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The stationary electric field, current pattern and coupling losses in a multfilamentary, superconducting, twisted, torus-shaped wire are calculated for a torus placed in a homogeneous magnetic field increasing in time at a constant rate and parallel to the torus plane. The radius of the wire is considered to be small compared to the mean radius of the torus. An important parameter for the problem is the ratio between the twist length of the superconducting filaments and the mean radius of the torus. In the configuration considered this parameter is small. The coupling losses are approximately inversely proportional to the square of this ratio. Furthermore, for the wire to have unsaturated parts, the analysis shows that the rate of change of the magnetic field must decrease when this ratio increases.

The application of small cryocoolers to cooling a superconducting magnet at 12 K has important advantages, especially for small and medium-size magnets. Simple construction and a helium-free magnet system were obtained. The demonstration magnet developed is a six-coil system with a volume of 75 L and can be regarded as a 1:3 scale MRI magnet. With a current of 100 A, a 1-T central field is generated with a maximum of 1.9 T in the windings. The magnet consists of six coil formers and five aluminum spacing rings, providing easy service and disassembly. The superconductor, a 0.6-mm-diameter Nb/sub 3/Sn wire, is wound on the thin-walled stainless steel coil formers, after which the coil is heat treated and vacuum impregnated. Afterwards, the coil system is assembled and the electrical and thermal connections are made. At an operating temperature of the demonstration magnet of 12 K the test coil reached its nominal current after a few training quenches. >

A method for the complete numerical solution of the Maxwell equation for a multifilamentary wire carrying a transport current and subject to applied fields of arbitrary direction, where both current and applied fields have arbitrary time dependence, has been developed. First results show unexpected differences from analytical models used in the past. From both approaches current degradation effects can be estimated and loss contributions resulting from the combined action of applied field and current can be calculated. >

The quench process of a multi-strand cable was investigated using the simplest system: two twisted wires. Several properties of the quench, such as the commutation of currents, the time scale, the resistance rate, and the maximum voltage, were determined experimentally or by calculation. Particular attention was given to the role of the cable length. Several samples with lengths varying from 1.5 cm to 12 m were made from an AC superconductor with CuNi matrix. In the experiment, the decay of the currents was measured after initiating a local normal spot in one of the wires. An important conclusion is that the quench propagation and stability of a cable depend on its length and can therefore be influenced by soldering it at certain intervals. >

With reference to the application of NbTi tape in a superconducting thermal switch, the critical current of a 20- mu m-thick NbTi tape was measured in several directions of the magnetic field. The critical current was found to behave strongly anisotropically, due to the deformation of the NbTi. The tape is extrasensitive to the component of the magnetic field perpendicular to the surface. Without an external field this component of the self-field reduces the critical current far below its intrinsic value. A one-dimensional model can describe the reduction of critical current due to the self-field in a thin tape. >

For pt.I, see ibid., vol.28, pp.735-738 (1992). The evolution of quenches in multi-strand cables with high resistive matrix is analyzed. During the quench process, the growing normal resistance in certain strands will cause commutation of their current to other strands with less resistance (or still superconductive). This redistribution of current can lead to a quench of the whole cable. Furthermore, above a certain level of the initial current, an extremely fast quench process occurs with an apparent propagation velocity on the order of several kilometers per second. A model is presented that describes the above phenomena and special attention is given to the fast quench. It is noted that the fast quench could be a useful phenomenon for protection purposes or for the realization of superconducting switches with very short opening times and large dR/dt. >

The stationary electric field and current distribution in a ring-shaped wire subject to both parallel and perpendicular applied magnetic fields are calculated. The time derivative of the parallel field is limited for the center of the wire to be unsaturated. The transient response of an infinitely long wire due to a parallel applied magnetic field B/sup A/ shows that B/sup A/ itself is limited for the center of the wire to be unsaturated. The measured V-I characteristic of a ring-shaped wire is linearly dependent on the frequency of the applied field but nonlinearly dependent on the amplitude. This means that the stationary analysis is not complete and transient effects must be considered. >

In the framework of the development of an experimental 10-T Nb/sub 3/Sn dipole coil for the LHC (Large Hadron Collider) at CERN, the effects of transverse stress on Rutherford-type Nb/sub 3/Sn cable were investigated. For this purpose a special facility was designed and put into operation in which the voltage-current behavior of short pieces of Nb/sub 3/Sn cables can be investigated in a background field of up to 11 T and an applied stress of 300 MPa. The repulsive Lorentz force of 250 kN, generated by a set of superconducting coils, is used to impress the cable over an area of 20*42 mm/sup 2/ maximum, in the presence of a transport current of up to 40 kA. The testing equipment is described, and the first results of the observed critical current degradation of two Nb/sub 3/Sn cables are discussed.

