损耗极其重要。
最后，考虑高温超导薄膜的二维超导电性效应以及磁场和电流密度的分布特征，研究了超导薄膜交流损耗的临界电流密度非均匀分布效应。理论计算发现：超导平板和薄膜样品对外加磁场和传输电流的电磁响应有着本质上的区别。磁场分别以线性和强非线性的形式穿透超导平板和薄膜。在超导平板中无场区电流密度为零而临界区以J_c传输电流，在薄膜中临界区电流密度为J_c而在无场区其连续变化且不为零。薄膜传输损耗的临界电流密度非均匀分布效应定性上与其它几何形状的超导体基本一致，在高场时薄膜磁化损耗的临界电流密度非均匀分布效应逐渐消失。
总之，通过本文对高温超导材料磁通跳跃和交流损耗的临界电流密度非均匀分布效应的研究，为准确测量和正确预测磁通跳跃发生场、交流损耗等性能参数提供很好的理论依据，并且本文研究对高温超导设备和高温超导薄膜器件的准确设计和应用具有重要意义。
As we all know, flux jump instability at the extreme low temperature and energylosses in alternating conditions in the high-temperature superconductors (HTSC) arefundamental subjects in application of superconductors, which are associated directlywith the security and the stability of the superconducting devices and systems, thusthey have been paid more attention in both theoretical and application research. Dueto that the effect of non-uniform distribution of flux-pinning potential andcritical-current density resulting from many types of lattice defects during thepreparation process of HTSC, flux jump instability and AC losses are arisen to be thekey issue in the design and optimization of the superconducting devices and systems.Based on the assumption of local adiabatic conditions and dynamic process ofmagneto-thermal interaction, this dissertation focuses on investigating the effects ofnon-uniform critical-current density distribution on flux jumps and AC losses inHTSC including thin film and many interesting theoretical results are obtained.
Firstly, the effects of non-uniform distributions of critical-current density on fluxjumps in HTSC are discussed. From the point of view of the dynamic process ofmagneto-thermal interaction, the ambient temperature and sweep rate of the externalmagnetic-field are taken into account to develop the theoretical models of the effect ofdistribution of non-uniform critical-current density on flux jumps by solvingpredicting equations for predicting the first flux-jump field. In the framework of thecritical state model, the influences of the thermal distribution and temperatureresponse are considered to present the analytic expression of flux jumps of HTSC. Itis found that the predictions from the proposed models are good agreement with theexisting experimental data and numerical results. The theoretical results display thatthe flux jumps are seriously dependent on the effect of non-uniform critical-currentdensity distribution, which can suppress the occurrence of flux jumps, and the effectbecome more and more remarkabe with the increase of theparameterγ=J_(cw)/J_(cs),which is characterized as the discrepancy of differentcritical-current density or pinning potential regions.
Secondly, for the transport AC losses in superconducting cylinder, the effects ofnon-uniform distributions of critical-current density on the transport AC losses arediscussed theoretically by considering the self-field effects on the basis of Norrisequations. It can be found from the calculations that the non-uniform critical-currentdensity distribution increase from center outwards along radius could reduce thelosses efficiently. When the normalized transport current is relatively high or approach the critical current, the transport losses are affected by the effects ofnon-uniform critical-current density distribution, meanwhile the normalized transportcurrent is relative small the effects usually could be neglected. For the variation oflosses performance, the distribution of critical-current density increase linearly andquadratic from center outwards are different from critical-current density increasestepwise from center outwards. In particular, the distribution of critical-currentdensity around the cross-section edge of superconducting cylinder is comparablyimportant to reduce the transport losses.
Finally, the effects of two-dimension superconductivity and distributioncharacteristic of magnetic field and current density are considered in superconductingthin film so as to predict the influence of non-uniform distributions of critical-currentdensity on AC losses. It can be noted from the theoretical calculations that there areessentially differences between the slab and thin film for the response to the externalmagnetic field and transport current. The slab and thin film are linearly and strongnon-linearly penetrated by field, respectively. In slab the current flow withcritical-current density in critical region and no current flow in field-free region, inthin film the current flow with critical-current density in critical region and the currentchanges continuously in field-free region, in which the current is not zero. The effectof non-uniform critical-current density distribution on transport losses in filmqualitatively is accord with other superconducting geometries. In addition, whenmagnetic field is relatively high, the effect of non-uniform critical-current densitydistribution on magnetization losses gradually disappears.
After all, the theoretical investigations of the effect of non-uniform critical-currentdensity distribution on flux jumps and AC losses of HTSC materials in this papermust be important and useful for the precise measurements and exact predictions ofthe materials properties of HTSC materials as well as the design and application of thesuperconducting devices and thin film.
首先，针对高温超导体磁通跳跃的临界电流密度非均匀分布效应，从磁热相互作用角度考虑环境初始温度和外加磁场变化速度的影响，通过求解初次磁通跳跃预测方程建立了磁通跳跃临界电流密度非均匀分布效应的理论模型，同时在临界态理论框架内考虑热量分布和温度响应给出了高温超导体磁通跳跃的解析表述。本文建立的理论模型能很好地预测已有的实验数据和数值结果，并且理论计算发现：临界电流密度非均匀分布效应严重影响磁通跳跃现象，对磁通跳跃的产生有抑制作用，并且随着表征不同临界电流密度区域强度差异的参数γ=J_(cw)／J_(cs)的增大，抑制作用变得越来越显著。
其次，基于Norris方程考虑自场作用，分析了临界电流密度非均匀分布效应对高温超导圆柱体线材传输交流损耗的影响。理论计算发现：临界电流密度沿着超导圆柱体线材径向由内及外递增的非均匀分布方式能够有效减小传输损耗。当规一化传输电流较大或接近临界电流时，临界电流密度的非均匀分布效应对传输损耗的影响比较显著；当规一化传输电流较小时，其影响一般情况下可以忽略不计。临界电流密度沿横截面径向由内及外以线性和平方的方式对损耗行为的改变与以阶梯状方式有所不同。特别指出，超导圆柱体横截面上边界处的临界电流密度分布对减小传输损耗极其重要。
最后，考虑高温超导薄膜的二维超导电性效应以及磁场和电流密度的分布特征，研究了超导薄膜交流损耗的临界电流密度非均匀分布效应。理论计算发现：超导平板和薄膜样品对外加磁场和传输电流的电磁响应有着本质上的区别。磁场分别以线性和强非线性的形式穿透超导平板和薄膜。在超导平板中无场区电流密度为零而临界区以J_c传输电流，在薄膜中临界区电流密度为J_c而在无场区其连续变化且不为零。薄膜传输损耗的临界电流密度非均匀分布效应定性上与其它几何形状的超导体基本一致，在高场时薄膜磁化损耗的临界电流密度非均匀分布效应逐渐消失。
总之，通过本文对高温超导材料磁通跳跃和交流损耗的临界电流密度非均匀分布效应的研究，为准确测量和正确预测磁通跳跃发生场、交流损耗等性能参数提供很好的理论依据，并且本文研究对高温超导设备和高温超导薄膜器件的准确设计和应用具有重要意义。
As we all know, flux jump instability at the extreme low temperature and energylosses in alternating conditions in the high-temperature superconductors (HTSC) arefundamental subjects in application of superconductors, which are associated directlywith the security and the stability of the superconducting devices and systems, thusthey have been paid more attention in both theoretical and application research. Dueto that the effect of non-uniform distribution of flux-pinning potential andcritical-current density resulting from many types of lattice defects during thepreparation process of HTSC, flux jump instability and AC losses are arisen to be thekey issue in the design and optimization of the superconducting devices and systems.Based on the assumption of local adiabatic conditions and dynamic process ofmagneto-thermal interaction, this dissertation focuses on investigating the effects ofnon-uniform critical-current density distribution on flux jumps and AC losses inHTSC including thin film and many interesting theoretical results are obtained.
Firstly, the effects of non-uniform distributions of critical-current density on fluxjumps in HTSC are discussed. From the point of view of the dynamic process ofmagneto-thermal interaction, the ambient temperature and sweep rate of the externalmagnetic-field are taken into account to develop the theoretical models of the effect ofdistribution of non-uniform critical-current density on flux jumps by solvingpredicting equations for predicting the first flux-jump field. In the framework of thecritical state model, the influences of the thermal distribution and temperatureresponse are considered to present the analytic expression of flux jumps of HTSC. Itis found that the predictions from the proposed models are good agreement with theexisting experimental data and numerical results. The theoretical results display thatthe flux jumps are seriously dependent on the effect of non-uniform critical-currentdensity distribution, which can suppress the occurrence of flux jumps, and the effectbecome more and more remarkabe with the increase of theparameterγ=J_(cw)/J_(cs),which is characterized as the discrepancy of differentcritical-current density or pinning potential regions.
Secondly, for the transport AC losses in superconducting cylinder, the effects ofnon-uniform distributions of critical-current density on the transport AC losses arediscussed theoretically by considering the self-field effects on the basis of Norrisequations. It can be found from the calculations that the non-uniform critical-currentdensity distribution increase from center outwards along radius could reduce thelosses efficiently. When the normalized transport current is relatively high or approach the critical current, the transport losses are affected by the effects ofnon-uniform critical-current density distribution, meanwhile the normalized transportcurrent is relative small the effects usually could be neglected. For the variation oflosses performance, the distribution of critical-current density increase linearly andquadratic from center outwards are different from critical-current density increasestepwise from center outwards. In particular, the distribution of critical-currentdensity around the cross-section edge of superconducting cylinder is comparablyimportant to reduce the transport losses.
