Pulse field magnetization of a ring-shaped bulk superconductor

Transcription

1 INSTITUTE OF PHYSICS PUBLISHING Supercond. Sci. Technol ) SUPERCONDUCTOR SCIENCE AND TECHNOLOGY PII: S ) Pulse field magnetization of a ring-shaped bulk superconductor Hiroyuki Ohsaki 1, Tatsuya Shimosaki 1 and Naoyuki Nozawa 2 1 Department of Advanced Energy, Graduate School of Frontier Sciences, The University of Tokyo, Hongo, Bunkyo, Tokyo , Japan 2 Institute of Industrial Science, The University of Tokyo, Komaba, Meguro, Tokyo , Japan Received 16 July 2001 Published 18 April 2002 Online at stacks.iop.org/sust/15/754 Abstract We have studied the pulse field magnetization of a YBCO bulk superconducting ring. In the experiments a 6 ms pulse magnetic field was applied to a ring-shaped YBCO superconductor with a 46 mm outer diameter, 16 mm inner diameter and 15 mm height, which was cooled by liquid nitrogen 77 K). Then, trapped magnetic field profiles were measured with a Hall sensor. For example, a single 1.2 T pulse field generated a hollow profile of the trapped magnetic field. In addition, the finite element method was used to solve the coupled problem of thermal and electromagnetic fields, where the power-n model was adopted for the E J E is the electric field and J is the current density) relation in the superconductor. A comparison between the results of experiment and analysis has shown that n = 6 gave good agreement between them. We have also discussed the current density distribution, temperature distribution, etc. 1. Introduction Recently high-performance RE)BaCuO RE = rare earth) bulk superconductors have been developed [1 3]. Among their applications, a trapped field magnet is considered to be the most promising [3, 4]. For practical application of trapped field magnets the magnetization should be more closely investigated. There are three typical ways to magnetize a bulk superconductor: field magnetization FC), zero field magnetization ZFC) and pulse field magnetization PFM). Of the three, PFM is considered to be the most practical method because it needs only a small and simple coil to apply a magnetic field and, consequently, no superconducting magnet is needed even to apply a high magnetic field [5]. Therefore PFM enables the design of a more compact and lighter electromagnetic system. However, it is important to consider how to integrate the PFM coils in the system. Numerical analysis is useful to obtain and understand electromagnetic phenomena in the superconductor during PFM and the design of a total system with in situ PFM coils. We have studied pulse field magnetization of a ringshaped bulk superconductor because a ring-shaped bulk superconductor can have a lower ratio of weight to trapped magnetic flux than a cylindrical bulk superconductor. So a lighter system could be designed with ring-shaped bulk superconductors used as trapped field magnets. We have performed PFM experiments on a ring-shaped bulk superconductor and numerical analysis of coupled problems of electromagnetic and thermal fields during PFM. In this paper we include the results of these PFM experiments, numerical analysis and a comparison between them. 2. Experiment In the PFM experiment we used a ring-shaped resinimpregnated YBCO bulk superconductor QMG), shown in figure 1, which had an outer diameter of 46 mm, an inner diameter of 16 mm and a height of 15 mm. For an examination of the fundamental macroscopic properties of the superconductor, FC of the superconductor was performed, where the superconductor was cooled in liquid nitrogen 77 K) in a uniform magnetic field of 1.0 T. Then a trapped field profile was measured with a Hall probe on a plane 0.5 mm above the top surface of the superconductor. A measured trapped field profile is shown in figure 2. The flux density in thecentre was 0.60 T. The profile indicates a rather good homogeneity of the superconductor. Furthermore the critical current density was estimated to be Am /02/ $ IOP Publishing Ltd Printed in the UK 754

