Table of contents

The focus of this special issue is small-scale and large-scale applications of both high and low temperature superconductors, which is the main theme of a conference to celebrate the long and distinguished career of Professor Archie Campbell, who will retire from the Department of Engineering, University of Cambridge, on 30th September 2007.

The areas of research include flux pinning in type-II superconductors, ac losses, understanding the critical state in these materials and investigating the penetration of flux in bulk superconductors.

The conference is the first to bring together these related areas and was attended by more than 60 colleagues from around the world, with every continent represented. This special edition of Superconductor Science and Technology contains most of the papers presented at the conference.

For thin superconducting platelets or films in a dc magnetic field, the application of a weak ac magnetic field in the plane of the platelet allows the vortices to drift. This vortex motion generates a dc voltage in the superconductor that causes the critical currents and irreversible magnetic moment to relax completely. This vortex shaking was explained quantitatively for long strips with weak ac field applied perpendicular or parallel to the critical screening currents that flow along the strip, and for films of rectangular shape. In all these cases the dc magnetic field was applied perpendicular to the film. The present work generalizes these theories to cases when the dc field is applied at an angle with respect to the film plane. It is found that an appropriate tilt of the dc field can strongly increase the anisotropy of the shaking-induced relaxation and accelerates the appearance of additional current loops, so that these effects may be observed more easily.

We calculate the magnetic-field dependence of the critical current due to both geometrical edge barriers and bulk pinning in a periodic coplanar array of narrow superconducting strips. We find that in zero or low applied magnetic fields the critical current can be considerably enhanced by the edge barriers, but in modest applied magnetic fields the critical current reduces to that due to bulk pinning alone.

The thickness dependence of the critical current density J_c(d) in films due to the two-dimensional–three-dimensional (2D–3D) pinning crossover at low magnetic fields is addressed, taking into account the spatial correlation of pinning centres, the combined effect of bulk and surface pinning, and the effect of thermal fluctuations. The whole J_c(d) curve for both the 3D and 2D pinning regimes, and the crossover thickness d_c are calculated using a dynamic approach for a random pinning potential characterized by the Gaussian correlation functions. It is shown that the spatial correlation of pinning centres can significantly increase d_c as compared to uncorrelated point pins, and the competition between pinning and thermal fluctuations gives rise to a nonmonotonic dependence of J_c(d). The account of multiscale spatial correlations in a uniform pinning nanostructure can result in behaviour of J_c(d) similar to that observed on YBa₂Cu₃O_7−δ. The ultimate limit of J_c is discussed.

This paper discusses the hysteretic vortex pinning recently observed in superconductor/ferromagnetic nanocomposites. We show that in nanocomposite thin films consisting of Gd particles incorporated in a Nb matrix the hysteresis and pinning are associated with magnetic reversal losses in the Gd particles. This mechanism is fundamentally different in origin to other magnetic pinning interactions previously proposed for ferromagnetic particles or other microstructural features. We demonstrate that this mechanism has wider relevance and may have been observed previously.

Insulating RE₂BaCuO₅ (RE-211) second-phase inclusions embedded within the REBa₂Cu₃O_7−δ (RE-123) superconducting phase matrix are known to contribute significantly to flux pinning in melt-processed superconductors. The critical current density in these materials has been observed to increase significantly in the presence of low external magnetic fields, in particular due to the presence of the RE-211 phase. J_c at higher applied magnetic field, however, is unaffected by these inclusions. Recently we have introduced successfully nanoscale (RE)₂Ba₄CuMO_y (RE-2411, where M = W,Nb,Ag and Bi) phase inclusions into the RE-123 phase matrix using a top-seeded melt growth (TSMG) technique. Here we report the flux pinning behaviour of various REBa₂Cu₃O_7−δ/(RE)₂Ba₄CuMO_y nanocomposites and compare their properties with those of REBa₂Cu₃O_7−δ/RE₂BaCuO₅ single-grain composites. A direct correlation between increased J_c and increased concentration of nanoscale inclusions is observed. Finally, the presence of RE-2411 nanoscale inclusions is observed generally to improve both J_c and the irreversibility field of bulk RE–Ba–Cu–O superconductors processed by TSMG.