Finally, the effects of two-dimension superconductivity and distributioncharacteristic of magnetic field and current density are considered in superconductingthin film so as to predict the influence of non-uniform distributions of critical-currentdensity on AC losses. It can be noted from the theoretical calculations that there areessentially differences between the slab and thin film for the response to the externalmagnetic field and transport current. The slab and thin film are linearly and strongnon-linearly penetrated by field, respectively. In slab the current flow withcritical-current density in critical region and no current flow in field-free region, inthin film the current flow with critical-current density in critical region and the currentchanges continuously in field-free region, in which the current is not zero. The effectof non-uniform critical-current density distribution on transport losses in filmqualitatively is accord with other superconducting geometries. In addition, whenmagnetic field is relatively high, the effect of non-uniform critical-current densitydistribution on magnetization losses gradually disappears.
After all, the theoretical investigations of the effect of non-uniform critical-currentdensity distribution on flux jumps and AC losses of HTSC materials in this papermust be important and useful for the precise measurements and exact predictions ofthe materials properties of HTSC materials as well as the design and application of thesuperconducting devices and thin film.
引文
1. H.K. Onnes, On the sudden change in the rate at which the resistance of mercury disappears, Commun. Phys. Lab. Univ. Leiden, 120b(1911), 122b.
2．刘在海编著，1992，超导磁体交流损耗和稳定性，国防工业出版社，北京．
3．张其瑞编著，1992，高温超导电性，浙江大学出版社，杭州．
4．章立源，张金龙，崔广霁，1995，超导物理学，电子工业出版社，北京．
5．王家素，王素玉，1995，超导技术应用，成都电子科技大学出版社，成都．
6. Y. Yang, X. J. Zheng (郑晓静), 2007, Method for solution of the interaction between superconductor and permanent magnet, J. Appl. Phys., 101, 113922(1-8).
7. X.J. Zheng, Y. Yang, 2007, Transition cooling height of high-temperature superconductor levitation system, IEEE Trans. Appl. Supercond, 17, 3862-3866.
8. X.F. Gou, Y. Yang, X. J. Zheng, 2004, Analytic expression of magnetic field distribution of rectangular permanent magnets, Appl. Math. Meth., 25, 271-178.
9. X.J. Zheng, X. F. Gou, Y. H. Zhou, 2005, Influence of flux creep on dynamic behavior of magnetic levitation systems with a high-Tc superconductor, IEEE Trans. Appl. Supercond., 15, 3856-3863.
10. X. F. Gou, X. J. Zheng, Y. H. Zhou, 2007, Drift of levitated/suspended body in high-Tc superconducting levitation systems under vibration - Part Ⅰ: A criterion based on magnetic-gap relaxation for gap varying with time, IEEE Trans. Appl. Supercond., 17, 3795-3802.
11. X. F. Gou, X. J. Zheng, Y. H. Zhou, 2007, Drift of levitated/suspended body in high-Tc superconducting levitation systems under vibration - Part Ⅱ: Drift velocity for gap varying with time, IEEE Trans. Appl. Supercond, 17, 3803-3808.
12. X.Y. Zhang, Y. H. Zhou, J. Zhou, 2007, Three-dimensional measurements of forces between magnet and superconductor in a levitation system, Physica C, 467, 125-129.
13. X.Y. Zhang, Y. H. Zhou, J. Zhou, Jun Zhou, 2008, Influence of waiting time on the levitation force between a permanent magnet and a superconductor, Mod. Phys. Lett. B, 22,499-506.
14. X. Y. Zhang, Y. H. Zhou, J. Zhou, 2008, Experimental observation of a crossing in the force-displacement hysteretic curve of a melt processed YBaCuO bulk superconductor, Physica C, 468, 369-373.
15. X. Y. Zhang, Y. H. Zhou, J. Zhou, 2008, Modeling of symmetrical levitation force under different field cooling processes, Physica C, 468, 401-404.
16. X. Y. Zhang, Y. H. Zhou, J. Zhou, 2008, Relaxation transition due to different cooling processes in a superconducting levitation system, J. Appl. Phys., 103, 123901.
17. Y.H. Zhou, H. D. Yong, 2007, Crack problem for a long rectangular slab of superconductor under an electromagnetic force, Phys. Rev. B, 76, 094523.
18. Y. H. Zhou (周又和), X. J. Zheng (郑晓静) and K. Miya, Magnetoelastic bending and buckling of three-coil superconducting partial torus, Fusion Eng. and Des., 30(1995), 275-289.
19. Y. H. Zhou and K. Miya, Mechanical behaviours of magnetoelastic interaction for superconducting helical magnets, Fusion Eng. Des., 38(1998), 283-293.
20. Zheng, X J, Zhou, Y H, Lee, J S, Instability of superconducting partial torus with two pin supports, ASCE J. Eng. Mech., 125(1999), 174-179.
21. Zheng, X J, Wang, X Z, Zhou, Y H, Magnetoelastic analysis of non-circular superconducting partial torus, Int. J. Solids Struct., 37 (2000), 563-576.
22．周又和，郑晓静，托克马克聚变堆中环向磁场超导线圈的磁弹性弯曲与稳定性，核聚变与等离子体物理，2(1997)，17-23．
23．郑晓静，周又和，D型超导线圈的磁弹性弯曲和屈曲，兰州大学学报，33(1997)，23-31．
24．杨勇，2007，高温超导体面内移动时的静力特性研究，兰州大学博士学位论文，兰州．
25. Z. W. Gao and Y. H. Zhou, 2008. Crack growth for a long rectangular slab of superconducting trapped-field magnets. Supercond. Sci. Technol., 21, 095010(1-5).
26．张裕恒编著，1997，超导物理，中国科技大学出版社，合肥．
27．伍勇，韩汝珊，1997，超导物理基础，北京大学出版社，北京．
28．林良真，张金龙等，1998，超导电性及其应用，北京工业大学出版社，北京．
29．张国民，2003，高温超导带材及线圈的交流损耗，中国科学院电工研究所博士学文论文，北京．
30．冯端华，姜山，超导材料的发展与研究现状，低温与超导，35(2007)，520-526．
31．钱廷欣，周雅伟，赵晓鹏，新型超导材料的研究进展，材料导报，20(2006)，98-101．
32. Patent claim filed to establish 150K High-Tc, Available from: Http://www.superconductors.org/150K_pat.htm.
33. J.G. Bednorz and K. A. MOiler, Possible high-Tc superconductivity in La-Ba-Cu-O system, Z. Physik B, 64(1986), 189-193.
34. H. Malettah, A. P. Malozemoff, D. C. Cronemeyer, C. C. Tsuei, R. L. Greene, J. G. Bednorz, and K. A. Mu|¨ller, Diamagnetic shielding and meissner effect in the high-Tc superconductor Sr_(0.2)La_(1.8)CuO_4 ,Solid State Commun., 62(1987), 323-326.
35. S. Uchida, H. Takagi, K. Kitazawa and S. Tanaka, High-Tc superconductivity of La-Ba-Cu oxides. 3. electrical-resistivity measurement, Jpn. J. Appl. Phys. Part 2-Lett., 26(1987), L151-L152.
36. M. K. Wu, J. R. Ashburn, C. J. Ioring, P. H. Hor, R. Z. Meng, L. Gao, Z. J. Huang, Y. Q. Wang and C. W. Chu, Superconductivity at 93 K in a new mixed-phase Y-Ba-Cu-O compound system at ambient pressure, Phys. Rev. Lett., 58(1987), 908-910.
37．赵忠贤，陈立泉，杨乾声等，Ba-Y-Cu氧化物液氮温区的超导电性，科学通报，32(1987)，412-414．
38．李景会，2004，Bi2223超导带材交流损耗研究，东北大学博士学文论文，沈阳．
39．孙晶，2004，Bi2212高温超导圆筒的研制及其性能研究，东北大学博士学文论文，沈阳．
40．胡立发，2003，Bi2223高温超导带材的交流损耗，东北大学博士学文论文，沈阳．
41．杨小斌，2004，高温超导交流损耗与磁热稳定性分析，兰州大学博士学位论文，兰州．
42. A. I. Larkin and Y. N. Ovchinnikov, Pinning in superconductors, J. Low. Temp. Phys., 34(1979), 409-427.
43．周又和，郑晓静，1999，电磁固体结构力学，科学出版社，北京．
44. E. Pardo, D.-X Chen, A. Sanchez, and C. Navau, Alternating current loss in rectangular superconducting bars with a constant critical-current density, Supercond. Sci. Technol., 17(2004), 83-87.
45. W.J. Carr, Toward a more understanding of AC loss in a high-temperature superconductor, Physia C, 310(1998), 1-5.
46. C. Schmidt, L. Krempasky, AC losses of superconducting Bi-2223 tapes with two different time constants, Cryogenics, 42(2002), 557-568.
47. M. Migita, T. Watanabe, E. S. Otabe and T. Matsushita, Theoretical analysis of AC transport current loss in bulk Y-123, Physia C, 392-396(2003), 639-642.
48. L.F. Hu, P. X. Zhang, X. K. Teng and L. Zhou, Transport AC and magnetic losses in Bi2223 HTS tapes subjected to external field, Physia C, 386(2003), 35-40.
