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Each of the eight huge coils of the Barrel Toroid of the ATLAS detector consists of two double pancakes which are embedded in an aluminum alloy coil casing. The 57 mm times 12 mm sized conductor is a Rutherford cable with NbTi-Cu strands co-extruded with a high purity aluminum stabilizer. The race track coils have overall dimensions of 25 m times 5 m and the length of the conductor in the windings is 6.7 km. The coils are conduction cooled with forced flow helium. The nominal operating current is 20.5 kA and the nominal ramp rate is 4 A/s. During the test program of the individual coils the ramp losses are measured to confirm that they do not exceed the design cooling capacity of the ATLAS cryogenic system. The losses are determined from the amount of evaporated helium in the return flow. The ramp losses in the conductor consist of the hysteresis and coupling current losses in the Rutherford cable and eddy current loss in the pure aluminum stabilizer. Ohmic losses are generated in the coil casing which acts as a low resistive secondary of a transformer formed by the coil and the casing. In this paper the results of the loss measurements on the different coils, with different RRR (residual resistance ratio), are presented. Measurements are performed at various ramp rates. The results are in good agreement with the calculated losses, which are dominated by the loss in the coil casing

Each superconducting coil of the ATLAS Barrel Toroid has to pass the commissioning tests on surface before the installation in the underground cavern for the ATLAS Experiment at CERN. Particular acceptance criteria have been developed to characterize the individual coils during the on-surface testing. Based on these criteria and the limited time of the test, a compressed test program was proposed and realized. In only a few cases some additional tests were required to justify the coil performance and acceptance. In this paper the analysis of the test results is presented and discussed with respect to the acceptance criteria. Some differences in the parameters found between the identical coils are analyzed in relation to coil production features

A method to calculate the AC loss of superconducting power devices from the measured AC loss of a short sample is developed. In coils and cables the magnetic field varies spatially. The position dependent field vector is calculated assuming a homogeneous current distribution. From this field profile and the transport current, the local AC loss is calculated. Integration over the conductor length yields the AC loss of the device. The total AC loss of the device is split up in different components. Magnetization loss, transport current loss and the loss due to the combined action of field and current all contribute to the AC loss of the device. Because ways to reduce the AC loss depend on the loss mechanism it is important to know the relative contribution of each component. The method is demonstrated on a prototype transformer coil wound from Bi/sub 2/Sr/sub 2/Ca/sub 2/Cu/sub 3/O/sub x//Ag superconducting tape. Differences between the model assumptions and devices are pointed out. Nevertheless, within the uncertainty margins the calculated AC loss is in agreement with the measured loss of the coil.

In some electrical apparatuses, superconducting tapes are exposed to the longitudinal magnetic field. In this work, AC losses were measured in twisted and untwisted Bi-2223 tapes carrying AC transport current in the AC longitudinal magnetic field. In twisted tapes, the transport, magnetization and total losses depend on the relative direction of the longitudinal magnetic field to the direction of the transport current, while the field direction does not influence the AC loss characteristics in untwisted tapes. In the Z-twisted tapes, the total AC loss is larger in the longitudinal magnetic field that is anti-parallel to the transport current than in the longitudinal magnetic field of another direction. Numerical analysis shows that this field direction dependence of the total AC loss results from the change in the current distribution. In the longitudinal magnetic field that is anti-parallel to the transport current, the total AC loss in the Z-twisted tape is more than that in the untwisted tape. This dependence on the field direction is reversed in S-twisted tapes. It is to be noted that the twist increases the total AC loss in a longitudinal magnetic field of a certain direction, while it reduces the AC loss in the transverse magnetic field.

Hysteresis loss is an important factor when the performance of superconducting electric power devices is evaluated. The non-ideal voltage–current relation in Bi2Sr2Ca2Cu3Ox/Ag conductors is one of the reasons that critical state based loss relations do not accurately predict the AC loss in these conductors. In this paper the influence of the magnetic field dependent voltage–current relation on the hysteresis loss is discussed. An analytical high-field approach is used to demonstrate the effect of the finite steepness of the voltage–current relation on the induced current. Besides, a numerical technique is used to calculate also for applied magnetic fields below the penetration field the influence of both a field dependent critical current density and a field dependent steepness of the voltage–current relation. Both the magnitude of the hysteresis loss and the field dependence of the loss are influenced by the voltage–current relation. Especially for small applied fields the field dependence of the loss deviates from the cubic dependence that is predicted by the critical state model based relations. Results of calculations are compared with measured data. An intrinsic critical current density vs. magnetic field relation is determined in order to obtain agreement between measurements and calculations.