A novel nanomaterial synthesis technique has been developed to introduce 0D (particles), 1D (columnar defects) and 3D (domains) nanoscale pinning centres in MOD Y₁Ba₂Cu₃O₇ (YBCO) coated conductors. We have succeeded in introducing nanoscale Y enriched particles, nanoscale 90° rotated Y_1/3Sm_2/3Ba₂Cu₃O₇ domains and nanoscale Zr enriched columnar defects into YBCO layers by different chemical doping. The pinning force density in Y₂O₃-doped YBCO film is found to be larger than that of pure YBCO film at all fields. Also it was found that YBCO films with Sm substituting for Y have yielded improved critical current density characteristics over a wide range of magnetic fields. Maximum pinning force densities exceeding 7 and 8 GN m⁻³ are obtained in 5% BZO-doped and Sm substituted YBCO films, respectively. Additionally, TEM studies revealed nanoscale Zr enriched columnar defects distributing in the matrix of the c-oriented YBCO film throughout the whole cross section. This indicates that chemical doping is a promising fabrication technique to create specific pinning landscapes in YBCO coated conductors.

We report the synthesis, high-resolution micro-structure, magneto-transport and magnetization of nano-diamond doped MgB₂–nD_x with x = 0.0–0.1. The superconducting transition temperature (T_c) is not affected by x up to x = 0.05, indicating that the added nano-diamond (1) does not decompose to C and (2) does not partially substitute for B in MgB₂. R(T) versus H measurements show higher T_c values under the same applied magnetic field for the nano-diamond added samples, resulting in higher estimated H_c2 values. Isothermal magnetization measurements show that above 2 T, the critical current density (j_c) is of the order of 10⁵ A cm⁻² for the pristine sample. j_c is further increased to three times for 3% nano-diamond doped samples. High-resolution transmission electron microscopy (HRTEM) observations clearly show the dispersion of nano-diamond particles, with an average particle size of 8–10 nm, in the MgB₂ matrix. It seems likely that the dispersed nano-diamond particles of below 10 nm in size are acting as effective pinning centres responsible for improving the superconducting performance of the parent MgB₂.

Substitutional studies have been carried out on sintered bulk samples of YBCO to determine the effect of doping it with Pr, Ca (at Y site) and Ni (at Cu site) in small concentrations on the formation of effective pinning centres for j_c enhancement. The results show Pr and Ca substitutions to be far more effective than Ni substitution. The former two give rise to formation of rows of oxygen vacancies with pronounced strain fields in CuO₂ planes where superconductivity resides. The defects thus formed seem to be analogous to arrays of normal nanodots in CuO₂ planes which are expected to have strong intragrain pinning interactions with pancake vortices of CuO₂ planes forming the mixed state structure. Both these substitutions tend to marginalize the adverse effects of grain boundaries. The superconducting volume fraction of the pristine sample is significantly raised by both these substitutions. These special features are, however, absent with Ni substitution. This paper brings out the importance of Pr substitution in significantly enhancing j_c(B).

We discuss an experiment on large-grain YBCO, the intent of which is to compare the effectiveness of continuous columnar pinning centres (CCPC) to that of discontinuous aligned pinning centres, in their ability to increase J_c. We find that discontinuous pinning is far superior. The motivation and design of the experiment are reviewed. High-energy heavy ions were utilized to produce pinning damage of controlled morphology. The resulting increase in J_c is presented as a function of the variable S_e, which is closely related to the discontinuity and diameter of the damage. The dependence of J_c on magnetic field, temperature, and F_i (the number of ion tracks per cm²) is presented and discussed. The dependence of H_irr on S_e and F_i, and the temperature and fluence dependence of a J_c fishtail effect, are presented. The experimental results indicate that multiple-in-line-damage (MILD), despite its discontinuities, is far more effective in increasing J_c than CCPCs are.