A description is given of a new test system currently under construction. The system will be used to measure the AC losses of subcables from Next European Torus (NET) conductors. A special feature of the test arrangement is that the losses will be determined while the sample carries a transport current and is at the same time subjected to a changing magnetic field in the transverse and longitudinal directions. Several aspects of the design, such as magnetic field, forces, and losses, are discussed.

A full-wave superconducting rectifier for 100 kA has been developed. Typical design values of this device are: a secondary current of 100 kA, a primary amplitude of 20 A, an operating frequency of 0.5 Hz, and an average power on the order of 100 W. The rectification is achieved by means of thermally controlled superconducting switches with recovery times of 150 to 300 ms. A description of the rectifier system is given. The first experiments, in which the rectifier was tested at up to 25 kA demonstrate reliable and fail-safe operation of the rectifier at lower current levels. It was, for example, successfully used to load and unload a 25-kA coil at a rectifier frequency of 0.4 Hz and an average power of 30 W. During tests without any load, it was found that the secondary circuit of the transformer quenches at about 60 kA. Therefore, it is unlikely that the rectifier in its present configuration will attain 100 kA.

A method to obtain systematic solutions for the conductor dimensions and their layout is described. From these solutions a selection can be made based on a number of practical requirements. The inclusion of a measured J/sub max/(B) relation of the superconductor in order to make the design practical has a large effect on the geometry. A dipole magnet with cables of equal width is not necessarily the best solution; it is often better to have a broader inner-layer cable. The volume of superconductor appeared to vary only within a few percent in the systematic solutions and is therefore not a relevant criterion. In the case of a 13-T dipole magnet and using the J/sub max/(B) relation described, more than two layers of conductors must be used in order to keep the design within practical limits. It appears to be difficult to obtain a convenient solution for a 13-T magnet, although the number of geometrical variants is very high.

A predesign of a split-pair magnet for a magnetohydrodynamic (MHD) facility for testing a 10-MW open-cycle disk or a 5-MW closed-cycle disk generator is presented. The magnet system consists of a NbTi and a Nb/sub 3/Sn section, which provide a magnetic field of 9 T in the active area of the MHD channel. The optimization process, which is based on minimum conductor costs is discussed, and the proposed conductor design is described. Basic solutions for the construction of the magnet, the cryostat and the cooling technique are also presented.

The commercial specification of superconducting NbTi and Nb/sub 3/Sn composite wires is normally given by parameters such as the critical current (which is dependent on conductivity, temperature, and magnetic field), an empirically deduced parameter for which the effective resistivity is about 10/sup -14/ Omega m, wire and filament diameter, and twist length. To some extent their values cannot be chosen independently, nor do they guarantee proper operation of the system in all aspects. It is argued that for Nb/sub 3/Sn composite, depending on the production process, an extra set of parameters describing the stress sensitivity seems to be needed to specify the quality of the composite.

During an experimental study of the time dependence of a HERA dipole, it was found that the sextupole field exhibits a sinusoidal structure along the axis of the magnet. A similar periodic structure was found for the main dipole field with the help of a nuclear magnetic resonance probe. The wavelength of the periodic pattern is compatible with the transposition pitch of the Rutherford-type cable in the magnet coils. The effect is related to superconducting currents in the cable because it vanishes when the magnet is warmed up above its critical temperature. The structure was found to exist in all HERA dipoles measured afterwards ( approximately 10) and also in a superconducting coil without iron yoke. With a specially developed 2-cm-long pickup coil, it was found that all accessible multipole components in dipole and quadrupole magnets are modulated along their axis. >

Model calculations of the electrodynamic properties of superconducting composites are usually carried out assuming that the material constants, such as critical current density and resistivity, are uniform over the cross-section of the composite, or at least rotationally symmetric. Also, the applied field is usually considered to be uniform over a distance compared to the composite diameter. In this paper the possibility will be discussed that non-uniformity in field and material properties may cause significant non-uniformity in heat production so to disturb the local temperature pattern and form sources of instabilities and quenches. The influence of the cooling conditions on the transport current-carrying capacity in the a.c. regime is also discussed.