49. L. F. Hu, P. X. Zhang, X. K. Teng and L. Zhou, Transport current losses in Bi2223 high temperature supercondutors, Physia C, 392-396(2003), 1107-1112.
50. K. Kajikawa, M. Iwakuma, and K. Funaki, Dependence of AC losses on aspect ratio in superconducting wires with rectangular cross section, Physica C, 412-414(2004), 1045-1049.
51. J.J. Rabbers, B. T. Haken, and H. Tenkate, Hysteresis loss and the voltage-current relation in BSCCO tape supercondutors, Physia C, 401 (2004), 165-170.
52. J. Lehtonen, M. Korpela and W. nah, Influence of self-field on the critical current of Bi-2223/Ag tapes, Physica C, 403(2004), 257-262.
53. J. Duron, F. Grilli, B. Dutoit, S. Stavrev, Modelling the E-J relation of high-temperature superconductors in an arbitrary current range, Physica C, 401(2004), 231-235.
54. Y. Ichiki, H. Ohsaki, Numerical analysis of AC losses in YBCO coated conductor in external magetic field, Physica C, 412-414(2004), 1015-1020.
55. T. Hayashi, R. Yoshida, K.Kajikawa and K. Funaki, Numerical calculation of magnetization losses in single Bi2223 tape with anisotropic transport properties by 2D-FEM directly analyzing the field distribution, Physica C, 412-414(2004), 1129-1133.
56. K.Kajikawa, T. Hayashi, D. Nakamura, K.Kajikawa and K. Funaki, Magnetization loss properties of thin superconducting tapes with field-dependent critical current, Physica C, 426-431(2005), 1295-1301.
57. R.V. Sarmago, M. P. Olbinado, AC loss intrinsic to MgB at low magnetic fields, Supercond Sci. Technol., 18(2005), 307-310.
58. H.Noji, K. Ikeda, K. Uto, and T. Hamada, calculation of the total AC loss of high temperature superconducting transmission cable, Physica C, 445-448(2006), 1066-1068.
59, F. G(?)m(?)ry, J. Souc, M. Vojenciak, and P. Fabbricatore, Predicting AC loss in practical superconductors, Supercond Sci. Technol., 19(2006), 560-566.
60. S.P. Chockalingam, S. Sarangi, S. V. Bhat, K. Oka, Y. Nishihara, Studies on ac losses in BiSr CaCuO single crystals, Physica C, 460-462(2007), 719-721.
61. C. H. Chen, H. -T. Lin, C. Sorrell, Y. Zhao, Theoretical analysis of ac losses in high temperature superconducting bulks, Physica C, 463-465(2007), 431-435.
62. Z.Hong, Q. Jiang, R. Pei, and A. M. Campbell, A numerical method to estimate AC loss in superconducting coated conductors by finite element modelling, Supercond Sci. Technol., 20(2007), 331-337.
63. R. Brambilla, F. Grilli, and L. Martini, Development of an edge-element model for AC loss computation of high-temperature superconductors, Supercond Sci. Technol., 20(2007), 16-24.
64. V. Sokolobsky, V. Meerovich, Analytical approximation for AC losses in thin power-low supercondutors, Supercond Sci. Technol., 20(2007), 875-879.
65. O. Tsukamoto, M. Ciszek, AC magnetization losses in striated YBCO-123/Hastelloy coated conductors, Supercond Sci. Technol., 20(2007), 974-979.
66. M. Majoros, L. Ye, T. A. Coombs and E. W. Collings, Transport AC losses in YBCO coated conductors, Supercond Sci. Technol., 20(2007), S299-S304.
67. J. Yoo, S. M. Lee, Y. Jung, D. Youm, Calculations of AC current losses and AC magnetic losses from the scanning Hall probe measurements for a coated conductors, Physica C, 468(2008), 160-168.
68. Y. Mawatari, K. Kajikawa, hysteretic ac loss of polygonally arranged superconducting strips carrying ac transport current, Appl. Phys. Lett., 92(2008), 012504-012507.
69．刘洋，罗虹，冷祥等，不均匀超导体中的历史效应，低温物理学报，24(2002)，241-247．
70. J. Lehtonen, M. Ahoranta and R. Mikkonen, AC losses in non-homogeneous HTS conductors, Physica C, 372-376(2002), 1743-1745.
71. G. Grasso, B. Hensel and A. Jeremie, Distribution of the transport critical current density in Ag sheathed (Bi, Pb)_2Sr_2Ca_2Cu_3O_x tapes produced by rolling, Physica C, 241(1995), 45-52.
72. M. Lelovic, P. Kdshnaraj, N. Eror and U. Balachandran, Minimum critical current density of 10~5A/cm~2 at 77 K in the thin layer of Bi_(1.8)Pb_(0.4)Sr_(2.0)Ca_(2.2)Cu_3O_y superconductor near the Ag in Ag-sheathed tapes, Physica C, 241(1995), 246-250.
73. M. Lelovic, P. Krishnaraj, N. Eror and U. Balachandran, Transport critical current density above 10~5A/cm~2 at 77 K in the thin layer of Bi_(1.8)Pb_(0.4)Sr_(2.0)Ca_(2.2)Cu_3O_y superconductor tapes made by the Ag wire-in-tube method, Supercond. Sci. Technol., 9(1996), 201-204.
74．曹效文，王智河，Bi系带材的临界电流密度性质，低温与超导，25(1997)，46-55．
75. R. Inada, K. Tateyama, Y. Nakamura and A. Oota, Total AC loss of Ag-sheathed Bi2223 tapes with various filament arrangements carrying AC transport current in AC parallel transverse magnetic field, Supercond Sci. Technol., 20(2007), 138-146.
76. P.X. Zhang, C. S. Li, L. Zhou and R. Inada, The effects of J_c distribution on transport AC losses for Ag-sheathed Bi2223 tapes, Physica C, 356(2003), 146-146.
77. F. G(?)m(?)ry, E. Seiler, G. Perkins, E. Pardo and C. Navau, The influence of filament arrangement on current distribution and AC loss in Bi2223/Ag tapes, Supercond. Sci. Technol., 17(2004), S150-S154.
78. J. Ogawa, Y. Sawai, H. Nakayama, O. Tsukamoto and D. Miyagi, n value and J_c distribution dependence of AC transport current losses in HTS conductors, Physica C, 401(2004), 171-175.
79. B. Haken, H. Eck, H. Kate, A new experimental method to determine the local critical current density in high-temperature superconducting tapes, Physica C, 334(2000), 163-167.
80. Y.B. Kim, C. F. Hempstead and A. R. Strnad, Magnetization and critical supercurrents, Phys. Rev., 129(1963), 528-536.
81. R.G. Mints, Flux creep and flux jumping, Phys. Rev. B, 53(1996), 12311-12317.
82. L. J. Neuringer, Y. Shapira, Nb-25%Zr in strong magnetic fields: magnetic, resistive, ultrasonic, and thermal behavior, Phys. Rev., 148(1966), 231-246.
83. N. H. Zebouni, A. Venkataram, G. N. Rao, C. G. Grenier and J. M. Reynolds, Magnetothermal effects in type Ⅱ superconductors, Phys. Rev. Lett., 13(1964), 606-609.
84. J. L. Tholence, H. Noel, J. C. Lever, M. Potel and P. Gougeon, Magnetization jumps in YBa_2Cu_3O_7 single crystal up to 18 T, Solid State. Commun, 65(1988), 1131-1134.
85. M. Guillot, M. Potel, P. Gougeon, H. Noel and G. Chouteau, Magnetization jumps and critical current of YBa_2Cu_3O_7 single crystal, Phys. Lett. A, 127(1988), 363-365.
86. K. Chen, S. W. Hsu, T. L. Chen, S. D. Lan, and P. T. Wu, High transport critical current and flux jumps in bulk YBa_2Cu_3O_x superconductors, Appl. Phys. Lett., 56(1990), 2675-2677.
87. K. -H. Mu|¨ller and C. Anddkidis, Flux jumps in melt-textured Y-Ba-Cu-O, Phys. Rev. B, 49(1994), 1294-1307.
88. G. C Han, K. Watanabe, S. Awaji, N. Kobayashi, and K. Kimura, Magnetisation and instability in melt-textured YBa_2Cu_3O_7 at low temperature and high fields up to 23T, Physica C, 274 (1997), 33-38.
89. L. Legrand, I. Rosenman, R. G. Mints, G. Collin, and E. Janod, Self-organized criticality effect on stability: magneto-thermal oscillations in a granular YBCO superconductor. Europhys. Lett., 34(1996), 287-292.
90. M. E. McHenry, H. S. Lessure, M. P. Maley, J. Y. Coulter, I. Tanaka, and H. Kojima, Systematics of flux jumps and the stabilizing effect of flux creep in a La_(1.86)Sr_(0.14)CuO_4 single crystal, Physica C, 190(1992), 403-414.
91. A. Gerber, Z. Tarnawski, and J. J. M. Franse, Magnetic instabilities in high temperature superconductors, Physica C, 209(1993), 147-150.
92. A. Milner, High-field flux jumps in BSCCO at very low temperature, Physica B, 294-295 (2001), 388-392.
93. A. Nabialek, M. Niewczas, H. Dabkowska, A. Dabkowski, J. P. Castellan, and B. D. Gaulin, Magnetic flux jumps in textured Bi_2Sr_2CaCu_2O_(8+δ), Phys. Rev. B, 67(2003), 024518.
