Jean Lévêque

A New Analytical Torque Formula for Axial Field Permanent Magnets Coupling

In this paper, we present a simple and accurate analytical expression to compute the torque of axial-field magnetic couplings. The torque expression is obtained by solving the three-dimensional (3-D) Maxwell equations by the method of separation of variables. Here, we adopt the assumption of linearization at the mean radius, the problem is then solved in 3-D Cartesian coordinate (we neglect the curvature effects). To show the accuracy of the torque formula, the results are compared with those obtained from 3-D finite-element simulations and from experimental tests. As the proposed formula needs very low computational time and depends directly on the geometrical parameters, it is used for a design optimization using multiobjective genetic algorithms.

New Hybrid FE-FV Method for Computing Current Distribution in 2-D Superconductors: Application to an HTS Cylinder in Transverse Magnetic Field

This paper presents a new numerical method based on finite elements - finite volumes (FE-FV) for solving 2-D diffusion problems in high temperature superconductors (HTS). The approach does not involve directly the resistivity term (rho), generally used to model the <i>E</i>(<i>J</i>) characteristic as a power law, i.e <i>E</i>(<i>J</i>) = rho(<i>J</i>)<i>J</i>, with rho(<i>J</i>) prop <i>J</i> ^n-1. Instead, we use a <i>J</i>(<i>E</i>) constitutive law <i>J</i> prop <i>E</i> ^(1/n), with <i>E</i> ^rarr = <i>Ee</i> ^rarr _z (a single component), which leads to a scalar non-linear differential equation. After presenting in details the developments, the method is tested in the case of a superconducting cylinder submitted to a transverse magnetic field. The current density obtained is compared to another numerical technique (the semi-analytical method) in order to validate the results. Although not fully optimized yet, it appears that the proposed method is very stable, especially for large n-values (greater than 100).

Theoretical studies and experimental results of a SMES used in a pulsed current supply

A superconducting magnet energy storage (SMES) can be used as a pulsed power supply. A superconducting coil stores energy without electrical losses and this energy can be recovered through a second wire on which the charge (electromagnetic launcher, for example) is linked. The design of such an apparatus needs to solve simultaneously thermal, magnetic, and electric equations. We proposed a three-dimensional finite difference method to solve these coupled problems. This tool enables us to describe resistive zones of expansion in thick coils during a quench and to predict the duration and the efficiency of the discharge. Moreover, it indicates if the coil is prevented from an excessive temperature increase. Then, a probative device is described and experimental results are compared with theoretical ones.

Original article: Analytical calculation of the flux density distribution in a superconducting reluctance machine with HTS bulks rotor

This paper deals with the analytical computation of the magnetic field distribution in a wholly superconducting reluctance motor. The rotor is made with high temperature superconductor bulks which nearly present a diamagnetic behavior under zero-field cooling. The stator consists of superconducting armature windings fed by AC currents of high amplitude. The superconducting stator winding can generate a high rotating magnetic field without the need of ferromagnetic material in the rotor. The electromagnetic torque is obtained by the interaction between the rotating magnetic field created by the superconducting stator windings and the variable reluctance due to the superconducting bulks. The proposed analytical method is based on the resolution of Laplaces equation (by the separation of variables method) for each sub-domain, i.e. rotor shaft, holes between superconducting bulks and air-gap. The global solution is obtained using boundary and continuity conditions. Magnetic field distribution and electromagnetic torque obtained by the analytical method are compared with those obtained from finite element analyses.

A 2-D Robust FE-FV Mixed Method to Handle Strong Nonlinearities in Superconductors

A robust numerical method based on 2-D mixed finite-elements-finite volumes (FE-FV) allows the solution of diffusion problems in superconducting (SC) materials. The proposed approach handles the strong nonlinearity of the E(J) constitutive power law of high-temperature superconductors (HTS). The method is tested for a SC cylinder submitted to a sinusoidal transport current or to a transverse sinusoidal external field. The current density distributions as well as the AC losses are computed. Comparisons to a FE analyses that use the magnetic field as state variable show the validity of the proposed approach. It can be seen that the proposed method is very stable even for large n-values for which the FE method does not converge.

AC losses in a BSCCO current lead: comparison between calculation and measurement

It is important to calculate the AC losses in the HTS material. The Bean model makes it possible analytically to calculate these losses in simple cases. A model which takes into account the characteristic E(Jn) exists. It does not allow an analytical study of the losses but allows a numerical calculation of those. In this article, we determine the distributions of E (r, t) and J (r, t), and deduce the losses, in a BSCCO current lead supplied by a sinusoidal current. First of all, we compare the distributions obtained with the Bean model and the E(Jn) model. Finally we compare the calculated losses using the two models, with measured losses, presented in a preceding article. We show the validity of our results, provided that the current remains sufficiently lower than the critical current.

Finite Element AC-Losses Computation in Multi-Layer HTS Cable Using Complex Representation of the Electromagnetic Field

The paper deals with the concept of effective resistivity to use in problems expressed in terms of phasor quantities under a sinusoidal time varying excitation. A single time-harmonic solution with several definitions of the effective electric conductivity is given. The losses in HTS tape and cable are obtained in steady state and the results are validated through Norris formulae.

Calculation of losses in a HTS current lead with the help of the dimensional analysis

Abstract The calculation of losses is highly required to design any superconducting device. To do that the analytical approach is the best way in term of parameter analysis. Bean’s model is based on the fact that the resistive transition is sudden. This assumption is more suitable for low critical temperature superconductors. For ceramics, the transition is smoother, so the variation of electric field E with current density is a function well approached by kJ n . Using this kind of function and a dimensional analysis the authors propose a new analytic formula to calculate the losses in the case of incomplete penetration of current. Calculated results are compared to measured ones and the validity limit is shown.

AC loss measurements of a high critical temperature superconductor transporting sinusoidal or non-sinusoidal current

In electrical engineering, static converters generate harmonics; consequently the losses in the conductors increase. To use High-Tc superconductors for current transportation, it is important to evaluate and to measure their losses. Under the assumption that the superconductor is only exposed to its self-field, Beans model is used to compute these losses. This work deals with the losses in a cylindrical High-Tc superconductor current-lead. It is made of compacted composite of Bi-Pb-Sr-Ca-Cu-O-2223, the value of its critical current is about 100 A (measured with I /spl mu/V/cm criteria). Two types of measuring methods are used. The first of them uses a differential amplifier associated with a computer, which calculate the instantaneous power by numerical integration. The second series of experiments, valid only with sinusoidal current, are made using a lock-in amplifier measuring the R.M.S. voltage. The value of transport current is high enough to be compatible with applications. Both methods give nearly the same results for sinusoidal signal. Measurements are made with non-sinusoidal current, to do that the superconductor sample is fed by a dimmer switch. The experiments show that the losses are essentially a function of the maximum value of the current, not of the firing angle. We conclude that the shape of the current is not important compared to its peak value.

3D-computation of a thermal process in a superconducting coil

This study deals with the resistive zone propagation in a superconducting coil during a quench, taking into account both the flux density distribution and the anisotropy of the thermal parameters. A Finite Difference Method is used to solve the heat diffusion equation and the flux density is calculated by means of a semi-analytical method. The 3-D model is suitable to describe the quench of thick coils and it can be applied to the study of thermal stability. As an application, a 10 kJ-solenoid is studied.