Bulk melt-processed Y–Ba–Cu–O (YBCO) has significant potential for a variety of high-field permanent-magnet-like applications, such as the rotor of a brushless motor. When used in rotating devices of this kind, however, the YBCO can be subjected to both transient and alternating magnetic fields that are not parallel to the direction of magnetization and which have a detrimental effect on the trapped field. These effects may lead to long-term decay of the magnetization of the bulk sample. In the present work, we analyze both experimentally and numerically the remagnetization process of a melt-processed YBCO single domain that has been partially demagnetized by a magnetic field applied orthogonal to the initial direction of trapped flux. Magnetic torque measurements are used as a tool to probe changes in the remanent magnetization during various sequences of applied field. The application of a small magnetic field between the transverse cycles parallel to the direction of original magnetization results in partial remagnetization of the sample. Rotating the applied field, however, is found to be much more efficient at remagnetizing the bulk material than applying a magnetizing field pulse of the same amplitude. The principal features of the experimental data can be reproduced qualitatively using a two-dimensional finite-element numerical model based on an E–J power law. Finally, the remagnetization process is shown to result from the complex modification of current distribution within the cross-section of the bulk sample.

A complete set of critical current data for a Nb₃Sn bronze wire under axial and transverse loads has been measured as a function of magnetic field in the range between 12 and 19 T. For this purpose a new probe was developed for the application of a transverse compressive force with a gauge length of 120 mm. The device is based on a one-turn Walters spring, thus circumventing the problem of current transfer. The probe allows the application of voltage criteria of 0.01 µV cm⁻¹ or less, allowing a detailed study of the n values. As expected, the conductor is more affected by transverse compressive stress than by axial tensile stress. The conductor already starts to degrade at small transverse stresses and the rate of degradation increases with the magnetic field. On the wires measured so far, unloading from 160 MPa yields a recovery of the critical current to 87% of its initial value. The obtained results encourage further investigations of differently processed Nb₃Sn superconductors (internal tin, powder in tube) or others (e.g. Nb₃Al) and may be helpful for modelling.

The thickness dependence of pinning properties is investigated in detail under various conditions of temperature, magnetic field and electric field for IBAD/PLD YBCO-coated conductors. The thickness-dependent critical current density in the three-dimensional pinning regime at low magnetic fields is attributed to the change in the morphology of the superconducting layer. It is found that while the irreversibility field increases with the thickness at low electric fields according to DC magnetization measurements, it decreases at usual electric fields corresponding to resistive measurements. This can be explained by the theoretical model of flux creep and flow with the irreversible thermodynamic principle that the transverse flux bundle size is determined so that the critical current density under the flux creep is maximized. The former model assumes the limitation of the longitudinal flux bundle size by the superconducting layer thickness, while the latter principle assumes a change in the transverse one from the value expected from the elasticity of flux lines. The observed n-value, the parameter describing the relationship between the electric field (E) and the current density (J) as , increases monotonically with the thickness in both electric field regions. This can be simply attributed to the increase in the pinning potential with the thickness.

Flux pinning properties and irreversibility fields B_irr(T) of melt-textured YBCO with discontinuous or multiple-in-line-damage (MILD) columnar defects produced by irradiation with high-energy U²³⁸ ions were studied at a constant matching field of B_ϕ = 10 T and for several energy losses between S_e = 1.67 and 2.4 keV Å⁻¹. With increasing S_e and increasing length of the MILD pins, the critical current density j_c(H,T) strongly increases and B_irr(T) for fields along the c axis progressively shifts upwards reaching 9 T at 77 K. For S_e = 2.4 keV Å⁻¹, a pronounced kink is observed in B_irr(T) at 8 T which is a strong indication of Bose-glass behaviour. The j_c(H) dependence of this sample shows a peak at a low applied field B_p. This peak effect is explained by the entanglement of vortices. It is argued that for MILD pins single vortices interact simultaneously with many short columnar defects in neighbouring ion trails resulting in an automatic splay in the vortex orientation. The observed decrease of B_p with increasing temperature is estimated taking the increasing thermal fluctuations into account.

