Jozef Pitel

Influence of external magnetic fields on critical currents of solenoids wound with anisotropic HTS tapes : theoretical analysis

Theoretical analysis of the critical currents in solenoids wound with anisotropic superconductors was performed. The results of the numerical calculations indicate that applying the external magnetic field to the cylindrical coils which are made of anisotropic HTS tapes may lead to some increase in their critical current. Taking into account the angle dependence of the of short Bi(2223)Ag tape samples measured at 77 K we have shown how the external homogeneous magnetic field parallel to the axis of cylindrical symmetry influences the value of the coils critical current. We also present the analysis of the influence of the external magnetic field on the change in position of weak turns in the winding. It is shown that determination of the magnet critical current represents mathematically the solution of a non-linear equation. The methods as well as the computer procedure enabling the evaluation of the coils expected critical current and the location of the position of weak places in the winding are described. Further, the expressions that can be applied to the calculation of critical currents of the magnets, made of superconducting wires and tapes, whose characteristics are isotropic, were derived. The possibility of obtaining analytical solutions for simplified linear and for the general case of is also discussed.

Compensation of the radial magnetic field component of solenoids wound with anisotropic Bi(2223)Ag tape

The critical current of a solenoid made of Bi(2223)Ag tape with a high anisotropy in the critical current - magnetic field characteristic at 77 K is determined in particular by the radial component of the magnetic field, which is large close to the coil flanges. The original idea of utilizing supplementary (e.g. copper) windings to compensate partially the undesired radial magnetic field component of the high-temperature superconducting (HTS) coil is described. The results of extensive numerical calculations on the model coil indicate that an increase of the critical current of more than 50% can be expected.

Influence of the winding geometry on the critical currents and magnetic fields of cylindrical coils made of Bi(2223)Ag anisotropic tapes

A theoretical model for the calculation of the critical currents of cylindrical magnets made of Bi(2223)Ag tapes has been developed. The model takes into account the real angle dependence of the critical current versus external magnetic field of a short sample, which enables to estimate the critical currents of individual turns of the winding. As a result figures in a 3-D representation showing the position of the weak spots in the winding were obtained. Consequently, a detailed analysis of the influence of the winding geometry on the critical currents and magnetic fields of the cylindrical magnets formed from the set of pancake coils was performed. It is shown that when optimizing the magnet geometry with respect to the inner bore diameter and the overall tape length, there exists only one winding configuration for which the central magnetic field has a maximum. An example of the optimum magnet design, utilizing the data measured on a 55 filament Bi(2223)Ag tape of Vacuumschmelze GmbH production, is presented.

Mathematical model of voltage–current characteristics of Bi(2223)/Ag magnets under an external magnetic field

We have developed a mathematical model, which enables us to predict the voltage–current V(I) characteristics of a solenoidal high-temperature superconductor (HTS) magnet subjected to an external magnetic field parallel to the magnet axis. The model takes into account the anisotropy in the critical current–magnetic field (Ic(B)) characteristic and the n-value of Bi(2223)Ag multifilamentary tape at 20 K. From the power law between the electric field and the ratio of the operating and critical currents, the voltage on the magnet terminals is calculated by integrating the contributions of individual turns. The critical current of each turn, at given values of operating current and external magnetic field, is obtained by simple linear interpolation between the two suitable points of the Ic(B) characteristic, which corresponds to the angle α between the vector of the resulting magnetic flux density and the broad tape face. In fact, the model is valid for any value and orientation of external magnetic field, and is only limited by the validity of the electric field power law as a function of operating current. Electric fields of individual turns of the model magnet, which consists of 22 pancake coils, have been analysed for different values of operating current and external magnetic field. The voltage distribution on individual pancake coils and the overall voltage between the magnet terminals have also been analysed. Finally, the influence of external magnetic field on the V(I) characteristics of the magnet have been studied for different values of operating current. We report on a new and rather unexpected behaviour of the HTS magnets at different operating conditions, together with a theoretical explanation.

The design and performance of a Bi-2223/Ag magnet cooled by a single-stage cryocooler

The design and fabrication of a split coil Bi-2223/Ag tape superconducting magnet cooled by a single-stage cryocooler is presented. The magnet consists of six double-wound pancakes impregnated by epoxy resin with inner diameter 50 mm and outer diameter 98 mm. Critical currents of individual pancakes, double pancakes and the whole magnet are measured, calculated and discussed. The magnets performance was tested at liquid helium and nitrogen temperatures as well as at solid nitrogen temperatures and cooled by an AL230 single-stage Gifford-McMahon cycle cryorefrigerator. The measured magnet currents are compared with those estimated by calculations using short sample data.

Calculation of the critical currents of Bi(2223)/Ag tapes and coils with reduced anisotropy in Ic(B) characteristic — effect of different proportional representations of the filaments oriented parallel and perpendicularly to the tape surface

Abstract A mathematical model was developed to allow for the prediction of critical currents in Bi(2223)/Ag-sheathed tapes that consist of two groups of filaments, having crystalline texture ( c -axis) predominantly in two directions orthogonal to each other and to the length of the conductor (filaments oriented parallel and perpendicular to the tape surface). Using the theory presented, it is possible to estimate the upper limit of critical currents in the tapes prepared with a two-axial rolling technique. Magnetic field and angular dependencies of critical currents were obtained at 77 K measuring tapes with various proportional representations of filaments oriented in both preferred directions, i.e., the parallel and perpendicular directions. The results of calculation indicate that the anisotropy in the I c ( B ) characteristic should be reduced considerably using the two-axial rolling. Unfortunately, the effect of anisotropy reduction is accompanied by simultaneous decrease in the current-carrying capacity of the tapes. The data obtained for short tape samples were utilised to estimate the critical currents of the individual turns of a small cylindrical magnet, assembled of eight pancake coils. It is shown that only a slight increase in the critical current of the magnet can be expected if the winding should be made of the tape with reduced anisotropy in the I c ( B ) characteristic. The factors that limit the increase of the magnet critical current are discussed in detail.