94. V. Chabanenko, R. Puzniak, A. Nabialek, S. Vasiliev, V. Rusakov, L. Huanqian, R. Szymczak, H. Szymczak, J. Jun, J. Karpinski, and V. Finkel, Flux jumps and H-T diagram of instability for MgB_2, J. Low Temp. Phys., 130(2003), 175-191.
95. Z. W. Zhao. S. L. Li, Y. M. Ni, H. P. Yang, Z. Y. Liu, H. H. Wen, W. N. Kang, H. J. Kim, E. M. Choi, and S. I.Lee, Suppression of superconducting critical current density by small flux jumps in MgB_2 thin films, Phys. Rev. B, 65(2002), 064512.
96. D. Monler, L. Fruchter, Magnetothermal instabilities in an organic superconductor. Eur. Phys. J. B., 3(1998), 143-148
97. S.L. Wipf, M. S. Lubell, Flux jumping in Nb-25% Zr under nearly adiabatic conditions, Phys. Lett., 16(1965), 103-105.
98. S. L. Wipf, Magnetic instabilities in type-Ⅱ superconductors, Phys. Rev., 161(1967), 404-416.
99. P. S. Swartz and C. P. Bean, A model for magnetic instabilities in hard superconductors: the adiabatic critical state, J. Appl. Phys., 39(1968), 4991-4998.
100. S. L. Wipf, Review of stability in high temperature superconductors with emphasis on flux jumping, Cryogenics, 31(1992), 936-948.
101. V. V. Chabanenko, A. I. Dyachenko, M. V. Zalutskll, V. F. Rusakov, H. Szymczak, S. Piechota, and A. Nabialek. Magnetothermal instabilities in type Ⅱ superconductors: The influence of magnetic irreversibility. J. Appl. Phys., 88(2000), 5875-5883.
102. Y. H. Zhou and X. B. Yang, Numerical simulation of thermomagnetic instability in high-Tc superconductors: Dependence on sweep rate and ambient temperature, Phys. Rev. B, 74(2006), 054507.
103. M. N. Wilson, 1983, Superconducting magnets, Clarendon Press, Oxford.
104. W. J. Carr, 1983, AC losses in type-Ⅱ superconducters, Science Publishers, New York.
105. W. T. Norris, Calculation of hysteresis losses in hard superconductors carrying ac: isoland conductors and edges of thin sheets, J. Phys. D: Appl. Phys., 3(1970), 489-507.
106. 王金星,1985,超导磁体,原子能出版社,北京.
107. M. Ohmer and J. P. Hearich, Magnetization of hysteretic superconductors for complete field penetration and a critical-state model with J_c(H)-α/H, J. Appl. Phys., 44(1973), 1804-1809.
108. J. Orehotsky, M. Garber, Y. Xu, Y. L. Wang, and M.Suenage, 60-Hz ac losses in YBa_2Cu_30_7 cylinders, J. Appl. Phys., 67(1990), 1433-1436.
109. E. S. Valkhov, K. A. Nenkov, and M. Ciszek, AC losses in polycrystalline YBa_2Cu_3O_y doped with Ag and Te, Physica C, 195(1992), 345-351
110. M. Ciszek, J. Olejniczak, E. Trojnar, A. J. Zaleski, J. Klamut, A. J. M. Roovers, and L. J. M. van de Klundert, AC losses and critical current density of superconducting GdBa_2Cu_3O_(7-x). Physica C, 152(1988), 247-250
111. Y. Xu, W. Guan, and K. Zeibig, Ac losses in REBa_2Cu_3O_(7-x) superconductors, Appl. Phys. Lett., 54(1989), 1699-1701.
112. S. Zannella, L. Jansak, M. Majoros, V. Selvamanickam, and K. Salama, AC energy dissipation in high-T_c superconductors, Physica C, 205(1993), 14-20.
113. T. H. Johnasen, H. Bratsberg, Critical-state magnetization of type-Ⅱ superconductors in rectangular slab and cylinder geometries, J. Appl. Phys., 77(1995), 3945.
114. P. O. Hetland T. H. Johansen, and H. Bratsberg, Magnetization in a generalized critical-state model for type-Ⅱ superconductors, Cryogenics, 36(1996), 41-46.
115．王银顺，林良真，4.5K下Bi2223／Ag多芯带材的磁化和磁滞损耗，低温物理学报，19(1997)，453-459．
116. E. H. Brant, Superconductor disks and cylinders in an axial magnetic field. I. Flux penetration and magnetization curves, Physical review B, 58(1998), 6506-6522.
117. V. Sokolovsky, V. Meerovich, S. Goren, and G. Jung, Analytical approach to AC loss calculation in high-Tc superconductors, Physica C, 306(1998), 154-162.
118. K. Kajikawa, M. Iwakuma, and K. Funaki, A heuristic description of AC losses in superconducting slab with smooth voltage-current characteristics represented by power law, Physica C, 378-381(2002), 1097-1101.
119. P. N. Mikheenko, J. Horvat, M. Ionescu, and S. X. Dou, Two-dimensional effects in AC losses of Bi_2Sr_2Ca_2Cu_3O_x tapes, ehysica C, 274(1997), 9-16
120. M. Watahiki, S. I. Yoo, and M. Murakami, A.C. susceptibility measurements in the presence of d.c. magnetic fields for Nd - Ba - Cu - O superconductors, Supercond Sci. Tech., 10(1997), 754-757.
121. H. Eckelmann, C. Schmidt, Temperature dependence of AC-losses in Bi-2223 superconducting tapes, Physica C, 372-376(2002), 1792-1796.
122. V. Sokolovsky and V. Meerovich, Heating due to AC losses in high-temperature superconductors, Physia C, 308(1998), 215-220.
123. Y. Zhao, C. H. Cheng, and H. Zhang, Influences of flux on a. c. loss per cycle in superconductors, Solid State Communications, 111(1999), 159-164.
124．胡立发，张平祥，王金星和周廉，高温超导体中的交流损耗，低温与超导，28(2000)，24-31．
125．胡立发，周廉，王金星等，磁化法测量Bi2223／Ag高温超导带材的超低频交流损耗，低温物理学报，22(2000)，462-466．
126. K. Kajikawa, Y. Mawatari, T. Hayashi and K. Funaki, AC loss evaluation of thin superconducting wires with critical current distribution along width, Supercond. Sci. Technol., 17(2004), 555-563.
127. A. Galkin, B. Ivanov, V. Kambersky, On the critical state in a non-uniform type Ⅱ superconductor, Physia C, 325(1999), 159-164.
128. D-X Chen, A. Sanchez and E. Pardo, Transport ac loss of a superconducting cylinder with field and radius dependent critical-current density, Supercond. Sci. Technol., 17(2004), 256-262.
129. N. Sekine, O. Tsukamoto, A. Utsunomiya and D. Miyagi, Dependence AC magnetization losses in thin film superconductor tape on J_c distribution along tape width, Physia C, 426-431(2005), 1284-1289.
130. O. Tsukamoto, AC losses in a type Ⅱ superconductor strip with inhomogeneous critical current distribution, Supercond Sci. Technol, 18(2005), 596-605.
131. R. Inada, Y. Nakamura and A. Oota, Evaluation of AC losses in cable conductors using thin superconducting tapes with non-uniform J_c distribution, Physia C, 442(2006), 139-144.
132. R. Inada, A. Oota, H. Fujimoto, Influence of locally varying J_c distribution on AC transport losses for superconductor wires and tapes with various cross sections, Physia C, 378-381(2002), 1133-1137.
133. Z. Jiang, N. Amemiya, O. Maruyama and Y. Shiohara, Critical current density distribution and magnetization loss in YBCO coated conductors, Physia C, 463(2007), 790-794.
134. F. G()m(?)ry, J. Souc, M. Vojenciak, and B. Klincok, Phenomenological description of flux pinning in non-uniform high-temperature superconductors in magnetic fields lower than the self-field, Supercond. Sci. Technol., 20(2007), S271-S277.
135. R. Inada, P. X. Zhang, Numerical modeling of Bi2223 multifilamentary tapes with position-dependence J_c, Physia C, 372-376(2002), 1800-1805.
136. R. Inada, Y. Nakamura and A. Oota, Numerical analysis for AC losses in single-layer cables composed of rectangular superconducting strips with various lateral J_c distributions, J. Phys: conference series, 97(2008), 012324-012329.
137. K. Chen, Y. C. Chen, S. W. Lu, W. H. Lee, and P. T. Wu, Magnetic and thermal instabilities in a textured YBa_2Cu_30_x superconductor with high transport J_c, Physica C, 173(1991),227-231.
138. J. Rhyner, Magnetic properties and AC-losses of superconductors with power law current-voltage characteristics, Physica C, 212(1993), 292-300.
139. Z. L. Xiao, P. Voss-de Hann, G. Jakob, T. Kluge, P. Haibach, H. Adrian, and E. Y. Andrei, Flux-flow instability and its anisotropy in Bi_2Sr_2CaCu_20_(8+δ) superconducting films. Phys,Rev.B., 59(1999), 1481-1490.