The dynamic resistance loss, DC transport current combined with external AC magnetic field, in a Bi2Sr2Ca2Cu3O10/Ag superconducting tape is measured as a function of the orientation of the external AC magnetic field. We investigate the possibility of describing the AC transport current loss in an externally applied AC magnetic field from the much simpler dynamic resistance measurement. The orientation angles of the magnetic field with respect to the plane of the tape are changed from 0° (perpendicular configuration) to 90° (parallel configuration). The angular dependence of the dynamic resistance energy dissipation is described with an empirical formula. It is very similar to the angular dependence observed for the hysteresis loss. The dynamic resistance in parallel and perpendicular applied magnetic field is fairly well described with theoretical predictions based on the critical state model. The increase of the AC transport current loss due to a simultaneously applied AC magnetic field is described quite well with the dynamic resistance in the fully saturated state.

Multifilamentary Bi2223 tapes are exposed to the longitudinal magnetic field as well as the transverse one in some electrical power apparatuses such as multilayer power transmission cables. Here, we define the longitudinal and transverse magnetic fields as the field components parallel and perpendicular to the tape axis, respectively. If the filament-bundle is twisted, it can couple to the AC longitudinal magnetic field to generate the longitudinal magnetization loss. Furthermore, the AC transport current flowing spirally in the twisted filament-bundle possibly influences the longitudinal magnetization. The longitudinal magnetization loss was measured in a twisted multifilamentary Bi2223 tape exposed to longitudinal magnetic field and carrying the transport current. The measured longitudinal magnetization loss in the twisted tape exposed to the longitudinal magnetic field is larger than that in another untwisted tape. Supplying the AC transport current changes the longitudinal magnetization loss in the twisted tape exposed to the AC longitudinal magnetic field. The influence of the transport current depends on the phase relation between the longitudinal magnetic field and the transport current. If their phase difference is 0°, the longitudinal magnetization loss decreases remarkably with increasing amplitude of the transport current. It means that the change in the current distribution due to the transport current results in the decrease in the power flow from the magnet power supply. But, a preliminary measurement of the transport loss shows that the total loss increases with increasing transport current.

The magnetisation loss in multifilament HTS tape superconductors can be reduced by twisting the filaments and increasing the matrix resistivity. In this paper the influence of filament twist on the coupling current loss of the tape is studied. Magnetisation measurements on multifilament Bi2223 tape conductors with different twist pitches are performed at 77 K in magnetic field applied parallel and perpendicular to the wide face of the conductor. Both frequency and magnetic field amplitude are varied. In perpendicular magnetic field the filaments are fully coupled. In parallel magnetic field the twisted filaments are decoupled, even for twist pitches around 10 mm and a pure silver core. However, for increasing magnetic field >0.04 T, the influence of the coupling current loss increases. The transition to full coupling and the coupling current loss are analysed with an existing analytical model for a tape superconductor.

Bi2Sr2Ca2Cu3Ox/Ag tape superconductors are used in applications like power cables and transformers. In these applications the superconductor is exposed to an alternating magnetic field that has different orientations with respect to the tape surface. In this paper the angle dependency of the magnetisation loss is considered from two points of view. First the measurement technique with pickup coils is analysed theoretically. Measured magnetisation loss in uni-directional magnetic field with various orientations and rotating magnetic field are compared. When the orientation is changed from perpendicular (0°) to parallel (90°) applied magnetic fields, the contribution of the perpendicular field component to the magnetisation loss is dominant up to 60°. A new model to describe the angle dependency of the magnetisation loss, based on the measured loss in perpendicular and parallel magnetic field is developed. Deviations between models and the measured loss are explained with the help of the theoretical analysis of the measurement technique. The new model is not only applicable for the magnetisation loss but also for other AC loss components.

