Induced currents in the bulk superconducting cylinder of a finite length placed in a transverse magnetic field are calculated by the partial and complete separation of variables. The Fourier ...transform over the angular and axial coordinates reduces the problem to the solution of 1-D integral equations. The harmonic balance method is applied to account for the highly nonlinear constitutive relation between the voltage and current. The current and field distribution is compared with the results of a finite-element analysis (FEA). The approximation of the current distribution by a set of cylindrical and disk layers is presented. The magnetic moment of induced currents is analyzed in the increasing applied field when the cylinder is magnetized up to the state of saturation.
The distribution of current density in bulk cylindrical superconductors is calculated by the method of separation of variables. The method is applied to conductors with and without the transport ...current in the transverse, longitudinal, or arbitrary directed magnetic fields. A significant reduction of the matrix equation is achieved due to the decomposition of the solution using the Fourier series over the polar angle. The method is validated on a range of test models comparing the results with the solutions found by the state-of-the-art finite-element analysis (FEA).
A ferroresonant transformer is analyzed based on the equivalent magnetic circuit and then using magnetic-field equations. It is shown that the Fourier analysis provides a quick and reliable method ...for the prediction of output voltage and current at resistive or reactive loads. The finite-element model with the voltage-driven coils is used to verify and correct the predicted fundamental and high harmonics as well as losses in the transformer. The direct solution of the nonlinear differential equations for the coupled electrical and magnetic circuits is also considered as an alternative way to analyze the resonance. However, this approach requires applying the appropriate initial conditions that are estimated from Fourier analysis. The voltage waveforms predicted from the calculation models are in good agreement with the oscilloscope screenshots.
A modified finite-element analysis (FEA) and hybrid numerical-analytical method for simulation of critical currents and magnetic fields in high-temperature bulk superconductors are discussed. It is ...shown that the hybrid method is more robust and efficient in terms of speed and accuracy as compared with the known integral method. The modified FEA method is more stable than a conventional transient solution especially at large n-value in J-E relation.
The magnetic field of bitter type rectangular coils is calculated accounting for eddy currents in the copper solid turns. The solution is found first by an integral equation method applied to the ...stacks of solid plates of finite cross section and length. Then, the results are compared with the solution by the 3-D finite element code in the exact formulation. The proximity effect of the finite length of the conductor on the eddy current distribution is discussed. The example of the design of the coil with the targeted field orientation is presented. The unidirectional magnetization of isotropic permanent magnets is then discussed.
Magnetic field and critical currents trapped in bulk superconductors are calculated by a moving front method. The fronts are predicted based on the solution of a series of static models. The critical ...currents are considered in both Bean and Kim approximations. The method has been implemented for the 2-D and 3-D test models. Good agreement in the prediction of trapped fields and magnetic moments of the superconducting rings and cylinders by the moving front and nonlinear conductivity methods has been achieved.
Magnetic field and impedance of short cylindrical conductors are calculated by Grinberg's method. The analytical solution is derived for the infinitely small and finite electrodes located at the ends ...of the cylinder. The impedance of short conductors is presented in the form of convergent series. The analytical formulas are validated by the numerical solution of the same problems in alternative formulation. The analytical solution is applied for the calculation of the impedance of a resistive cylinder between two superconductors.
A three-dimensional (3-D) magnetic field problem in an axial flux machine with a toroidal winding is considered. The precise solutions generated by the integral transform and Fourier methods in ...elementary subregions are joined using the iterative Schwartz algorithm. The comparison between two dimensional and 3-D models is performed and a correction factor taking into account the radial variation of the magnetic flux is given.