140. M. J. Qin and X. X. Yao, Ac susceptibility of high-temperature superconductors, Phys. Rev. B., 54(1996), 7536-7543.
141. R. Griessen, Resistive behavior of high-T_c superconductors: influence of a distribution of activation energies, Phys. Rev. Lett., 64(1990), 1674-1677.
142. E. T. Swartz and R. O. Pohl, Thermal boundary resistance, Rev. Mod. Phys., 61 (1989), 605-668.
143. J. R. Clem, 1991, AC losses in type-Ⅱ superconducters, Magnetic susceptibility of superconductors and other Spin system, Plenum Press, New York.
144. M. Ciszek, S. P. Ashworth, B. A. Glowacki, A. M. Campell and P. Haldar, Transport AC losses in multifilamentary Ag/Bi2223 tapes in low external DC magnetic fields, Physica C, 272(1996), 319-325.
145. M. Dhalle, A. Polcari, F. Mufti, Y. B. Huang, and G. Witz, Effects of alternating magnetic field losses in high-temperature multifilament Bi2223/Ag tapes by high resistive barriers, IEEE Trans. Appl. Supercond., 9(1999), 782-784.
146. M. P. Oomen, J. Rieger, H. Tenkate, Field-angular dependence of alternating current loss in multifliamentary high-temperature superconducting tapes, Appl. Phys. Lett., 70(1997), 3038-3040.
147. J. J. Rabbers, B. T. Haken, O. A. Shevechenko, and H. Tenkate, An engineering formula to describe the AC loss of BSCCO/Ag tape, IEEE Trans. Appl. Supercond, 11(2001), 2623-2626.
148. T. Yazawa, J. J. Rabbers, O. A. Shevechenko, B. T. Haken and H. Tenkate, Modeling the current distribution in HTS tapes with transport current and applied magnetic field, IEEE Trans. Appl. Supercond, 9(1999), 797-800.
149. T. Yazawa, J. J. Rabbets, B. T. Haken and Y. Yamada, Numerical calculation of current distributions in high temperature superconducting tapes with finite thickness in self field and external field, Physia C, 310(1998), 36-41.
150. W. D. Lee, L. Horong, T. J. Yang and B. S. Chiou, Analysis of transport critical current density in a bent BiPbSrCaCuO silver sheathed tape, Physica C, 247(1995), 215-220.
151. E. Pardo, D.-X Chen, A. Sanchez, and C. Navau, Alternating current loss in rectangular superconducting bars with a constant critical-current density, Supercond. Sci. Technol., 17(2004), 83-87.
152. M. Lahtinen, J. Passi, Z. Hun and J. Sarkaniemi, Microstructure of the ceramic in superconducting Bi2223 composite tapes after bending strain cycle, Physica C, 277(1997), 186-194.
153. R. Wesche, A. M. Fuchs, B. Jakob and G. Pasztor, Axial and bending strain effects in Ag and AgNiMg.Bi2212 wires, Cryogenics, 36(1996), 419-426.
154. B. T. Haken, 1994, Strain effects on the critical properties of high-field superconductor, Twemte University, Netherland..
155. M. Ciszek, B. A. Ashworth, A. M. Campell, S. P. Ashworth, and W. L. Yang, Influence of external magnetic fields and its orientation on transports AC losses in Bi2223 and Tl2223 silver sheathed tapes, IEEE Trans. Appl. Supercond., 7(1997), 314-317.
156. M. Ciszek, S. P. Ashworth, B. A. Ashworth and W. Y. Liang, Low magnetic field study of ac losses on monocore Bi2223 and T12223 silver sheathed tapes, Cryogenics, 36(1997), 637-641.
157. J. J. Rabbers, D. C. Laan, B. T. Haken, and H. H. Tenkate, Magnetization and transport current loss of a BSCCO/Ag tape in an external AC magnetic field carrying an AC transport current, IEEE Trans. Appl. Supercond, 9(1999), 1185-1188.
158. E. H. Brandt, Superconductors of finite thickness in a perpendicular magnetic field: strips and slab, Phys. Rev. B, 54(1996), 4246.
159. E. H. Brandt, Thin superconductors in a perpendicular magnetic ac field: General formulation and strip geometry, Phys. Rev. B, 49(1994), 9024.
160. E. H. Brandt, Thin superconductors in a perpendicular magnetic ac field: circular disk, Phys. Rev.B, 50(1994), 4034.
161. E. H. Brandt, Type II superconductor strip with current in a perpendicular magnetic field, Phys. Rev. B, 48(1993), 12893
162. M. Suenaga and V. F. Solovyov, ac losses in circular disks of thin YBa_2Cu_3O_7 films in perpendicular magnetic fields, J. Appl. Phys., 94(2003), 502-506.
163. J. R. Clem, Field and current distributions and ac losses in a bifilar stack of superconducting strips, Phys. Rev. B, 77(2008), 134506
164. C. A. Duran, P. L. Gammel, R. wolfe, et al., Magneto-optical imaging of flux penetration in high temperature superconducting thin films, Nature, 357(1992), 474-550.
165. D. A. Brawner, A. Schilling, H. R Ott, R. J. Haug, K. Ploog, and K. von. Klitzing, Superconductivity at 93 K in a new mixed-phase Y-Ba-Cu-O compound system at ambient pressure, Phys. Rev. Lett., 71(1993), 785-788.
166. D. A. Brawner and N. P. Ong, Scanning Hall microprobe measurements of magnetization profiles in YBa_2Cu_3O_(7-y) single crystals, J. Appl. Phys., 73(1993), 3890-5645.
2．刘在海编著，1992，超导磁体交流损耗和稳定性，国防工业出版社，北京．
3．张其瑞编著，1992，高温超导电性，浙江大学出版社，杭州．
4．章立源，张金龙，崔广霁，1995，超导物理学，电子工业出版社，北京．
5．王家素，王素玉，1995，超导技术应用，成都电子科技大学出版社，成都．
6. Y. Yang, X. J. Zheng (郑晓静), 2007, Method for solution of the interaction between superconductor and permanent magnet, J. Appl. Phys., 101, 113922(1-8).
7. X.J. Zheng, Y. Yang, 2007, Transition cooling height of high-temperature superconductor levitation system, IEEE Trans. Appl. Supercond, 17, 3862-3866.
8. X.F. Gou, Y. Yang, X. J. Zheng, 2004, Analytic expression of magnetic field distribution of rectangular permanent magnets, Appl. Math. Meth., 25, 271-178.
9. X.J. Zheng, X. F. Gou, Y. H. Zhou, 2005, Influence of flux creep on dynamic behavior of magnetic levitation systems with a high-Tc superconductor, IEEE Trans. Appl. Supercond., 15, 3856-3863.
10. X. F. Gou, X. J. Zheng, Y. H. Zhou, 2007, Drift of levitated/suspended body in high-Tc superconducting levitation systems under vibration - Part Ⅰ: A criterion based on magnetic-gap relaxation for gap varying with time, IEEE Trans. Appl. Supercond., 17, 3795-3802.
11. X. F. Gou, X. J. Zheng, Y. H. Zhou, 2007, Drift of levitated/suspended body in high-Tc superconducting levitation systems under vibration - Part Ⅱ: Drift velocity for gap varying with time, IEEE Trans. Appl. Supercond, 17, 3803-3808.
12. X.Y. Zhang, Y. H. Zhou, J. Zhou, 2007, Three-dimensional measurements of forces between magnet and superconductor in a levitation system, Physica C, 467, 125-129.
13. X.Y. Zhang, Y. H. Zhou, J. Zhou, Jun Zhou, 2008, Influence of waiting time on the levitation force between a permanent magnet and a superconductor, Mod. Phys. Lett. B, 22,499-506.
14. X. Y. Zhang, Y. H. Zhou, J. Zhou, 2008, Experimental observation of a crossing in the force-displacement hysteretic curve of a melt processed YBaCuO bulk superconductor, Physica C, 468, 369-373.
15. X. Y. Zhang, Y. H. Zhou, J. Zhou, 2008, Modeling of symmetrical levitation force under different field cooling processes, Physica C, 468, 401-404.
16. X. Y. Zhang, Y. H. Zhou, J. Zhou, 2008, Relaxation transition due to different cooling processes in a superconducting levitation system, J. Appl. Phys., 103, 123901.
17. Y.H. Zhou, H. D. Yong, 2007, Crack problem for a long rectangular slab of superconductor under an electromagnetic force, Phys. Rev. B, 76, 094523.
18. Y. H. Zhou (周又和), X. J. Zheng (郑晓静) and K. Miya, Magnetoelastic bending and buckling of three-coil superconducting partial torus, Fusion Eng. and Des., 30(1995), 275-289.
19. Y. H. Zhou and K. Miya, Mechanical behaviours of magnetoelastic interaction for superconducting helical magnets, Fusion Eng. Des., 38(1998), 283-293.
20. Zheng, X J, Zhou, Y H, Lee, J S, Instability of superconducting partial torus with two pin supports, ASCE J. Eng. Mech., 125(1999), 174-179.
21. Zheng, X J, Wang, X Z, Zhou, Y H, Magnetoelastic analysis of non-circular superconducting partial torus, Int. J. Solids Struct., 37 (2000), 563-576.