An analytical approximation is developed for the magnetization of an infinitely long superconductor with an elliptical transverse cross-section. The superconductor is modeled in the critical state with a critical current density that is not dependent on the magnetic field. The aspect ratio of the ellipse is varied from one (=circle) to infinitely large. The magnetic field is applied perpendicular or parallel to the broadest face. The analytical expression is compared with a more detailed model that utilizes a numerically optimized contour for the boundary of the saturated zone. The two methods are compared and the maximum error is estimated at 2% for the optimized contour approach and 5% for the analytical approximation. The analytical model is compared with a magnetization loss measurement on a high-Tc superconducting tape with an aspect ratio of nearly 20. A good agreement is obtained for a magnetic field pointing perpendicular as well as parallel to the broadest face of the tape. An interesting result for the magnetic behavior determined for the ellipse is that it contradicts with the behavior that is predicted for an infinitely thin strip in perpendicular field. The difference is attributed to the two specific assumptions made in the thin strip model: the constant critical current density distribution across the tape and the magnetic-field profile that does not exclude unsaturated currents in the shielded zone.

A high quality factor, superconducting resonator coil is developed in cooperation with the Dutch companies SMIT Transformers and SMIT DRAAD. The coil system is manufactured in industry, using industrial tooling. It has a design reactive power rating of 1 MVA at a frequency of 50 Hz and the operating temperature is 64 K. The system consists of four concentric but separate coils, made of 2 km of Bi-2223 conductors from two different manufacturers. The coils are optimized by shaping the magnetic field around the coil edges with ferro-magnetic C-cups to reach a design electrical quality factor of 1000. The system is operated in a glass-epoxy cryostat at 64 K and 77 K. The resonator coil design demonstrates all the superconducting elements that are essential for manufacturing superconducting transformers. A numerical model has been developed to predict the DC and AC behavior of the system based on measurements of short samples and test coils. A comparison is made between the experiment and model calculations.

Potentially, coils made with BSCCO-2223/Ag tape and operating in liquid nitrogen at 50-60 Hz are interesting for power related applications. The electrical characteristics of such a coil depend on the radial magnetic field in the windings. One way to suppress the radial field is by placing small iron pieces around coil edges. V-I curves of the 100 kVA coil are calculated and measured for two cases: coil edges without and with iron pieces. The coil is a solenoid with inner and outer diameters and a height of 470, 474 and 614 mm respectively. A numerical model adapted to the coil geometry is used to calculate the conductor losses. The loss voltage is also evaluated by measuring the coil temperature. The total loss of the coil is measured electromagnetically. Calculated and measured losses are in agreement. Finally, the loss V-I curves of the coil are simulated in the frequency range of 0 to 400 Hz. The results are applied to the design of a 1 MVA resonator coil.

An engineering function to describe the AC loss of BSCCO/Ag tape conductors is developed. For a wide range of transport currents and magnetic fields (with different orientation) the loss is described with an uncertainty of 10%. The equation is based on the analytical expressions available, BSCCO/Ag tapes used in power applications at liquid nitrogen temperature are fed with an AC transport current and exposed to an AC magnetic field. The magnetic field in a device has different orientations with respect to the position of the conductor in the device. In this contribution, AC loss measurements for simultaneously applied magnetic field (with different orientation) and transport current are presented for a high quality tape conductor that is used in a transformer coil. The results are separated into a magnetic and a transport current loss component.

Magnetisation loss is an important factor in the design of superconducting transformers and motors. In these devices the tapes are usually placed face-to-face. Then the magnetisation loss is influenced by the mutual magnetic shielding between adjacent tapes. The shielding is investigated by measuring the magnetisation loss in stacks with various numbers of Bi-2223 tapes, exposed to a 48-Hz perpendicular magnetic field at 77 K. In a stack the penetration field is increased and the magnetisation loss below penetration is greatly decreased, compared to the behaviour of a single tape. The loss at high magnetic-field amplitudes is unaffected. The measured loss is compared to the loss calculated with two different models. The effect of shielding is qualitatively well described with an analytical model. However, predictions made with a numerical model display a better quantitative agreement with the measurement results.

The ac loss plays an important role in the design of electro-technical components based on high-temperature superconductors. It is important to have reliable techniques for the measurements of the ac loss under application-like conditions. This paper contains a comparison between the ac loss results obtained with a calorimetric measurement method and those obtained with an electromagnetic measurement method. The measurements were performed on a Bi-2223 silver-sheathed non-twisted multi-filamentary tape. The sample was exposed to combinations of an ac transport current and an ac applied magnetic field (oriented perpendicular or parallel to the tape surface). The results obtained with the two measuring methods show good agreement with each other.