In this article a review is given of analytical and numerical calculations on the electromagnetic properties of composite superconducting wires. The review is based on the research performed at the University of Twente during the last ten years. Due attention is given to related results in the literature.

The degradation of the critical current of impregnated Rutherford type Nb/sub 3/Sn cables was investigated as a function of the transverse force applied to the cable surface. Voltage-current characteristics were measured between 9 and 11 T by which the cable is supplied with the full transport current while a section on the broad side of the cable with a length of 40 mm is under pressure. A few samples were investigated as a function of the transverse force strands in the cable. It appears that the degradation of the strands is not uniform; for example, at 200 MPa some strands show 10% while others have 40% critical current degradation, also depending on the critical current criterion used. The global degradation of the cable is 12+or-2% at 200 MPa, though it is possible that a single bad strand in a cable limits the cable to below this value due to premature quenching of that strand. >

The operation of superconducting magnets is usually involved with the handling of cryogenic liquids and the associated aspects of availability and safety. In order to improve this a magnet system is developed which is cooled by small cryocoolers in the absence of liquids. The dry magnet having Nb3Sn windings is mounted in a vacuum vessel with only one intermediate thermal shield. Three small model coils were fabricated, one made with the react and wind technique, the other two were first wound and then reacted. case specific conduction cooled leads were designed and tested. Also a dummy coil at full scale was cooled down to 11 K for which the shield temperature had values between 41 K and 46 K.

A discrete modeling technique is used to analyze the 29-strand NET (Next European Torus) braid in changing magnetic fields. Input for the model is the V-I relation of an individual strand and the contact resistance between touching strands. The model gives three-dimensional current patterns, V-I relations, and corresponding energy losses for the cable. The analysis shows a strong dependence of the cable properties on the direction of the field.

The magnetization of hollow superconducting filaments in a perpendicular applied field is calculated numerically using a mathematical model. With this model the hysteresis losses over a closed cycle of the applied field, as well as the instantaneous power dissipation in the filament, can be calculated. Theoretical results are compared with data from experiments using wire with hollow Nb3Sn filaments. Demagnetization effects caused by the influence of the field of one filament on another are studied and, finally, bridging between neighouring filaments and its influence on the effective filament diameter and the hysteresis losses are discussed.

The authors have developed a model to calculate the response of the current distribution in disks and rings to a time-dependent applied magnetic field. In the model, the ring (or disk) is divided into concentric segments. The segments are assumed to be inductively coupled to each other and to the applied field. A time-dependent magnetic field induces a finite electric field in the ring/disk. The induced currents will then depend on the magnitude of the electric field and the current-voltage (I-V) characteristic. The current-voltage characteristic is modeled by a nonlinear resistivity. The currents determined from AC magnetization measurements on rings and experimental I-V characteristics are compared with the results of the proposed model. It is found that the shape of the magnetization curves can be easily reproduced. However, the frequency dependence of the current in the ring shows a discrepancy. The experimental frequency dependence of the currents is much smaller than that expected on the basis of the I-V characteristics and the model calculations. A possible cause could be inhomogeneities in the sample influencing the current distribution.

Two methods of loss calculations are reviewed. The first method, for loss calculations in wires, uses a numerical solution of the Maxwell equations. The second method makes use of Kirchhoff's equations and is much better suited to cables, including braids. Both methods require a knowledge of the constitutive equations relating E and j or V and l in the composite conductor. Experimental results regarding the stability of large cables are presented and a way of improving the stability of a single strand is suggested.