22．周又和，郑晓静，托克马克聚变堆中环向磁场超导线圈的磁弹性弯曲与稳定性，核聚变与等离子体物理，2(1997)，17-23．
23．郑晓静，周又和，D型超导线圈的磁弹性弯曲和屈曲，兰州大学学报，33(1997)，23-31．
24．杨勇，2007，高温超导体面内移动时的静力特性研究，兰州大学博士学位论文，兰州．
25. Z. W. Gao and Y. H. Zhou, 2008. Crack growth for a long rectangular slab of superconducting trapped-field magnets. Supercond. Sci. Technol., 21, 095010(1-5).
26．张裕恒编著，1997，超导物理，中国科技大学出版社，合肥．
27．伍勇，韩汝珊，1997，超导物理基础，北京大学出版社，北京．
28．林良真，张金龙等，1998，超导电性及其应用，北京工业大学出版社，北京．
29．张国民，2003，高温超导带材及线圈的交流损耗，中国科学院电工研究所博士学文论文，北京．
30．冯端华，姜山，超导材料的发展与研究现状，低温与超导，35(2007)，520-526．
31．钱廷欣，周雅伟，赵晓鹏，新型超导材料的研究进展，材料导报，20(2006)，98-101．
32. Patent claim filed to establish 150K High-Tc, Available from: Http://www.superconductors.org/150K_pat.htm.
33. J.G. Bednorz and K. A. MOiler, Possible high-Tc superconductivity in La-Ba-Cu-O system, Z. Physik B, 64(1986), 189-193.
34. H. Malettah, A. P. Malozemoff, D. C. Cronemeyer, C. C. Tsuei, R. L. Greene, J. G. Bednorz, and K. A. Mu|¨ller, Diamagnetic shielding and meissner effect in the high-Tc superconductor Sr_(0.2)La_(1.8)CuO_4 ,Solid State Commun., 62(1987), 323-326.
35. S. Uchida, H. Takagi, K. Kitazawa and S. Tanaka, High-Tc superconductivity of La-Ba-Cu oxides. 3. electrical-resistivity measurement, Jpn. J. Appl. Phys. Part 2-Lett., 26(1987), L151-L152.
36. M. K. Wu, J. R. Ashburn, C. J. Ioring, P. H. Hor, R. Z. Meng, L. Gao, Z. J. Huang, Y. Q. Wang and C. W. Chu, Superconductivity at 93 K in a new mixed-phase Y-Ba-Cu-O compound system at ambient pressure, Phys. Rev. Lett., 58(1987), 908-910.
37．赵忠贤，陈立泉，杨乾声等，Ba-Y-Cu氧化物液氮温区的超导电性，科学通报，32(1987)，412-414．
38．李景会，2004，Bi2223超导带材交流损耗研究，东北大学博士学文论文，沈阳．
39．孙晶，2004，Bi2212高温超导圆筒的研制及其性能研究，东北大学博士学文论文，沈阳．
40．胡立发，2003，Bi2223高温超导带材的交流损耗，东北大学博士学文论文，沈阳．
41．杨小斌，2004，高温超导交流损耗与磁热稳定性分析，兰州大学博士学位论文，兰州．
42. A. I. Larkin and Y. N. Ovchinnikov, Pinning in superconductors, J. Low. Temp. Phys., 34(1979), 409-427.
43．周又和，郑晓静，1999，电磁固体结构力学，科学出版社，北京．
44. E. Pardo, D.-X Chen, A. Sanchez, and C. Navau, Alternating current loss in rectangular superconducting bars with a constant critical-current density, Supercond. Sci. Technol., 17(2004), 83-87.
45. W.J. Carr, Toward a more understanding of AC loss in a high-temperature superconductor, Physia C, 310(1998), 1-5.
46. C. Schmidt, L. Krempasky, AC losses of superconducting Bi-2223 tapes with two different time constants, Cryogenics, 42(2002), 557-568.
47. M. Migita, T. Watanabe, E. S. Otabe and T. Matsushita, Theoretical analysis of AC transport current loss in bulk Y-123, Physia C, 392-396(2003), 639-642.
48. L.F. Hu, P. X. Zhang, X. K. Teng and L. Zhou, Transport AC and magnetic losses in Bi2223 HTS tapes subjected to external field, Physia C, 386(2003), 35-40.
49. L. F. Hu, P. X. Zhang, X. K. Teng and L. Zhou, Transport current losses in Bi2223 high temperature supercondutors, Physia C, 392-396(2003), 1107-1112.
50. K. Kajikawa, M. Iwakuma, and K. Funaki, Dependence of AC losses on aspect ratio in superconducting wires with rectangular cross section, Physica C, 412-414(2004), 1045-1049.
51. J.J. Rabbers, B. T. Haken, and H. Tenkate, Hysteresis loss and the voltage-current relation in BSCCO tape supercondutors, Physia C, 401 (2004), 165-170.
52. J. Lehtonen, M. Korpela and W. nah, Influence of self-field on the critical current of Bi-2223/Ag tapes, Physica C, 403(2004), 257-262.
53. J. Duron, F. Grilli, B. Dutoit, S. Stavrev, Modelling the E-J relation of high-temperature superconductors in an arbitrary current range, Physica C, 401(2004), 231-235.
54. Y. Ichiki, H. Ohsaki, Numerical analysis of AC losses in YBCO coated conductor in external magetic field, Physica C, 412-414(2004), 1015-1020.
55. T. Hayashi, R. Yoshida, K.Kajikawa and K. Funaki, Numerical calculation of magnetization losses in single Bi2223 tape with anisotropic transport properties by 2D-FEM directly analyzing the field distribution, Physica C, 412-414(2004), 1129-1133.
56. K.Kajikawa, T. Hayashi, D. Nakamura, K.Kajikawa and K. Funaki, Magnetization loss properties of thin superconducting tapes with field-dependent critical current, Physica C, 426-431(2005), 1295-1301.
57. R.V. Sarmago, M. P. Olbinado, AC loss intrinsic to MgB at low magnetic fields, Supercond Sci. Technol., 18(2005), 307-310.
58. H.Noji, K. Ikeda, K. Uto, and T. Hamada, calculation of the total AC loss of high temperature superconducting transmission cable, Physica C, 445-448(2006), 1066-1068.
59, F. G(?)m(?)ry, J. Souc, M. Vojenciak, and P. Fabbricatore, Predicting AC loss in practical superconductors, Supercond Sci. Technol., 19(2006), 560-566.
60. S.P. Chockalingam, S. Sarangi, S. V. Bhat, K. Oka, Y. Nishihara, Studies on ac losses in BiSr CaCuO single crystals, Physica C, 460-462(2007), 719-721.
61. C. H. Chen, H. -T. Lin, C. Sorrell, Y. Zhao, Theoretical analysis of ac losses in high temperature superconducting bulks, Physica C, 463-465(2007), 431-435.
62. Z.Hong, Q. Jiang, R. Pei, and A. M. Campbell, A numerical method to estimate AC loss in superconducting coated conductors by finite element modelling, Supercond Sci. Technol., 20(2007), 331-337.
63. R. Brambilla, F. Grilli, and L. Martini, Development of an edge-element model for AC loss computation of high-temperature superconductors, Supercond Sci. Technol., 20(2007), 16-24.
64. V. Sokolobsky, V. Meerovich, Analytical approximation for AC losses in thin power-low supercondutors, Supercond Sci. Technol., 20(2007), 875-879.
65. O. Tsukamoto, M. Ciszek, AC magnetization losses in striated YBCO-123/Hastelloy coated conductors, Supercond Sci. Technol., 20(2007), 974-979.
66. M. Majoros, L. Ye, T. A. Coombs and E. W. Collings, Transport AC losses in YBCO coated conductors, Supercond Sci. Technol., 20(2007), S299-S304.
67. J. Yoo, S. M. Lee, Y. Jung, D. Youm, Calculations of AC current losses and AC magnetic losses from the scanning Hall probe measurements for a coated conductors, Physica C, 468(2008), 160-168.
68. Y. Mawatari, K. Kajikawa, hysteretic ac loss of polygonally arranged superconducting strips carrying ac transport current, Appl. Phys. Lett., 92(2008), 012504-012507.
69．刘洋，罗虹，冷祥等，不均匀超导体中的历史效应，低温物理学报，24(2002)，241-247．
70. J. Lehtonen, M. Ahoranta and R. Mikkonen, AC losses in non-homogeneous HTS conductors, Physica C, 372-376(2002), 1743-1745.
71. G. Grasso, B. Hensel and A. Jeremie, Distribution of the transport critical current density in Ag sheathed (Bi, Pb)_2Sr_2Ca_2Cu_3O_x tapes produced by rolling, Physica C, 241(1995), 45-52.
72. M. Lelovic, P. Kdshnaraj, N. Eror and U. Balachandran, Minimum critical current density of 10~5A/cm~2 at 77 K in the thin layer of Bi_(1.8)Pb_(0.4)Sr_(2.0)Ca_(2.2)Cu_3O_y superconductor near the Ag in Ag-sheathed tapes, Physica C, 241(1995), 246-250.
73. M. Lelovic, P. Krishnaraj, N. Eror and U. Balachandran, Transport critical current density above 10~5A/cm~2 at 77 K in the thin layer of Bi_(1.8)Pb_(0.4)Sr_(2.0)Ca_(2.2)Cu_3O_y superconductor tapes made by the Ag wire-in-tube method, Supercond. Sci. Technol., 9(1996), 201-204.
