Hysteresis Modelling of High Temperature Superconductors

The present dissertation considers the capabilities, limitations and possible extensions of modelling the hysteresis that is exhibited by type-II superconductors, especially those with high critical temperature. Superconductors of type-II, including high temperature superconductors, are partially penetrated by magnetic flux. The tubes, through which the flux passes the superconductor, are `pinned' to certain locations due to impurities in the crystal structure of the material, and they must be forced by an external magnetic field or a transport current in order to move. Thus, the pinning of flux tubes constitutes a memory that gives rise to a hysteresis with corresponding losses. The critical state model is a well-known, macroscopic model that describes well this partial flux penetration. Furthermore, the flux tubes can start to flow due to the Lorenz-force when a large transport current flows in the superconductor. This produces an additional resistive voltage. The concept of hysteresis and its main properties are discussed, and a number of various models describing this phenomenon are presented. An emphasis is made on the classical Preisach model of hysteresis, which is a weighted superposition of relay operators. A hysteretic system produces higher harmonics, just as most nonlinear systems. An investigation reveals under what conditions the Preisach model generates only odd harmonics, and also when all odd harmonics are present, as well as how this knowledge can be utilised. A parameterised Preisach model is proposed, which always applies when the critical state model is an acceptable approximation of the superconductor hysteresis. Its capabilities and limitations as a hysteresis model for superconductors are investigated. It is demonstrated how the parameters can be estimated from different electric measurements on high temperature superconductors and that the output and the losses can quickly and accurately be computed for an arbitrary signal, once the parameter identification is made. Moreover, the structure of the parameterised model is such that an inverse model can easily be obtained. It is also shown that the hysteresis saturation, which occurs when the flux flow starts, can be modelled by introducing limiting functions in the model. A generalised equivalent circuit has been proposed that takes into account both the hysteretic and resistive behaviour, the latter being due to flux flow. This extended model describes the global electric behaviour of a superconducting device, which can be applied either when the superconductor is part of a larger system or when it stands alone. A few examples of its application are given.

Hysteresis modelling of high temperature superconductors

Marten Sjöström

The present dissertation considers the capabilities, limitations and possible extensions of modelling the hysteresis that is exhibited by type-II superconductors, especially those with high critical temperature. Superconductors of type-II, including high temperature superconductors, are partially penetrated by magnetic flux. The tubes, through which the flux passes the superconductor, are 'pinned' to certain locations due to impurities in the crystal structure of the material, and they must be forced by an external magnetic field or a transport current in order to move. Thus, the pinning of flux tubes constitutes a memory that gives rise to a hysteresis with corresponding losses. The critical state model is a well-known, macroscopic model that describes well this partial flux penetration. Furthermore, the flux tubes can start to flow due to the Lorenz-force when a large transport current flows in the superconductor. This produces an additional resistive voltage. The concept of hysteresis and its main properties are discussed, and a number of various models describing this phenomenon are presented. An emphasis is made on the classical Preisach model of hysteresis, which is a weighted superposition of relay operators. A hysteretic system produces higher harmonics, just as most nonlinear systems. An investigation reveals under what conditions the Preisach model generates only odd harmonics, and also when all odd harmonics are present, as well as how this knowledge can be utilised. A parameterised Preisach model is proposed, which always applies when the critical state model is an acceptable approximation of the superconductor hysteresis. Its capabilities and limitations as a hysteresis model for superconductors are investigated. It is demonstrated how the parameters can be estimated from different electric measurements on high temperature superconductors and that the output and the losses can quickly and accurately be computed for an arbitrary signal, once the parameter identification is made. Moreover, the structure of the parameterised model is such that an inverse model can easily be obtained. It is also shown that the hysteresis saturation, which occurs when the flux flow starts, can be modelled by introducing limiting functions in the model. A generalised equivalent circuit has been proposed that takes into account both the hysteretic and resistive behaviour, the latter being due to flux flow. This extended model describes the global electric behaviour of a superconducting device, which can be applied either when the superconductor is part of a larger system or when it stands alone. A few examples of its application are given.