2 Pulse field magnetization of a ring-shaped bulk superconductor Figure 1. The ring-shaped YBCO bulk superconductor used in the PFM experiment. The outer diameter is 46 mm, the inner diameter is 16 mm and the height is 15 mm. It was produced by the QMG method with resin impregnation. This figure is in colour only in the electronic version) Figure 3. Experimental setup for PFM. Coil current waveform. Figure 2. The trapped field profile measured after FC at 1 T. It was measured on a plane 0.5 mm above the top surface of the superconductor. The experimental set-up for the PFM is shown in figure 3. The superconductor in liquid nitrogen 77 K) was placed between two electric coils, which were used to apply a pulse magnetic field. Figure 3 shows the waveform of the coil current, which was supplied by a pulse power supply of 5 kv, 2 ka and 4 kj with a capacitor bank of 320 µf. Two experiments were performed separately where the pulse width was 6 ms, and the peak flux density of the applied magnetic field at the centre B a ) was 0.6 T and 1.2 T. Figure 4 shows the trapped field profiles measured on a horizontal line 0.5 mm above the top surface of the superconductor after PFM of 0.6 T and 1.2 T. A rapid change in the externally applied magnetic field induced a large shielding current in the bulk superconductor, which limits the penetration of magnetic flux into the superconductor, so the flux density in the centre region remained low. Although a higher trapped field is required for practical applications, the experimental results shown in figure 4 are sufficient for a comparison of the results of experiment and analysis using the finite element method FEM). Figure 4 shows the flux density profile on a plane for 1.2 T PFM. A slight asymmetry coincides with the facet lines of the superconductor. The PFM with a rapid change in the externally applied magnetic field is sensitive to varying superconducting properties, so the flux density profile after PFM becomes asymmetric. However, the asymmetry of the flux density profiles was not taken into account in the numerical analysis. 3. Numerical analysis method The physical phenomena during PFM are described by electromagnetic and thermal fields. The fundamental equations on the axisymmetric coordinate r z) are as follows: r ρc T [ ν r = r ra) κ ab 2 T r 2 ] + z + κ 1 ab r ν A z ) = σ A 1) T r + κ 2 ) T c + Q 2) z 2 where A is the magnetic vector potential, T is temperature, ν is magnetic reluctivity, σ is electric conductivity, ρ is mass 755

3 HOhsakiet al Figure 4. Trapped field profiles measured on a horizontal line 0.5 mm above the top surface of the superconductor after PFM at 0.6Tand1.2T. Flux density profile on a horizontal plane 0.5 mm above the top surface of the superconductor for a 1.2 T PFM. density, C is specific heat, k ab is thermal conductivity in the ab plane, k c is thermal conductivity in the c-axis direction, and Q is heat generation. The current density in the superconductor J is given by the following equation: J = σe = σ A 3) where E is the electric field. The FEM analysis of the coupled problem described by these equations was performed. σ is nonlinear and dependent on E and J. The power-n model is used to describe the nonlinear E J characteristics of the superconductor, E = E c J J c ) n 4) J c = σ initial E c 5) where J c is the critical current density, σ initial is the initial electric conductivity, and E c is the reference electric field. The dependence of J c on temperature and flux density is taken into account in the FEM analysis. The flux density dependence of J c was described by the Kim model, B 0 J c = J c0 6) B + B 0 where J c0 is J c for B = 0andB 0 is constant. The temperature dependence was given by the following equation: Figure 5. Flux density profiles of FEM analysis where B a = 1.2 T, and n = 4, 6 and 8 with no heat generation in the superconductor taken into account. The experimentally obtained profile is also shown. { ) } T 2 2 J c0 T ) = α 1 7) T c0 where T c0 is the critical temperature at B = 0andα is constant. The heat generation in the superconductor Q is given by Q = J E. An iterative calculation is necessary to obtain the convergence of σ at each time step. A modified σ is calculated from the following equation: σ new = σ initial Jc J m ) n 1 = J c E m Em where E m is the electric field at the mth iteration step. A new σ at the m + 1)th step is calculated by the following equation: σ m+1 = βσ new + 1 β)σ m 9) where β is the relaxation parameter. The numerical analysis model on the axisymmetric coordinate r z) has geometrical parameters consistent with the experimental system. In the electromagnetic field analysis a coil current is a half-cycle sinusoidal wave with a pulse width of 6 ms. In the thermal field analysis two kinds of boundary conditions were applied on the superconductor surface: a fixed temperature boundary condition and an adiabatic boundary condition. The fixed temperature boundary condition is simple but rather different from the actual conditions, while the adiabatic boundary condition seems to be a good approximation for the short pulse used in PFM. In the analysis, first-order triangular elements were used; the number of elements was 8840, and the number of nodes was The critical current density of the bulk superconductor was assumed to be Am 2 based on the FC experiment. The parameters used in the analysis were as follows: σ initial = Sm 1 ; E c = Vm 1 ; B 0 = 0.4 T; T c0 = 92 K; α = Am 2 ; ρ = kg m 3 [6]; C = kg m 3 [6]; k ab = 14.5 W m 1 K 1 [7]; and k c = 3.0 W m 1 K 1 [7]. 4. Numerical analysis results E c ) 1 n Figure 5 shows the flux density profiles for B a = 1.2 T, and n = 4, 6 and 8 with no heat generation in the superconductor 8) 756