Differences between two definitions of the critical current of HTS coils

Definition of the critical current of a coil made of anisotropic high temperature superconducting conductor is rather complicated and ambiguous, since the magnetic field generated across the winding can differ considerably in relation to both its magnitude and orientation. Two definitions of the critical current of such coils are discussed. The first definition, very often used in calculations to analyze the current carrying capacity, electric field and power dissipation of individual turns, represents an operating current at which an electric field of 1 μV cm−1 appears on one turn. The second definition represents an integral approach, and is used in experiments. This definition introduces the critical current of the coil as an operating current at which an average electric field Es, usually 0.1 μV cm−1, appears on coil terminals. As an example, the distribution of the critical current and electric field of individual turns in the winding of a BSCCO model coil was analyzed. Critical currents of the coil as a function of an external magnetic field parallel with the coil axis were calculated according to both definitions. The results show that the first definition, which characterizes the winding at the local level, is suitable for HTS coils either operating in self-field or in a low external field, because the differences between the critical currents and n-indices of individual turns are considerable. The second criterion is suitable for the HTS coils operating in high fields, i.e. like high field insert coils. The self-field of a high field insert coil is negligible if the external field is high. As a result, the critical currents of all turns are almost identical, and the anisotropy in Ic(B) characteristic plays practically no role. Rather unexpected behavior of the voltage–current characteristic of the model coil is predicted if an external field is applied.

Relation between different critical current criteria and quench current in HTS magnets

Abstract In practice, the critical current of an HTS magnet is the current at which a thermal runaway (quench) occurs. The stability analysis required to determine the quench current, Iq is often a time consuming numerical problem. Usually the short sample critical current, Ic is measured by using some electric field criterion. In trained LTS magnets Iq can be estimated from Ic due to a steep electric field (E)–current density (J) characteristic. For HTS magnets the situation is more complicated due to the anisotropy and slanted E(J)-characteristics. In this paper the theoretical maximum of Iq, I q max of conduction cooled HTS magnets is computationally compared with different critical current criteria at 20 K. Computations are based on the Ic data measured with a Bi-2223/Ag tape. Two electric field criteria, 1 and 0.1 μV/cm, are applied to the magnets by investigating both the maximum electric field in a single turn of the coil and the voltage between the magnet poles. The critical currents obtained by these criteria are compared with I q max in several coil geometries of a solenoidal conduction cooled HTS magnet having the wire length of 2, 5 and 10 km. I q max is determined from the balance between the available cooling power and the total loss power generated inside the magnet. The objective is to enable a magnet designer to determine a safe operation current for an HTS magnet without performing a detailed stability analysis.

Study of the potential of three different MgB2 tapes for application in cylindrical coils operating at 20 K

The goal of this theoretical study is to illustrate the potential of three different MgB2 tapes, developed by Columbus Superconductors, for application in cylindrical coils. First, the distribution of critical currents and electric fields of individual turns is compared when the winding of the model coil is made with tapes having different Ic(B) and anisotropy values. Second, the influence of the winding geometry on basic parameters of cylindrical coils which consist of a set of pancake coils, such as critical current Icmin, central magnetic field B0 and stored energy E, is analysed. The winding geometry of the coils, i.e. the outer winding radius and the coil length, with the same inner winding radius, was changed from a disc shape to a long thin solenoid in such a way that the overall tape length was held constant, and considered as a parameter. Finally, the winding cross-section of the coil is optimized with respect to the constant tape length in order to reach the maximum central field. The results of calculations show that for a given overall tape length and inner winding radius there exists only one winding geometry which generates the maximum central field. The overall tape length, as a parameter, is changed in a broad range from 500 m to 10 km. All calculations were performed using the experimental data measured at 20 K while the effect of the anisotropy in the Ic(B) characteristic of the short samples is taken into account.

Energy and critical current considerations of Bi(2223)/Ag coils for micro-superconducting magnetic energy storage: influence of operating temperature and winding geometry within the same overall tape length

A detailed theoretical qualitative, as well as quantitative, analysis of the influence of the dimensions of Bi(2223)/Ag based cylindrical magnets on the energy stored in the magnets winding was performed for various operating temperatures. The results achieved can be used to consider the potential suitability of the high-temperature superconductivity magnets for the purposes of micro-superconducting magnetic energy storage applications. A mathematical model which enables one to calculate the values of basic parameters, such as the critical current and stored energy of cylindrical magnets consisting of the set of Bi(2223)/Ag pancake coils, was developed with respect to the real distribution of the magnetic field in the winding and the angular dependence (anisotropy) of the Ic(B) characteristic of the tape. An example of a detailed analysis of the influence of the winding geometry, which is changed within the same overall length of 1, 2 and 5 km of the multifilamentary Bi(2223)/Ag tape, was performed at the temperatures of 77, 65 and 4.2 K. The most interesting and important result achieved is that the geometry of the winding that corresponds to the maximum stored energy differs according to the temperature. The disc-shaped magnets, which consist of a very low number of pancake coils, are the most suitable solution at 77 and 65 K. Simultaneously, the value of the stored energy is practically independent of the bore diameter of the magnet. On the other hand, when looking for the optimum winding geometry at 4.2 K, the magnets with the smallest bore diameter are more suitable, while the value of the energy stored does not depend on the number of pancake coils.