EPFL2001

Numerical modelling of high temperature superconducting tapes and cables

Francesco Grilli

This Ph.D. thesis is focused on the numerical modelling of high-Tc superconductors (HTS) at the operating temperature of 77 K (liquid nitrogen). The purpose of numerical modelling is to precisely calculate the current and field distributions inside HTS devices (tapes, cables) and the corresponding AC losses, which are one of the most important limiting factors for a large-scale application of such materials. From the electrical point of view, superconductors are characterized by a strongly non-linear voltage-current relation, which defines the transition from superconducting to normal state. In the case of HTS, the steepness of this transition is smoother than for low-Tc superconductors (LTS), so that the commonly used critical state model (CSM) gives a too simplified representation of their electromagnetic behaviour and can be used for a qualitative description only. In this thesis the finite element method (FEM) has been used for precisely computing the current and field distributions as well as for evaluating the AC losses in HTS devices. The superconducting transition is modelled with a power-law relation, E(J) = Ec(J/Jc)n, which is derived from the fit of transport measurements. Firstly, the results obtained with the software package FLUX3D on multi-filamentary tapes have been validated by means of a comparison with the ones obtained by another software package (FLUX2D). The results from FLUX2D, having already been successfully compared with experimental measurements within the framework of two previous Ph.D. theses at LANOS, have been used as reference. Secondly, two power-law models, which take into account the spatial variation of the critical current density inside HTS tapes and its strongly anisotropic dependence on the magnetic field, have been implemented in FLUX3D. In most cases, this latter dependence is extremely important, since the transport capacity of the superconductor is considerably reduced (and its power loss sensibly increased) by the presence of a magnetic field. Afterwards, FEM modelling of HTS tapes has been extended to cables. HTS cables are in general composed by different layers of several tapes and have a quite complex three-dimensional structure: in fact, the layers are wound around a central cylindrical support with different pitch lengths and relative winding orientations, in order to obtain a uniform repartition of the transport current among the layers, which minimizes the total AC losses. For overcoming the difficulties of a direct 3D FEM simulation, a simple electrical model, which allows to find the optimal pitch lengths and whose results are the input data for a 2D FEM evaluation of the AC losses, has been developed. FEM computations have also been used to investigate the influence of the non-uniformity of the tape properties (contact resistance, critical current, power index) on the global loss performance of a single-layer HTS cable. As an alternative to FEM computations, an equivalent circuit model of HTS cables has been utilized. It describes the cable from the macroscopic point of view and allows to compute the current repartition among the layers and the corresponding AC losses, without the necessity of having detailed information about individual tapes. In the framework of the European project BIG-POWA, I have collaborated to the assembling process of a HTS power-link at the Pirelli Labs, in the Milan region, Italy. Finally, 3D simulations have been performed to extensively study the coupling effect between two superconducting filaments via the resistive matrix, which is a typical case where analytical solutions exist for very peculiar geometries and physical conditions only. FEM simulations have been utilized to study the dependence of the filament coupling on the physical and geometrical parameters of the conductors.