74．曹效文，王智河，Bi系带材的临界电流密度性质，低温与超导，25(1997)，46-55．
75. R. Inada, K. Tateyama, Y. Nakamura and A. Oota, Total AC loss of Ag-sheathed Bi2223 tapes with various filament arrangements carrying AC transport current in AC parallel transverse magnetic field, Supercond Sci. Technol., 20(2007), 138-146.
76. P.X. Zhang, C. S. Li, L. Zhou and R. Inada, The effects of J_c distribution on transport AC losses for Ag-sheathed Bi2223 tapes, Physica C, 356(2003), 146-146.
77. F. G(?)m(?)ry, E. Seiler, G. Perkins, E. Pardo and C. Navau, The influence of filament arrangement on current distribution and AC loss in Bi2223/Ag tapes, Supercond. Sci. Technol., 17(2004), S150-S154.
78. J. Ogawa, Y. Sawai, H. Nakayama, O. Tsukamoto and D. Miyagi, n value and J_c distribution dependence of AC transport current losses in HTS conductors, Physica C, 401(2004), 171-175.
79. B. Haken, H. Eck, H. Kate, A new experimental method to determine the local critical current density in high-temperature superconducting tapes, Physica C, 334(2000), 163-167.
80. Y.B. Kim, C. F. Hempstead and A. R. Strnad, Magnetization and critical supercurrents, Phys. Rev., 129(1963), 528-536.
81. R.G. Mints, Flux creep and flux jumping, Phys. Rev. B, 53(1996), 12311-12317.
82. L. J. Neuringer, Y. Shapira, Nb-25%Zr in strong magnetic fields: magnetic, resistive, ultrasonic, and thermal behavior, Phys. Rev., 148(1966), 231-246.
83. N. H. Zebouni, A. Venkataram, G. N. Rao, C. G. Grenier and J. M. Reynolds, Magnetothermal effects in type Ⅱ superconductors, Phys. Rev. Lett., 13(1964), 606-609.
84. J. L. Tholence, H. Noel, J. C. Lever, M. Potel and P. Gougeon, Magnetization jumps in YBa_2Cu_3O_7 single crystal up to 18 T, Solid State. Commun, 65(1988), 1131-1134.
85. M. Guillot, M. Potel, P. Gougeon, H. Noel and G. Chouteau, Magnetization jumps and critical current of YBa_2Cu_3O_7 single crystal, Phys. Lett. A, 127(1988), 363-365.
86. K. Chen, S. W. Hsu, T. L. Chen, S. D. Lan, and P. T. Wu, High transport critical current and flux jumps in bulk YBa_2Cu_3O_x superconductors, Appl. Phys. Lett., 56(1990), 2675-2677.
87. K. -H. Mu|¨ller and C. Anddkidis, Flux jumps in melt-textured Y-Ba-Cu-O, Phys. Rev. B, 49(1994), 1294-1307.
88. G. C Han, K. Watanabe, S. Awaji, N. Kobayashi, and K. Kimura, Magnetisation and instability in melt-textured YBa_2Cu_3O_7 at low temperature and high fields up to 23T, Physica C, 274 (1997), 33-38.
89. L. Legrand, I. Rosenman, R. G. Mints, G. Collin, and E. Janod, Self-organized criticality effect on stability: magneto-thermal oscillations in a granular YBCO superconductor. Europhys. Lett., 34(1996), 287-292.
90. M. E. McHenry, H. S. Lessure, M. P. Maley, J. Y. Coulter, I. Tanaka, and H. Kojima, Systematics of flux jumps and the stabilizing effect of flux creep in a La_(1.86)Sr_(0.14)CuO_4 single crystal, Physica C, 190(1992), 403-414.
91. A. Gerber, Z. Tarnawski, and J. J. M. Franse, Magnetic instabilities in high temperature superconductors, Physica C, 209(1993), 147-150.
92. A. Milner, High-field flux jumps in BSCCO at very low temperature, Physica B, 294-295 (2001), 388-392.
93. A. Nabialek, M. Niewczas, H. Dabkowska, A. Dabkowski, J. P. Castellan, and B. D. Gaulin, Magnetic flux jumps in textured Bi_2Sr_2CaCu_2O_(8+δ), Phys. Rev. B, 67(2003), 024518.
94. V. Chabanenko, R. Puzniak, A. Nabialek, S. Vasiliev, V. Rusakov, L. Huanqian, R. Szymczak, H. Szymczak, J. Jun, J. Karpinski, and V. Finkel, Flux jumps and H-T diagram of instability for MgB_2, J. Low Temp. Phys., 130(2003), 175-191.
95. Z. W. Zhao. S. L. Li, Y. M. Ni, H. P. Yang, Z. Y. Liu, H. H. Wen, W. N. Kang, H. J. Kim, E. M. Choi, and S. I.Lee, Suppression of superconducting critical current density by small flux jumps in MgB_2 thin films, Phys. Rev. B, 65(2002), 064512.
96. D. Monler, L. Fruchter, Magnetothermal instabilities in an organic superconductor. Eur. Phys. J. B., 3(1998), 143-148
97. S.L. Wipf, M. S. Lubell, Flux jumping in Nb-25% Zr under nearly adiabatic conditions, Phys. Lett., 16(1965), 103-105.
98. S. L. Wipf, Magnetic instabilities in type-Ⅱ superconductors, Phys. Rev., 161(1967), 404-416.
99. P. S. Swartz and C. P. Bean, A model for magnetic instabilities in hard superconductors: the adiabatic critical state, J. Appl. Phys., 39(1968), 4991-4998.
100. S. L. Wipf, Review of stability in high temperature superconductors with emphasis on flux jumping, Cryogenics, 31(1992), 936-948.
101. V. V. Chabanenko, A. I. Dyachenko, M. V. Zalutskll, V. F. Rusakov, H. Szymczak, S. Piechota, and A. Nabialek. Magnetothermal instabilities in type Ⅱ superconductors: The influence of magnetic irreversibility. J. Appl. Phys., 88(2000), 5875-5883.
102. Y. H. Zhou and X. B. Yang, Numerical simulation of thermomagnetic instability in high-Tc superconductors: Dependence on sweep rate and ambient temperature, Phys. Rev. B, 74(2006), 054507.
103. M. N. Wilson, 1983, Superconducting magnets, Clarendon Press, Oxford.
104. W. J. Carr, 1983, AC losses in type-Ⅱ superconducters, Science Publishers, New York.
105. W. T. Norris, Calculation of hysteresis losses in hard superconductors carrying ac: isoland conductors and edges of thin sheets, J. Phys. D: Appl. Phys., 3(1970), 489-507.
106. 王金星,1985,超导磁体,原子能出版社,北京.
107. M. Ohmer and J. P. Hearich, Magnetization of hysteretic superconductors for complete field penetration and a critical-state model with J_c(H)-α/H, J. Appl. Phys., 44(1973), 1804-1809.
108. J. Orehotsky, M. Garber, Y. Xu, Y. L. Wang, and M.Suenage, 60-Hz ac losses in YBa_2Cu_30_7 cylinders, J. Appl. Phys., 67(1990), 1433-1436.
109. E. S. Valkhov, K. A. Nenkov, and M. Ciszek, AC losses in polycrystalline YBa_2Cu_3O_y doped with Ag and Te, Physica C, 195(1992), 345-351
110. M. Ciszek, J. Olejniczak, E. Trojnar, A. J. Zaleski, J. Klamut, A. J. M. Roovers, and L. J. M. van de Klundert, AC losses and critical current density of superconducting GdBa_2Cu_3O_(7-x). Physica C, 152(1988), 247-250
111. Y. Xu, W. Guan, and K. Zeibig, Ac losses in REBa_2Cu_3O_(7-x) superconductors, Appl. Phys. Lett., 54(1989), 1699-1701.
112. S. Zannella, L. Jansak, M. Majoros, V. Selvamanickam, and K. Salama, AC energy dissipation in high-T_c superconductors, Physica C, 205(1993), 14-20.
113. T. H. Johnasen, H. Bratsberg, Critical-state magnetization of type-Ⅱ superconductors in rectangular slab and cylinder geometries, J. Appl. Phys., 77(1995), 3945.
114. P. O. Hetland T. H. Johansen, and H. Bratsberg, Magnetization in a generalized critical-state model for type-Ⅱ superconductors, Cryogenics, 36(1996), 41-46.
115．王银顺，林良真，4.5K下Bi2223／Ag多芯带材的磁化和磁滞损耗，低温物理学报，19(1997)，453-459．
116. E. H. Brant, Superconductor disks and cylinders in an axial magnetic field. I. Flux penetration and magnetization curves, Physical review B, 58(1998), 6506-6522.
117. V. Sokolovsky, V. Meerovich, S. Goren, and G. Jung, Analytical approach to AC loss calculation in high-Tc superconductors, Physica C, 306(1998), 154-162.
118. K. Kajikawa, M. Iwakuma, and K. Funaki, A heuristic description of AC losses in superconducting slab with smooth voltage-current characteristics represented by power law, Physica C, 378-381(2002), 1097-1101.
119. P. N. Mikheenko, J. Horvat, M. Ionescu, and S. X. Dou, Two-dimensional effects in AC losses of Bi_2Sr_2Ca_2Cu_3O_x tapes, ehysica C, 274(1997), 9-16
120. M. Watahiki, S. I. Yoo, and M. Murakami, A.C. susceptibility measurements in the presence of d.c. magnetic fields for Nd - Ba - Cu - O superconductors, Supercond Sci. Tech., 10(1997), 754-757.