We report on the thickness and angular dependence of the critical current density J_c(H,θ), the irreversibility field H^irr, and the bulk pinning force F_p(H) of a metal-organic chemical vapour deposition (MOCVD) grown YBa₂Cu₃O_7−x (YBCO) coated conductor, which contains ∼17 vol% of ∼10 nm sized (Y,Sm)₂O₃ precipitates with an average spacing of ∼10–15 nm. Some surface porosity and amorphous second-phase particles on the scale of ∼0.5–1 µm appear to reduce the current-carrying cross-section, which controls the magnitude of J_c but not the vortex pinning. We observed an enhanced H^irr∼9  T at 77 K along the c-axis which, like the shape of J_c(H) and F_p(H), was independent of thickness as the sample was milled down to ∼0.16 µm. Angular-dependent measurements of J_c showed the usual excess vortex pinning along the c-axis and along the ab-plane, but with a background that could only be fitted with an unusually small anisotropy parameter of 3, which, like the high H^irr and the thickness-independent shape of F_p(H), we ascribe to strong vortex pinning centre interactions. Together, these measurements show very different behaviour from most pulsed-laser-deposited films, which exhibit strong thickness-dependent properties. We ascribe the present different results to the dense array of small, insulating precipitates, which act as strong pinning centres and produce strong three-dimensional (3D) vortex pinning, because their separation of 10–15 nm is always much smaller than the film thickness.

The deformation behaviour of a YBa₂Cu₃O_x (YBCO)-coated conductor based on Ni–W substrate and its influence on the critical current were precisely investigated. From a room temperature tensile test, the change of permanent strain as a whole of the coated conductor was divided into two regions of micro- and macroscopic yielding. The precise lattice constant measurement by synchrotron radiation at Spring8 revealed that the permanent strain in the YBCO layer was characterized by two regimes related just to the two regions of yielding mentioned above. In the micro-yielding region, the permanent strain in the YBCO layer was identical with that in the metallic components, suggesting that the YBCO layer behaves elastically and any damage-like cracks were not introduced. In the macroscopic yielding region, the smaller permanent strain in the YBCO layer compared with the metallic components suggested that damage-like cracks were introduced in the YBCO layer during loading and remains under zero external load. There the invariant of total length is accommodated by the existence of damage-like cracks. The reversibility of the critical current was evaluated by loading/unloading experiments. The permanent strain ensuring the reversible limit and the corresponding applied strain were found to be 0.17% and 0.52%, respectively. This reversible limit coincided with the limit of micro-yielding. Furthermore the irreversible degradation of the critical current as a function of strain is suggested to relate to the macroscopic yielding.

We have investigated the influence of two different Ti doping methods on the superconducting properties of bronze route Nb₃Sn multifilamentary wires. The first doping method introduces NbTi rods into NbTa filaments embedded in a Cu15.4Sn bronze matrix ('internal' Ti). The second method uses Cu15.5Sn0.25Ti bronze as an external source of Ti ('external' Ti). The wires prepared by 'external' Ti doping were found to exhibit the highest critical current values although the conductor configurations were identical.

In order to understand the origin of the observed differences in transport properties, the grain morphology and the local composition profile of the A15 layer have been studied by means of systematic TEM/EDX measurements, which revealed a Sn gradient within the filaments. In addition, specific heat measurements have also been carried out for determining the T_c distribution in the whole wire volume, using a data deconvolution at the superconducting transition. A T_c distribution over a wide range of temperatures was found, corresponding to the Sn gradient revealed by TEM/EDX. Combining TEM/EDX analysis and calorimetry, it was possible to explain the differences between the two Ti doping methods studied in this work. As supplied from an internal source (cores), a higher overall Ti concentration was obtained, pushing the total Ta+Ti alloying content beyond the value of optimal doping corresponding to a maximum of T_c and B_c2.

The influence of film thickness and growth rate on the vortex pinning in hybrid liquid phase epitaxy (HLPE) films was explored. Film growth rates as high as 12 nm s⁻¹ (0.7 µm min⁻¹) produced high J_c films. Weak or no thickness dependence was found in films of thickness ranging from 0.4 to 3 µm. Field and angular measurements of the critical current density (J_c) and the power-law exponent (N) of the current–voltage curves were used to determine the nature of pinning. Films thinner than 0.6 µm showed a higher density of correlated defects parallel to the ab plane than thicker films. Using HLPE, it was possible to achieve very strong pinning in films ∼3 µm thick, yielding critical currents over 300 A cm⁻¹ width at self-field, and as high as 35 A cm⁻¹ width at μ₀H = 3 T at T = 75.5 K. Decreasing the deposition rate allowed improving the high field performance, opening up the possibility to engineer the pinning landscape of the HLPE films.