At high amplitudes and frequencies of the external magnetic field, the superconducting filaments in a composite conductor are fully coupled. This causes a high magnetisation loss. Methods to decouple the filaments are well known for the low-Tc superconductors and have recently been applied also to high-Tc composites. In this paper, expressions are derived for the magnetic-field amplitude and frequency where full coupling sets in, as well as for the twist length required for decoupling the filaments in a general rectangular composite. A comparison is made with other expressions found in the literature. The filaments in a typical Bi-2223/Ag tape in parallel magnetic fields are decoupled just by twisting. In perpendicular fields a high transverse resistivity is required to decouple the filaments and decrease the magnetisation loss.

Characteristics of a circular superconducting coil made with BSCCO-2223/Ag tape depend on the amplitude and direction of the magnetic field in the windings. The effect can be estimated by studying a short sample of the same tape. However, the loss voltage-current and the frequency characteristics of a coil deviate considerably from those that are measured on a short sample. In order to estimate the deviation, the authors compared measured characteristics of a few small coils employing up to /spl sim/10 m of tape with those calculated from the short samples data. The comparison includes several arrangements of coils and field shaping elements around the coil edges and is performed in the frequency and temperature range typical for power applications (1-100 Hz and 64-78 K respectively). The results are applied to the design of a 100 kVA-50 Hz resonator coil with a high quality factor.

BSCCO/Ag tape superconductors are used in applications like power cables, transformers and motors/generators. In these applications, the superconductor is exposed to an alternating magnetic field that can have different orientations with respect to the tape. In applications like three-phase power cables and motors/generators, the tape is exposed to a rotating magnetic field. This paper describes a measurement setup to determine the magnetisation loss of short pieces (10 cm) of tape superconductor in uni-directional magnetic field with arbitrary direction and rotating magnetic field. Measurements are performed in liquid nitrogen using the pick-up coil technique. The sensitivity of the setup is sufficient to measure the magnetisation loss accurate down to magnetic field amplitudes of 0.5 mT, also in magnetic field applied parallel to the wide face of the conductor. A relation is verified that described the measured magnetisation loss in a rotating magnetic field with the results obtained for a uni-directional field. The magnetisation loss in a rotating magnetic field can be described, in most cases, with the component of the magnetic field perpendicular to the wide face of the tape conductor. Only when the parallel magnetic field component becomes more than two times larger than the perpendicular component that its contribution to the loss becomes significant.

BSCCO/Ag tape superconductors are developed for electrical power applications at liquid nitrogen temperatures. In these applications, e.g., superconducting transformers and power cables, an AC transport current and an AC magnetic field are present at the same time. A set-up to measure the influence of external AC magnetic field on the transport current loss, i.e., the voltage drop across a sample supplied with an AC transport current, has been developed. The magnetic field can be applied both parallel and perpendicular to the broad side of the tape conductor. An increase of the transport current loss due to the external AC magnetic field is observed. When a DC external magnetic field is applied the increase of the self-field loss can be described well by the decrease of the critical current due to the magnetic field. In the case of an AC external magnetic field this is only a minor effect. For magnetic field amplitudes higher than a certain threshold value the transport current loss is described reasonably well by the self-field loss and a dynamic resistance contribution calculated from the DC voltage–current relation in AC magnetic field.

A numerical model is developed for the current distribution in high-temperature superconductors (HTS conductors) subjected to self and applied field. This analysis is based on the two-dimensional Poisson equation for the vector potential. The vector potential is rewritten into an equation of motion for the current density J. The finite thickness of the conductor and the n-power law electric field-current density relations (E-J relations) of the conductor are included in the model. The magnetic field dependence of critical current density Jc is also included in this E-J relation. The self-field loss obtained with this analysis has good agreement with experimental data. Also the effects of aspect ratio and n value on ac loss are pointed out to be important on the ac loss.

The self-field loss of BSCCOrAg tapes has been measured in combination with an external AC magnetic field. This situation occurs when conductors are used in applications such as coils or cables. An increase of the self-field loss due to external AC magnetic field is observed. An increase of the self-field loss caused by a decrease of the critical current is only a minor effect. For magnetic field amplitudes higher than 10 mT, the self-field loss is described reasonably well by the self-field loss and a dynamic resistance contribution calculated from the DC voltage–current relation in AC magnetic field. For magnetic field amplitudes smaller than 10 mT, the dynamic resistance contribution from the DC voltage–current relation only describes a small part of the increased self-field loss.