In this paper loss measurements on various superconductors are presented. The measurements were performed on samples in a coil configuration. Most of the results will be used in the VAMAS Round Robin Test, in the course of which the experimental data of several laboratories throughout the world are compared. The characteristic loss parameters of the conductors are extracted from the experimental results, when possible, using classical loss theories. Except from the loss measurements, also data concerning the critical currents of various conductors have been obtained. In order to investigate the effect of the filament diameter on the current carrying capacity of multifilamentary superconductors the results of critical current measurements on conductors, others than used in the VAMAS project, are also presented. Comparing these data indicates that the transport current at lower fields consists for fine filament conductors of bulk currents and surface currents.

We studied the influence of using different powders and several additives on the shaping process and critical current density of sintered bulk YBa2Cu3OX. It was found that all additives used facilitated the shaping process. Silver and most organic additives influenced the critical current density only little, Zinc reduced it to zero, but an ethylenebisstearoylamide compound doubled the critical current density as compared to samples without additives.

Superconducting cables with critical currents in the range of 50 kA to 200 kA are presently under investigation in Twente. Therefore, a low-cost test facility has been developed in which the required current is generated inductively, allowing cables to be tested up to at least 200 kA. A superconducting transformer induces the current through the sample and provides the background magnetic field. The secondary part of the transformer consists of one turn of the test cable. A part of it can be varied in temperature by means of a heater. The data aquisition, analysis and storage is accomplished by means of a microcomputer system. So far, two cables having critical currents in the order of 100 kA have been successfully tested concerning their maximum current, stability and quench behaviour. The paper describes the test set-up and presents some first results.

In this paper loss measurements on a prototype NbTi cable for the Large Hadron Collider dipole magnets are presented. The cable is meant to be used for the outer layer of the magnets. It is a trapezium-shaped (key-stoned) Rutherford cable. The experimental results were obtained in a Twente test facility. Magnetization loss measurements as well as transport current loss measurements were performed. The results are compared with classical loss models. From the magnetization experiments the coupling time constant of the cable at different magnetic fields can be obtained. It is also possible to estimate the critical current density from these measurements. The critical current and the effective transverse resistivity are important for calculations concerning the loss during ramping the magnetic field and the field disturbance due to shielding currents in the filaments and to the coupling currents.

Measurement of voltage-current characteristics in multifilamentary wires, showing the transition from the superconducting to normal state, provides information about the quality of the wires and their production techniques. Two methods of describing this transition are discussed. In general, the so-called n-power law turns out to be adequate in the critical current region. The dependence of n on the magnetic field yields information about the inner structure of the wire, especially whether the limitation of the current is caused by intrinsic or extrinsic effects. Measurements were carried out at 4.2 K on several wires in order to investigate the above mentioned aspects with respect to the critical current transition. The current range in which the n-power law was valid was tested for two wires with highly resistive matrices. Then the dependence of n on the applied field was investigated. A wire with very thin filaments and one with thicker filaments were used. When submicrovolt measurements were carried out, it was found that in several ranges of current other n-values can be distinguished. This is thought to be caused by a current diffusion process. In an alternate way of assessing the resistive transitions, the authors used a critical current distribution function found by calculating the second derivative of the voltage with respect to the current. >

The switches of a superconducting rectifier can be controlled either magnetically or thermally. The authors point out the differences between these methods of switching and discuss the consequences for the operation of the rectifier. The discussion is illustrated by the experimental results of a rectifier which was tested with magnetically as well as thermally controlled switches. It has an input current of 30 A, an output current of more than 1 kA and an operating frequency of a few Hz. A superconducting magnet connected to this rectifier can be energized at a rate exceeding 1 MJ/h and an efficiency of about 97%. >

Spectroscopic techniques based on Larmor precession of particle spins require that for all trajectories of a diverging beam the path integral of the modulus of the magnetic field must be a constant. The amount of precession performed by each spin is then a function of the particle energy only. For cylinder magnets this homogeneity condition can be expressed as a variational problem. An analytical solution is presented for this variation problem. This solution describes the optimal field shape (OFS) to obtain the best possible homogeneity for a given magnet length. In practice the ideal shape can be obtained by superposing a series of solenoids of different lengths but the homogeneity is generally not good enough so that in-beam correction coils are needed that include corrections for the line integral differences caused by the finite-beam divergence. The solution is presented together with a method to implement it in practice using discrete in-beam current distributions. The resulting magnet has a homogeneity of 10/sup -6/, so that the Larmor precession angle is still well defined after 10/sup 4/ turns. >

The successful test of a 25 kA superconducting rectifier is reported. This rectifier is an important component of a complete cryogenic power system to energise high current superconducting magnets.