121. H. Eckelmann, C. Schmidt, Temperature dependence of AC-losses in Bi-2223 superconducting tapes, Physica C, 372-376(2002), 1792-1796.
122. V. Sokolovsky and V. Meerovich, Heating due to AC losses in high-temperature superconductors, Physia C, 308(1998), 215-220.
123. Y. Zhao, C. H. Cheng, and H. Zhang, Influences of flux on a. c. loss per cycle in superconductors, Solid State Communications, 111(1999), 159-164.
124．胡立发，张平祥，王金星和周廉，高温超导体中的交流损耗，低温与超导，28(2000)，24-31．
125．胡立发，周廉，王金星等，磁化法测量Bi2223／Ag高温超导带材的超低频交流损耗，低温物理学报，22(2000)，462-466．
126. K. Kajikawa, Y. Mawatari, T. Hayashi and K. Funaki, AC loss evaluation of thin superconducting wires with critical current distribution along width, Supercond. Sci. Technol., 17(2004), 555-563.
127. A. Galkin, B. Ivanov, V. Kambersky, On the critical state in a non-uniform type Ⅱ superconductor, Physia C, 325(1999), 159-164.
128. D-X Chen, A. Sanchez and E. Pardo, Transport ac loss of a superconducting cylinder with field and radius dependent critical-current density, Supercond. Sci. Technol., 17(2004), 256-262.
129. N. Sekine, O. Tsukamoto, A. Utsunomiya and D. Miyagi, Dependence AC magnetization losses in thin film superconductor tape on J_c distribution along tape width, Physia C, 426-431(2005), 1284-1289.
130. O. Tsukamoto, AC losses in a type Ⅱ superconductor strip with inhomogeneous critical current distribution, Supercond Sci. Technol, 18(2005), 596-605.
131. R. Inada, Y. Nakamura and A. Oota, Evaluation of AC losses in cable conductors using thin superconducting tapes with non-uniform J_c distribution, Physia C, 442(2006), 139-144.
132. R. Inada, A. Oota, H. Fujimoto, Influence of locally varying J_c distribution on AC transport losses for superconductor wires and tapes with various cross sections, Physia C, 378-381(2002), 1133-1137.
133. Z. Jiang, N. Amemiya, O. Maruyama and Y. Shiohara, Critical current density distribution and magnetization loss in YBCO coated conductors, Physia C, 463(2007), 790-794.
134. F. G()m(?)ry, J. Souc, M. Vojenciak, and B. Klincok, Phenomenological description of flux pinning in non-uniform high-temperature superconductors in magnetic fields lower than the self-field, Supercond. Sci. Technol., 20(2007), S271-S277.
135. R. Inada, P. X. Zhang, Numerical modeling of Bi2223 multifilamentary tapes with position-dependence J_c, Physia C, 372-376(2002), 1800-1805.
136. R. Inada, Y. Nakamura and A. Oota, Numerical analysis for AC losses in single-layer cables composed of rectangular superconducting strips with various lateral J_c distributions, J. Phys: conference series, 97(2008), 012324-012329.
137. K. Chen, Y. C. Chen, S. W. Lu, W. H. Lee, and P. T. Wu, Magnetic and thermal instabilities in a textured YBa_2Cu_30_x superconductor with high transport J_c, Physica C, 173(1991),227-231.
138. J. Rhyner, Magnetic properties and AC-losses of superconductors with power law current-voltage characteristics, Physica C, 212(1993), 292-300.
139. Z. L. Xiao, P. Voss-de Hann, G. Jakob, T. Kluge, P. Haibach, H. Adrian, and E. Y. Andrei, Flux-flow instability and its anisotropy in Bi_2Sr_2CaCu_20_(8+δ) superconducting films. Phys,Rev.B., 59(1999), 1481-1490.
140. M. J. Qin and X. X. Yao, Ac susceptibility of high-temperature superconductors, Phys. Rev. B., 54(1996), 7536-7543.
141. R. Griessen, Resistive behavior of high-T_c superconductors: influence of a distribution of activation energies, Phys. Rev. Lett., 64(1990), 1674-1677.
142. E. T. Swartz and R. O. Pohl, Thermal boundary resistance, Rev. Mod. Phys., 61 (1989), 605-668.
143. J. R. Clem, 1991, AC losses in type-Ⅱ superconducters, Magnetic susceptibility of superconductors and other Spin system, Plenum Press, New York.
144. M. Ciszek, S. P. Ashworth, B. A. Glowacki, A. M. Campell and P. Haldar, Transport AC losses in multifilamentary Ag/Bi2223 tapes in low external DC magnetic fields, Physica C, 272(1996), 319-325.
145. M. Dhalle, A. Polcari, F. Mufti, Y. B. Huang, and G. Witz, Effects of alternating magnetic field losses in high-temperature multifilament Bi2223/Ag tapes by high resistive barriers, IEEE Trans. Appl. Supercond., 9(1999), 782-784.
146. M. P. Oomen, J. Rieger, H. Tenkate, Field-angular dependence of alternating current loss in multifliamentary high-temperature superconducting tapes, Appl. Phys. Lett., 70(1997), 3038-3040.
147. J. J. Rabbers, B. T. Haken, O. A. Shevechenko, and H. Tenkate, An engineering formula to describe the AC loss of BSCCO/Ag tape, IEEE Trans. Appl. Supercond, 11(2001), 2623-2626.
148. T. Yazawa, J. J. Rabbers, O. A. Shevechenko, B. T. Haken and H. Tenkate, Modeling the current distribution in HTS tapes with transport current and applied magnetic field, IEEE Trans. Appl. Supercond, 9(1999), 797-800.
149. T. Yazawa, J. J. Rabbets, B. T. Haken and Y. Yamada, Numerical calculation of current distributions in high temperature superconducting tapes with finite thickness in self field and external field, Physia C, 310(1998), 36-41.
150. W. D. Lee, L. Horong, T. J. Yang and B. S. Chiou, Analysis of transport critical current density in a bent BiPbSrCaCuO silver sheathed tape, Physica C, 247(1995), 215-220.
151. E. Pardo, D.-X Chen, A. Sanchez, and C. Navau, Alternating current loss in rectangular superconducting bars with a constant critical-current density, Supercond. Sci. Technol., 17(2004), 83-87.
152. M. Lahtinen, J. Passi, Z. Hun and J. Sarkaniemi, Microstructure of the ceramic in superconducting Bi2223 composite tapes after bending strain cycle, Physica C, 277(1997), 186-194.
153. R. Wesche, A. M. Fuchs, B. Jakob and G. Pasztor, Axial and bending strain effects in Ag and AgNiMg.Bi2212 wires, Cryogenics, 36(1996), 419-426.
154. B. T. Haken, 1994, Strain effects on the critical properties of high-field superconductor, Twemte University, Netherland..
155. M. Ciszek, B. A. Ashworth, A. M. Campell, S. P. Ashworth, and W. L. Yang, Influence of external magnetic fields and its orientation on transports AC losses in Bi2223 and Tl2223 silver sheathed tapes, IEEE Trans. Appl. Supercond., 7(1997), 314-317.
156. M. Ciszek, S. P. Ashworth, B. A. Ashworth and W. Y. Liang, Low magnetic field study of ac losses on monocore Bi2223 and T12223 silver sheathed tapes, Cryogenics, 36(1997), 637-641.
157. J. J. Rabbers, D. C. Laan, B. T. Haken, and H. H. Tenkate, Magnetization and transport current loss of a BSCCO/Ag tape in an external AC magnetic field carrying an AC transport current, IEEE Trans. Appl. Supercond, 9(1999), 1185-1188.
158. E. H. Brandt, Superconductors of finite thickness in a perpendicular magnetic field: strips and slab, Phys. Rev. B, 54(1996), 4246.
159. E. H. Brandt, Thin superconductors in a perpendicular magnetic ac field: General formulation and strip geometry, Phys. Rev. B, 49(1994), 9024.
160. E. H. Brandt, Thin superconductors in a perpendicular magnetic ac field: circular disk, Phys. Rev.B, 50(1994), 4034.
161. E. H. Brandt, Type II superconductor strip with current in a perpendicular magnetic field, Phys. Rev. B, 48(1993), 12893
162. M. Suenaga and V. F. Solovyov, ac losses in circular disks of thin YBa_2Cu_3O_7 films in perpendicular magnetic fields, J. Appl. Phys., 94(2003), 502-506.
163. J. R. Clem, Field and current distributions and ac losses in a bifilar stack of superconducting strips, Phys. Rev. B, 77(2008), 134506
164. C. A. Duran, P. L. Gammel, R. wolfe, et al., Magneto-optical imaging of flux penetration in high temperature superconducting thin films, Nature, 357(1992), 474-550.
165. D. A. Brawner, A. Schilling, H. R Ott, R. J. Haug, K. Ploog, and K. von. Klitzing, Superconductivity at 93 K in a new mixed-phase Y-Ba-Cu-O compound system at ambient pressure, Phys. Rev. Lett., 71(1993), 785-788.
166. D. A. Brawner and N. P. Ong, Scanning Hall microprobe measurements of magnetization profiles in YBa_2Cu_3O_(7-y) single crystals, J. Appl. Phys., 73(1993), 3890-5645.