Superconducting YBa₂Cu₃O₇ (YBCO) thin films were grown by the trifluoroacetates route onto metallorganic deposited La_0.7Sr_0.3MnO₃ (LSMO) buffer layers. The growth conditions of the LSMO films have been studied in detail and fully strained epitaxial layers with atomically flat surfaces have been obtained with local roughness ∼1 nm, as determined by atomic force microscopy. We prove that this surface morphology is a key parameter for achieving YBCO/LSMO multilayers with high critical current densities in self-field, J_c^sf (77 K) = 1.8 MA cm⁻². Angular pinning studies demonstrate that the defect structure is modified with respect to standard TFA–YBCO films as a pronounced peak in J_c is observed for at high temperatures. This indicates the presence of anisotropic defects playing an important role in vortex pinning even at the irreversibility line stressing the suitability of these all-chemical TFA–YBCO/LSMO multilayers as conductive coated conductor architectures.

Y₂O₃ nanoparticles prepared by an inert gas phase condensation process were used to introduce artificial pinning centres in YBa₂Cu₃O_7−δ thin films. The areal density of the particles was varied between 120 and 4200 particles µm⁻² without changing the mean particle diameter of approximately 9 nm. Y₂O₃ particles were deposited on TiO₂ terminated SrTiO₃ (100) single-crystal substrates with areal densities up to 1654 particles µm⁻² and subsequently covered with YBa₂Cu₃O_7−δ by off-axis pulsed laser deposition (PLD). The areal density of the room temperature deposited particles is not changed by the substrate heating during PLD although their height on the substrate decreases. An influence on J_c is demonstrated for particle densities above 1588 particles µm⁻², indicating that the substrate decoration with Y₂O₃ nanoparticles from the gas phase affects the formation of artificial pinning centres in the YBa₂Cu₃O_7−δ films and can be applied to further study of the effect of particle size and areal density on defect formation in YBa₂Cu₃O_7−δ.

We report on the order–disorder transition line (B_od) in the flux line lattice—illustrated by the fishtail effect—of pure and carbon doped superconducting MgB₂ single crystals. Neutron irradiation offers a unique opportunity for varying the defect density (n_d) in a controlled way and to determine B_od not only as a function of temperature (T), but also as a function of n_d. Experimental data are compared with theoretical predictions and found to be in good agreement over most of the available parameter range, both for B_od(T) and B_od(n_d). Including two-band effects in MgB₂ in quite a rough way leads to even better agreement.

A systematic study of the structure and superconductive characteristics of high-pressure–high-temperature (2 GPa, 700–1000 °C)-synthesized and sintered MgB₂ without additions from different initial powders was performed. Among various secondary phases Mg–B inclusions with a stoichiometry close to MgB₁₂ were identified. With an increasing amount of these inclusions the critical current density increased. So these inclusions can be feasible pinning centres in MgB₂. The highest j_c values in zero field were 1300 kA cm⁻² at 10 K, 780 kA cm⁻² at 20 K and 62 kA cm⁻² at 35 K and in 1 T field were 1200 kA cm⁻² at 10 K, 515 kA cm⁻² at 20 K and 0.1 kA cm⁻² at 35 K for high-pressure-synthesized magnesium diboride and the field of irreversibility at 20 K reached 8 T. The average grain sizes calculated from x-ray examinations in materials having high j_c were 15–37 nm.

We report the grain size dependence of critical current and grain boundary pinning in bulk MgB₂. By combining polarized optical microscopy and electron backscatter diffraction, we obtain evidence of special grain boundaries with a high density of dislocations that are able to provide high critical current in MgB₂ polycrystals. We argue that reduction of grain size to the nanoscale level is sufficient to provide the critical current densities required for large-scale applications at the boiling temperature of liquid hydrogen.