EPFL2004

Normal state transport properties of novel superconductors

Balazs Sipos

The discovery of high temperature superconductivity in the cuprates in 1986 has boosted the research in strongly correlated materials. One strong motivation was and stays the understanding the high-Tc phenomenon with the hope that one can ultimately engineer new materials with even higher Tc. Besides the in-depth investigation of cuprates, there is a strong tendency in the solid state community to find new superconductors, which by themselves are interesting for applications, or by their properties they can contribute to the understanding of the high-Tc phenomenon. The program of my doctoral thesis was three-fold: i) to address one important issue in the cuprate superconductors, that of the role of homogeneity in the underdoped part of the phase diagram; ii) what is the effect of disorder in MgB2 superconductor, which has high potentials for applications; iii) to discover new superconductors in the family of transition metal dichalcogenides. All these materials are in some sense unconventional superconductors. The cuprates by their high Tc and the symmetry of the order parameter, MgB2 by its two-band superconductivity and Tc of 39 K, and the dichalcogenides by the appearance of superconductivity on the background of competing interactions. Measurements of transport properties, such as resistivity and thermoelectric power, were used to get insight in the behavior of these materials. Besides temperature as variable, I applied high pressure, extreme magnetic fields and controlled disorder introduced by fast electron irradiation. In the first part I present the pressure dependent study of two members of the transition metal dichalcogenides having 1T structure, 1T-TiSe2 and 1T-TaS2, where superconductivity was never observed in a pristine sample. 1T-TiSe2 has a CDW phase below 220 K which origin, weather it is driven by an excitonic mechanism or by a Jahn-Teller distortion, is an ongoing question. By applying pressure I showed that the pristine sample is superconducting in the pressure range of 2.0–4.0 GPa. This range remarkably coincides with the short range fluctuating CDW before its disappearance at the upper pressure value. If CDW is due to excitonic interactions than our observations suggest that it can be at the origin of superconductivity, as well. The second dichalcogenide is the 1T-TaS2, where a Mott-insulator phase appears on the top of a commensurate CDW. By applying pressure I was able to melt that Mott-phase, and reveal that the material is superconducting above 2.5 GPa with Tc of 5.9 K. Unexpectedly, superconductivity is born from a nonmetallic phase, and stays remarkably stable up to the highest applied pressure of 24 GPa. In the second part I tried to give my contribution to the field of high-Tc superconductors. I carefully selected few high quality underdoped Bi2Sr2PrxCa1-xCu2O8-δ sample, to address the nature of the low temperature ground state by applying high magnetic field. Although former measurements by other groups showed that at high underdoping, the ground state is an insulator, I found that a sample with as low Tc as 15 K exhibits metallic behavior up to 60 T. Furthermore, I showed that a inhomogeneous distribution of the doping atoms can completely mask the intrinsic normal state of a high-Tc superconductor. In the last part of my thesis I focused on the two-band superconductor MgB2 by studying the scattering between the bands by the means of the Matthiessen's rule. I made a systematic study of the influence of defects created by fast electron irradiation, and found that the the Matthiessen's rule is satisfied for the defect concentration range I induced. I further compare the influence of defects on the critical temperature and the residual resistivity in MgB2 with superconductors with various order parameters, and found that the decrease-rate of Tc in our system is within the range of a response of a superconductor with an s-wave order parameter.

EPFL2008

Normal state transport properties of novel superconductors

Balazs Sipos

EPFL2008

Numerical modelling of high temperature superconducting tapes and cables

Francesco Grilli

EPFL2004

Hysteresis modelling of high temperature superconductors

Marten Sjöström

The present dissertation considers the capabilities, limitations and possible extensions of modelling the hysteresis that is exhibited by type-II superconductors, especially those with high critical temperature. Superconductors of type-II, including high temperature superconductors, are partially penetrated by magnetic flux. The tubes, through which the flux passes the superconductor, are 'pinned' to certain locations due to impurities in the crystal structure of the material, and they must be forced by an external magnetic field or a transport current in order to move. Thus, the pinning of flux tubes constitutes a memory that gives rise to a hysteresis with corresponding losses. The critical state model is a well-known, macroscopic model that describes well this partial flux penetration. Furthermore, the flux tubes can start to flow due to the Lorenz-force when a large transport current flows in the superconductor. This produces an additional resistive voltage. The concept of hysteresis and its main properties are discussed, and a number of various models describing this phenomenon are presented. An emphasis is made on the classical Preisach model of hysteresis, which is a weighted superposition of relay operators. A hysteretic system produces higher harmonics, just as most nonlinear systems. An investigation reveals under what conditions the Preisach model generates only odd harmonics, and also when all odd harmonics are present, as well as how this knowledge can be utilised. A parameterised Preisach model is proposed, which always applies when the critical state model is an acceptable approximation of the superconductor hysteresis. Its capabilities and limitations as a hysteresis model for superconductors are investigated. It is demonstrated how the parameters can be estimated from different electric measurements on high temperature superconductors and that the output and the losses can quickly and accurately be computed for an arbitrary signal, once the parameter identification is made. Moreover, the structure of the parameterised model is such that an inverse model can easily be obtained. It is also shown that the hysteresis saturation, which occurs when the flux flow starts, can be modelled by introducing limiting functions in the model. A generalised equivalent circuit has been proposed that takes into account both the hysteretic and resistive behaviour, the latter being due to flux flow. This extended model describes the global electric behaviour of a superconducting device, which can be applied either when the superconductor is part of a larger system or when it stands alone. A few examples of its application are given.

EPFL2001