In electric power applications, BSCCO superconducting tapes are exposed to an alternating magnetic field while simultaneously an alternating transport current is flowing through the conductor. The magnetic field has various orientations with respect to the tape surface. An engineering function to describe the AC loss in a BSCCO/Ag tape is developed. The expression describes the total AC loss in a wide range of magnetic fields (with different orientations) and transport currents. In this approach the specific properties of BSCCO tape e.g. the shape of the conductor cross-section and the magnetic field dependent voltage–current relation are taken into account. The equation is based on the analytical expressions available, and adjusted to measured data. The AC loss of a coil wound of BSCCO tape is calculated, the result is compared with measured data and possibilities to reduce the loss are considered.

The Barrel Toroid (BT) provides the magnetic field for the muon detectors in the ATLAS experiment at CERN. The Toroid is built up from eight superconducting coils. Each coil consists of two 25 m times 5 m racetrack shape double pancakes impregnated and pre-stressed inside an aluminum coil casing. The 42-tons cold mass is cooled by forced-flow liquid helium circulating in aluminum pipes glued to its surface. The coils are tested on surface prior to their underground installation. The test program has started in September 2004 and finished in June 2005. This paper describes the test set up and various commissioning tests performed at the ATLAS Magnet Test Facility. It includes the aspects of test preparation, vacuum pumping, leak testing, cooling down, powering and warming up. The 8 coils have passed the tests successfully and have been assembled into the Toroid in the ATLAS cavern. The testing completes the production of the so far largest racetrack coils in the world

The Superconducting Barrel Toroid is providing (together with the two End-Cap Toroids not presented here) the magnetic field for the muon detectors in the ATLAS Experiment at the LHC at CERN. The toroid with outer dimensions of 25 m length and 20 m diameter, is built up from 8 identical racetrack coils. The coils with 120 turns each are wound with an aluminum stabilized NbTi conductor and operate at 20.5 kA at 3.9 T local field in the windings and is conduction cooled at 4.8 K by circulating forced flow helium in cooling tubes attached to the cold mass. The 8 coils of 25 m /spl times/ 5 m are presently under construction and the first coils have already been fully integrated and tested. Meanwhile the assembly of the toroid 100 m underground in the ATLAS cavern at CERN has started. The 8 coils are individually tested on surface before installation. In this paper the test of the first coil, unique in size and manufacturing technology, is described in detail and the results are compared to the previous experience with the 9 m long B0 model coil.

Preface to the Proceedings of the International Cryogenic Materials Conference: Topical Conference on the Voltage-Current Relation in Technical Superconductors (25 to 28 May 2003)

A high-quality superconducting resonator coil system has been developed in the Netherlands in cooperation with the companies SMIT Transformers and SMIT Draad. The coil system was manufactured in industry, using industrial tooling. It has a reactive power rating of 1 MVA at a frequency of 50 Hz and a temperature of 64 K. The system consists of four concentric solenoidal coils, including 2 km of Bi-2223 conductors from two manufacturers. The coil performance has been optimized by shaping the magnetic field around the coil edges with laminated ferro-magnetic C-cups to reduce the AC loss to about 1 kW at 1 MVA reactive power. The system is operated in a glass-epoxy cryostat at either 64 or 77 K. The resonator coil demonstrates all superconducting elements that are essential for manufacturing superconducting transformers. The construction of the system is finalized and the total system has been tested in various operational configurations. The results of the system test at full power are presented and analyzed.

Advanced ac loss measurement methods for superconducting tapes are described in detail and demonstrated on BSCCO/Ag (Bi2Sr2Ca2Cu3Ox with a Ag matrix) tapes in liquid nitrogen at 77 K. The aim of the measurements is to simulate the situation of a tape conductor in an electric power application like a transformer coil or a power cable. In this class of devices the conductor is fed with an alternating transport current and simultaneously exposed to an alternating magnetic field. In many devices the magnetic field vector points in a single direction but in some devices such as three-phase power cables and motors the magnetic field rotates around the conductor. In all cases described above an electromagnetic approach with pick-up coils and voltage taps is used to measure the ac loss. This method enables a separate study of magnetization loss and transport current loss when both the magnetic field and transport current are present simultaneously. The magnetization loss measurement setup for unidirectional and rotating magnetic field is described. The transport current loss measurement setup is described, focusing on the suppression of cross effects of ac transport current and ac magnetic field that disturb accurate measurements. Finally several relevant examples of the results obtained are shown.