4 Pulse field magnetization of a ring-shaped bulk superconductor Figure 6. Flux density profiles where B a = 1.2 T, and n = 4, 6 and 8 with heat generation taken into account using the fixed temperature boundary condition. Figure 8. Time evolution of flux density profiles for the same model as shown in figure 7 while increasing and decreasing the applied field. Figure 7. Flux density profiles for n = 6 with heat generation in the superconductor taken into account using the adiabatic boundary condition: B a = 1.2 T; B a = 0.6 T. taken into account, while figure 6 shows those with heat generation using the fixed temperature boundary condition. The profile obtained by the experiment is also shown in these figures. The introduction of heat generation enhances the penetration of magnetic flux and increases the flux density in the whole region. However, the analysis results deviate largely from the experimental curves. Figure 7 shows the flux density profiles for n = 6 with heat generation in the superconductor taken into account using the adiabatic boundary condition: for B a = 1.2TandforB a = 0.6 T. The n value of 6 almost coincides with that reported in [8] on current limiting elements using bulk superconductors that were prepared by the same method as used in this research. Tokunaga et al [8] reported that n was dependent on temperature and samples 7.9 at 77 K and 5.4 at 87 K for one sample, and 5.7 at 77 K and 4.9 at 87 K for another sample). In the experiment presented in this paper, during PFM the temperature rises in the superconductor due to ohmic losses. Thus, it cannot simply be concluded that the n of the superconductor is 6. However, this condition gave rather good agreement between the numerical analysis and experimental results. Figure 8 shows the time evolution of flux density profiles for the same model as shown in figure 7. The flux density increased up to 1.2 T at the edge of the superconductor but was still less than 0.4 T in the central region due to the shielding current in the superconductor. Then the flux density decreased with the decreasing applied field, and the maximum flux density at t = 6 ms was about 0.35 T. 757

5 HOhsakiet al to a large part of the cross section, the applied field changes direction and a positive current is induced from the peripheral region. At t = 6 ms the current density distribution becomes that shown in figure 9, and the maximum is still a little larger than Am 2. The temperature of the superconductor increases while a pulse field is applied. Figure 10 shows the temperature distribution in the bulk superconductor at t = 6 ms. Joule heating increased the temperature in the outer region and the maximum temperature reached about 83 K at the outer corners, which decreases the critical current density. The temperature rise in the outer region influences the final distribution of flux density. 5. Conclusions Figure 9. Current density distribution in the superconductor at t = 6 ms when the pulse magnetic field becomes zero. We have studied the PFM of a YBCO bulk superconducting ring. In the PFM experiments a single 6 ms pulse generated a hollow profile of the trapped magnetic field. FEM analysis was carried out to solve the coupled problem of the thermal and electromagnetic fields, where the power-n model was adopted for the E J relation of the superconductor. A model, in which n = 6 using the adiabatic boundary condition for thermal field analysis, gave good agreement between the results of experiment and analysis. References Figure 10. Temperature distribution in the bulk superconductor at t = 6ms. Figure 9 shows the current density distribution in the superconductor at t = 6 ms when the pulse magnetic field becomes zero. A positive current is induced in the outer region, and a negative current is induced in the middle region. No current flows in the innermost region. When a pulse magnetic field is applied, negative current is first induced from the peripheral region, and then a negative current region extends towards the centre. But the applied field is not large enough to spread the negative current into the whole area of the superconductor. When a negative current region extends [1] Gruss S, Fuchs G, Krabbes G, Verges P, Schaetzle P, Mueller K-H, Fink J and Schultz L 2001 Trapped field beyond 14 Tesla in bulk YBa 2 Cu 3 O 7 δ IEEE Trans. Appl. Supercond [2] Nariki S, Sakai N and Murakami M 2001 Processing of GdBa 2 Cu 3 O 7 γ bulk superconductor and its trapped magnetic field Physica C [3] Ikuta H, Yanagi Y, Yoshikawa M, Itoh Y, Oka T and Mizutani U 2001 Melt processing and the performance as a superconducting permanent magnet of RE Ba Cu O/Ag RE=Sm, Nd) Physica C [4] Fujimoto H and Kamijo H 2001 Trapped magnetic field of a mini-bulk magnet using YBaCuO at 77 K Physica C [5] Ikuta H, Ishihara H, Hosokawa T, Yanagi Y, Itoh Y, Yoshikawa M, Oka T and Mizutani U 2000 Pulse field magnetization of melt-processed Sm Ba Cu O Supercond. Sci. Technol [6] Tsuchimoto M and Morikawa K 1999 Macroscopic numerical evaluation of heat generation in a bulk high Tc superconductor during pulsed field magnetization IEEE Trans. Appl. Supercond [7] Fujishiro H, Ikebe M, Naito T, Noto K, Kobayashi S and Yoshizawa S 1994 Anisotropic thermal diffusivity and conductivity of YBCO123) and YBCO211) mixed crystals-i Japan. J. Appl. Phys [8] Tokunaga T, Morita M, Miura O and Ito D 1999 DC transport properties of QMG current limiting elements IEEE Trans. Appl. Supercond