Takafumi Yokono

High performance method for determination of shielding current density in HTS plate

The numerical method for determining the shielding current density in the high-Tc superconducting plate is investigated. After being discretized by means of the finite element method and the backward Euler method, the governing equation of the shielding current density is reduced to the nonlinear system. If the B dependence of the flow resistivity and the critical current density is neglected, the nonlinear system is easily solved by use of the deaccelerated Newton method (DNM). Once their B dependence is taken into consideration, a decrease in the relaxation factor will not always improve the convergence behavior of the DNM. In order to resolve this difficulty, the DNM has been modified so that the relaxation factor can be chosen adaptively. The results of computations show that the CPU time required for the modified method is about 1/21 times as much as that for the DNM.

Numerical simulation of shielding current density in HTS by element-free Galerkin method

Abstract The numerical code for calculating the shielding current density in the high- T c superconductor is developed by using the element-free Galerkin method. The behavior of the shielding current density is expressed by the system of the integro-differential equations. Coupled with the J – E constitutive relation, the initial-boundary-value problem of the system is solved to obtain the time evolution of the shielding current density. In order to solve the problem, the equivalent weak form is derived. Since the essential boundary conditions are directly incorporated into the weak form, neither the test function nor the trial one needs to satisfy them. Hence, the weak form is easily discretized by using the shape functions. In the numerical code, the resulting nonlinear system is solved at each time step. By means of the code, the magnetic field generated by the shielding current density is calculated as a function of time and its spectral analysis is performed.

Influence of B-dependence of critical current density on magnetic shielding performance of MPMG-YBCO plate

The magnetic shielding performance of the MPMG-YBCO plate is investigated numerically by assuming the flux-flow and flux-creep model as the J-E constitutive relation. The magnetic-field dependence of the critical current density and the flow resistivity is also taken into consideration through the Kim model and the Bardeen-Stephan model. Under these assumptions, the damping coefficients and the shielding factors are calculated as functions of the frequency and the amplitude of the applied AC magnetic field. The results of computations show that an increase in the frequency will enhance the shielding performance of the MPMC-YBCO plate. In addition, there exists the lowest limit of the frequency, above which the shielding performance is saturated, and the limit increases with the amplitude of the applied magnetic field. Furthermore, it turns out that the magnetic shielding performance is hardly influenced by the magnetic-field dependence of the critical current density.

Spectral analysis of magnetic fields generated by shielding current density in a high-temperature superconductor

The magnetic fields generated by the shielding current density are numerically investigated by use of spectral analysis. Coupled with the J-E constitutive relation, the governing equation of the shielding current density is numerically solved to obtain the time sequence of the magnetic fields. By means of the fast Fourier transform (FFT), the spectral analysis of the time sequence is performed. The results of the analysis show that the flux flow over the whole volume of the superconductor can be detected from the onset of the third harmonics of the magnetic fields.

Three-dimensional analysis on time evolution of shielding current density in HTS

The numerical method for calculating the shielding current density in the high-T/sub c/ superconductor (HTS) is developed by use of the element-free Galerkin method. The behavior of the shielding current density is expressed by the integro-differential equations. In order to solve the initial-boundary-value problem of the equations, the weak form is derived that is equivalent to the problem. Since the essential boundary conditions are directly incorporated into the weak form by using the Lagrange multipliers, both the test and the trial functions do not need to satisfy the conditions. The numerical code for analyzing the time evolution of the shielding current density has been developed by using the above method. The time sequence of the magnetic field is calculated by means of the code and its spectral analysis is performed.

Magnetic shielding analysis of high-T/sub c/ superconducting plates by power law, flux-flow, and flux-creep models

The magnetic shielding performance of a high-T/sub c/ superconducting (HTS) plate is investigated numerically. By taking account of the crystallographic anisotropy in the shielding current density of the melt-powder-melt-growth YBa/sub 2/Cu/sub 3/O/sub x/ plate, the multiple-layer structure is introduced to modelize the HTS plate. In this case, the shielding current density is governed by the integral-differential equation of the scalar potential. In addition, the power law is used as the J-E constitutive equation for description of the characteristics of the Type-II superconductor. When the equation is descretized by using the finite element method and the weighted average method, the resulting algebraic equation is solved by using the decelerated Newton method. A numerical code for analyzing the time evolution of the shielding current density has been developed and, by use of the code, the shielding performance of HTS plates is investigated. In addition, the results obtained by using the power law, the flux-flow and the flux-creep models are compared.

Shielding current analysis of HTS plate by deaccelerated Newton method with variable relaxation factor

Abstract The numerical method for determining the shielding current density in the high- T c superconductor has been developed by modifying the deaccelerated Newton method (DNM). After the discretization, the governing equation of the shielding current density is reduced to the nonlinear system. Once the B -dependence of the flow resistivity and the critical current density is taken into account, the convergence property of the DNM is degraded considerably. Thus, the DNM is modified so as to choose the relaxation factor adaptively. The numerical code for calculating the shielding current density has been developed on the basis of the modified method and, by use of the code, the magnetic field generated by the shielding current density is investigated from the standpoint of the spectral analysis.

Numerical investigations on relation between critical current density and third harmonic voltage in HTS

The inductive method for measuring the critical current density is investigated by using the numerical simulation. When the high-temperature superconductor is exposed to the magnetic field generated by the ac coil current, the voltage induced in the coil contains not only a linear component but higher harmonics. The harmonic voltages are numerically calculated as a function of the coil current. The results of computations show that, above a certain limit of the coil current, the third harmonic voltage is suddenly excited. In addition, it is also found that the square root of the third harmonic voltage is approximately a linear function of the coil current.

Numerical method for determination of shielding current density in axisymmetric high Tc superconducting plates under ac magnetic field

Abstract The numerical method for determining the shielding current density in the high Tc superconducting (HTS) plate is developed by modifying the deaccelerated Newton method (DNM). After discretized with respect to time and space, the governing equation of the shielding current density is reduced to the problem in which the nonlinear equation is solved at each time step. When the B-dependence of the critical current density and the flow resistivity is taken into consideration, the decrease in the relaxation factor γ of the DNM will not always ensure the convergence. For this reason, the DNM is modified so that γ can be determined adaptively. The results of computations show that the CPU time required for the modified method is about 1/18 times as much as that for the DNM.

Numerical simulation on contactless measurement of critical current density in HTS

According to the experiments by Claassen et al., (1991), the odd harmonics of the magnetic field are excited with an increase in the amplitude of the applied ac magnetic field. Especially, the third harmonic is suddenly excited after the amplitude exceeds a certain limit. This onset of the third harmonics indicates that the critical current density is following in all over the HTS. On the basis of the experimental results, Claassen developed the contactless method for measuring the critical current density. The purpose of this study is to reproduce Claassens results by means of the numerical simulation. To this end, the governing equation of the shielding current density has been formulated and the numerical code for solving the initial-boundary-value problem of the equation has been developed. After the shielding current density is evaluated by using the code, the magnetic field generated by the shielding current density is calculated as a function of time. Spectral analysis of the field is performed. The results of computations show that the flux-flow region covers the whole volume of the HTS above a certain limit of the amplitude of the applied magnetic field.