In practical applications, BSCCO/Ag tapes are exposed to external AC magnetic field and fed with an AC transport current. The total AC loss can be separated in two contributions: first, the transport current loss influenced by an external AC magnetic field, and second, the magnetisation loss that depends on the transport current running through the conductor. In this paper the total AC loss is considered and the role of the electric and magnetic components is compared. This comparison is made with an available analytical model for the AC loss in an infinite slab and verified experimentally for a BSCCO/Ag tape conductor. For small transport currents the magnetisation loss dominates the total loss. When the current increases, a field dependent crossover occurs, after which the transport current loss also plays a role. Qualitatively the measurements can be described well in terms of the critical state model. For magnetic field parallel to the wide side of the conductor the CSM for an infinite slab describes the measurements also quantitatively.

BSCCO/Ag tapes are being developed for electrical power applications at liquid nitrogen temperatures. In these applications, conductors are exposed to an alternating magnetic field and fed simultaneously with an alternating transport current. In this contribution the influence of an external alternating magnetic field on the transport current loss of a single tape is studied experimentally. Special attention is paid to the loss as a function of the orientation of the external magnetic field. The transport current loss in a DC external magnetic field can be described well by the decrease of the critical current due to the magnetic field. In the case of an AC external magnetic field this is only a minor effect. Effects responsible for the increase of the transport current loss in external AC magnetic field are investigated with respect to their angle dependency. A model based on a 1 dimensional modelling of the conductor and an average critical current density during the magnetic field cycle is presented. This model describes the measured results reasonably well below the critical current.

The AC loss of various silver-sheathed high Tc superconducting Bi-2223 tapes is measured by means of the transport method, as a function of frequency and current amplitude. The frequency dependence of the power loss (in W/m) is used to separate different loss components: the frequency independent part is attributed to the resistive loss, the linear part to the hysteresis loss (self-field loss in J/m per cycle), and the quadratic part, if it appears, may be assigned to other losses such as the eddy current loss. The separated loss components are evaluated with the existing models and the DC voltage-current characteristics of the sample. In general, the self-field loss is dominant when the transport current amplitude is smaller than the critical current of the tape. For larger currents the resistive loss is the most important component. At small transport current, the AC transport loss signal is very small and is sensitive to the phase correction and other disturbances from the surrounding metallic parts in the vicinity of the sample. The signal picked-up from these disturbances shows the quadratic frequency dependence.

In a typical superconducting coil made of BSCCO/Ag tape, both amplitude and direction of the magnetic field determine the critical current, resistive voltage and AC loss. The distribution of the magnetic field along and across the superconducting tape in a coil is rather complex. This gives rise to the question: how accurate can one predict the critical current, V–I characteristic and AC loss of the AC coil from results of short sample measurements? To answer this question, we have measured and compared the characteristics of a short sample and a small coil employing 14 m of the same tape at 77 K. The comparison is performed as follows. First, a short sample is characterised with regard to the field dependence of the critical current, V–I characteristic and the AC loss. Second, the distribution of the magnetic field along the tape in a coil is accurately calculated. From the data, the voltage along the tape and the loss of the tape in the coil are found. Finally, the resistive voltage and the AC loss of the complete coil are calculated and compared to measured AC losses in the frequency range of 0 to 160 Hz, typical for power applications.

The current density distribution of high temperature superconducting (HTS) tapes is modeled for the combined case of an alternating self and applied magnetic field. This numerical analysis is based on the two-dimensional Poisson equation for the vector potential. A one-dimensional current (z-direction) and a one-dimensional applied field (y-direction) are assumed. The vector potential is rewritten into an equation of motion for the current density J(x,y,t). The model covers the finite thickness of the conductor and an n-power E–J relation. The magnetic field dependence of Jc is also included in this E–J relation. A time-dependent two-dimensional current distribution that is influenced by the aspect ratio of the conductor and the material properties in E=f(J,B) is calculated numerically. The numerical results are compared with the experimental results for the AC loss of a tape driven by a transport current. Finally, a total AC loss factor is given for two cases in magnetic field direction, perpendicular and parallel to the conductor broad side.