Flux penetration into a hollow superconducting filament in a time-varying transverse magnetic field is determined numerically. The magnetization of the filaments is calculated for field variations below and above the penetration field of the filament. The influence of the inner radius of the superconducting filament on the magnetization and the hysteresis losses in the filament is shown. The critical current density is taken to be constant during the external field cycle and depends within the superconducting filament on the local magnetic field, which is the sum of the externally applied field and the field induced by the local screening currents. Calculations based on the theory presented here show good agreement with experimental results. >

Above a certain current level, the use of a superconducting rectifier as a cryogenic current source offers advantages compared to the use of a power supply at room temperature which requires large current feed-throughs into the cryostat. In some cases, the power of such a rectifier is immaterial, for example if it is to be used as a current supply for short test samples with low inductances. Usually, however, a rectifier is intended to energize large superconducting magnets, so the maximum power available becomes an important parameter since it determines the loading time. One method of increasing the power of a rectifier is to raise the operating frequency. In this respect, magnetically controlled switches with very fast switching times are preferable to thermally controlled ones. This paper reports on the design, as well as the experimental results of a magnetically switched full-wave superconducting rectifier. Once this rectifier is brought to its design frequency of 5 Hz, the average power delivered to the cryogenic load will be 500 W.

Ac loss measurements have been performed on a superconducting transformer. The transformer is a part of a 25 kA thermally switched superconducting rectifier operating at a frequency of 0.1 Hz. The loss measurements have been automatized by means of a microcomputer sampling four relevant signals and processing these data to reliable loss numbers. Results were obtained at amplitudes of the secondary current between 5 and 15 kA at various current rates between 5 and 30 kA s−1.

Energy losses occurring in a cylindrical sample of Gd-Ba-Cu-O, subjected to an external AC magnetic field were examined. The loss dependence on the amplitude of the magnetic induction exhibits two stages of flux penetration into the superconductor. Critical current densitities for both stages of penetration were examined and an explanation for such behaviour is proposed. Support for this point of view is obtained by measurements on pulverized sample material. All measurements were performed at a temperature of 4.2 K and in absence of a background field. Analysis of the data provides two critical current densities: an inter-granular critical current density at weak alternating magnetic fields and an intra-granular critical current density at higher magnetic fields. The intra-granular critical current density is at least two orders of magnitude larger than the inter-granular one.

As part of a study to develop thermally controlled switches for use in superconducting rectifiers operating at a few hertz and 1 kA, a theoretical model is presented of the thermal behavior of such a switch. The calculations are compared with experimental results of several switches having recovery times between 40 and 200 ms. A discussion is given of the maximum temperature T/sub N/ that occurs in the normal regions when the switch is in the resistive state. Once T/sub N/ is known, it is possible to predict the recovery time, activation energy, stationary dissipation and minimum propagation current. The calculated and measured results, in good agreement, show that T/sub N/ is approximately 12 K and largely independent of the thickness or material of the insulation layer. Mention is made of some problems, related to the room-temperature equipment which drives the rectifier, that so far have prevented the rectifiers from being used at their design specifications. >

The power of fully superconducting rectifiers can be improved by increasing either the operating frequency or the transformer primary inductance [1]. The frequency is usually limited by the recovery time of thermally controlled switches. In order to achieve a higher switching speed, magnetically controlled switches are preferable [1,2]. This paper describes a magnetically controlled switch which can be used for currents up to 500 A at 25 Hz. The switch element, consisting of several Nb1%Zr multifilamentary superconductors, is placed between two concentric solenoids which generate the necessary magnetic field. The Nb1%Zr superconductor is well suited for this purpose because of its relatively low critical field (¿ 0.75 T) and high maximum current density (about 5.109A/m2below 0.3 T).

The longitudinal propagation of the normal zone in superconducting wires was experimentally investigated in order to evaluate existing analytical expressions which attempt to describe the propagation velocity in a more or less simple manner. The availability of a reliable expression is important for application in computer codes that calculate quench evolutions in superconducting magnets. We measured the propagation velocity as function of transport current and magnetic field in five different insulated NbTi superconductors having a copper, a copper-nickel or a mixed matrix. The comparison to calculated velocities using five existing models showed that large quantitative and qualitative differences exist.

Within the scope of a research program of superconducting rectifiers software is being developed to take care of the control of such systems. The hard-ware architecture which interferes with the in and output signals is based on a LSI-11/2 microprocessor with sufficient mass storage for data logging, console and printer. The flexibility inherent to this hardware configuration is desired for optimalisation of the rectifier concerning maximum current, power, efficiency and quench stability. The paper describes the structure of the program and the interaction between both computer hardware and software and the superconducting rectifier. However, because the reliability of computersystems is unsatisfactory an additional hardware protection system still handles the most important alarms.

Loss measurements are presented on an ultrafine filament composite and on a regular AC conductor, having "thick" filaments. The wires have been subjected to an alternating transverse magnetic field. An AC as well as a DC transport current have been fed through the wires. The magnetic field and the AC transport current have been sinusoidal functions in phase. The magnetization losses and the transport current losses have been measured separately. The critical current - according to the 10-14Ωm criterium - and the quality factor n - according to V = V 0 (I/I c )n- have been determined.

The inductive response of type II superconductors to applied fields with trapezoidal time dependence is described for samples with a slab geometry. An extension of the critical state model which accounts for the observed waveform of the voltage, induced in the pick-up coil, is given. Typical experiments on Nb-slabs with weak pinning and flux flow in fields with both small and large amplitudes are reported.

The AC loss measurement system in the Twente test facility is operational. Preliminary results of the first loss measurements on a vacuum-welded conductor are presented. The Twente test facility is a high-current system in which superconductors can be tested up to 7 T and 25 kA. The loss measurements were done on a monolith conductor designed for TORE SUPRA, manufactured by Vacuumschmelze. >

A description is given of the cryogenic part of an electron paramagnetic resonance (EPR)/ferromagnetic resonance (FMR) spectrometer using Ka-band (26.5-40 GHz) and U-band (40-60 GHz) frequencies for resonance measurements on large magnetic thin-films. The unit has two cryostats; the first has a room-temperature vertical inlet tube giving access to the center of the superconducting magnet. This cryostat can be rotated around the central axis of the inlet tube and enables rotation of the magnetic field around a fixed sample, placed in the center of the magnet. This cryostat also contains a superconducting Helmholtz-like coil (up to 5 T at the center). Also there is a flow cryostat placed freely in the inlet tube of the first cryostat. This cryostat is used to cool the EPR/FMR sample. The discussion of the EPR/FMR presented places emphasis on the construction of both cryostats, as well as on the design calculations and construction of the superconducting magnet coil. The calculations are compared with experimental data. >

The inductive response of normal metals to trapezoidal a.c. fields is studied theoretically as well as experimentally. A method is presented to determine the conductivity and its magnetic induction dependence from the decay of the induced voltage during periods of constant field. The correctness of the analysis is confirmed by the close agreement between the complete experimental and theoretical voltage waveforms.

Results on three experimental superconducting rectifiers are reported. Two of them are 1 kA low frequency flux pumps, one thermally and magnetically switched. The third is a low-current high-frequency magnetically switched rectifier which can use the mains directly.

Superconducting cables are described by current sheets using the continuum model of W. Carr Jr. [1] and assuming an anisotropic conductivity. Two different situations are considered: a) finite length of cable in spatially independent magnetic field; b) infinitely long cable in a periodical magnetic field.

The authors develop a numerical method for calculating the transverse resistivity of superconducting cables. A superconducting cable consists of a twisted bundle of strands with a nonconducting inner region. If such a cable is placed in an external magnetic field, the induced currents will not merely flow in the axial direction, but also around the center, in the plane of the cross section. It is shown that the transverse transport current, which is induced by external fields acting on the cable, can saturate most of the filaments of the superconducting layer. This results in a smaller maximal value of a longitudinal transport current and small coupling losses. >