Critical currents measured on a commercial Bi-2223/Ag tape in applied magnetic fields ranging from zero to 100 mT are analysed in order to demonstrate the validity of the phenomenological description proposed by the authors for flux pinning in polycrystalline high-temperature superconductors in low magnetic fields. The four-parameter model is a generalization of the Kim formula describing the magnetic field dependence of the critical current density. When combined with the finite-element calculation, it is able to predict the critical currents measured in different field orientations with an average accuracy better than 0.2%. The volume density of the flux pinning force is easily evaluated from the parameters of the model. Particular attention is paid to the problem of a possible sample non-uniformity. In fact, the experimental data can be better explained assuming the hypothesis of better filament texturing in outer filaments. This also means that the accurate determination of critical currents in low magnetic fields can be used to reveal a non-uniformity in the current-carrying capability of the superconducting material.

In this study we compare the critical current density, the irreversibility line and the upper critical field of four MgB₂ polycrystalline samples, which are either undoped or have 5% carbon or 5% carbon plus either 1% aluminium or 2% zirconium. We discuss how care must be taken for the extraction of the irreversibility line in such samples. We also show how ac susceptibility and Hall probe imaging can be used to examine whether the samples remain fully connected to the highest available fields. Compared to simple 5% carbon doping we find that co-doping provides modest improvement in the pinning properties at intermediate fields in the carbon plus zirconium doped sample.

The influence of uniaxial tensile stress–strain on the AC loss characteristics of multifilamentary Bi2223/Ag sheathed tape wires was investigated. The uniaxial tensile stress–strain was applied to the sample wire in liquid nitrogen at atmospheric pressure, and the AC losses (transport, magnetization and total losses) were measured by an electric method. Two kinds of wire, oxide-dispersion strengthened Ag-alloy sheathed and Ag-alloy sheathed wires, were tested. The stress–strain curves of the tested wires were divided in three regions, i.e. elastic deformation, continuous plastic deformation and serrated-like plastic deformation regions, though the ranges of those regions were different for different kinds of wire. In the elastic and continuous plastic regions, the stress–strain curve was smooth and continuous, and in the serrated-like plastic region, the curve was rough. In the serrated-like plastic region, the wires kept elongating, while increase of the tensile stress was suspended. Dependences of the critical currents on the stress–strain were generally as follows. While decreases of the wire critical currents were in the range of less than 4% of the original values of the no-stress condition, the critical currents of the wires were reversible, that is, the critical currents recovered the original values at zero stress when the stress were released, regardless of whether the wires were in the elastic or continuous plastic region. In the continuous plastic region, the critical currents decreased up to 10%–15% of the original values and the critical currents were irreversible when the degradations of the critical currents exceeded about 4%. In the serrated-like plastic regions, the critical currents were more severely degraded. The AC loss characteristics of the wires are different in those regions. In the elastic and continuous plastic regions, the absolute values of AC losses were dependent on the stress–strain. However, the dependences of those normalized losses on the stress–strain are negligibly small when the losses are properly normalized by the stress–strain-dependent critical currents. In the serrated-like plastic region, the AC loss characteristics are different from those in the elastic and continuous plastic regions and can be characterized by defects grown almost tape wide, causing serious degradation of the critical currents.

There are various origins of defects causing the degradations of the wire critical currents. However, as a result of this investigation, the influence of the tensile stress–strain on the AC losses can be basically estimated by knowing the degrees of the degradations of the wire critical currents caused by the stress–strain and in which regions the stress–strain characteristics are, regardless of the origins of the defects.

We measured the frequency dependence of hysteresis loss in non-striated and striated YBCO coated conductors in the frequency range from 1 mHz up to 350 mHz at 77 K. At these frequencies the coupling losses in YBCO coated conductors do not exist and in filamentary YBCO tapes they can be practically neglected. The dominant loss component is the hysteresis loss. We have found that for magnetic fields above the full penetration field the hysteresis loss increases with increasing frequency and this dependence can be described by a power law function. For magnetic fields below the penetration field the hysteresis loss decreases with frequency. This behaviour supports the previous theoretical results indicating that the field dividing the behaviour of hysteresis losses versus frequency is the penetration field. The experiments with YBCO samples on non-metallic substrate at frequencies up to 600 Hz show that the dependence of hysteresis losses measured at millihertz frequencies can be extrapolated to higher frequencies of the order of 100 Hz. We propose a simple procedure to separate the hysteresis losses from the total measured losses based on the measurement of the frequency dependence of losses at low frequencies. Taking into account the frequency dependence of hysteresis losses we can considerably reduce the errors in the separation of hysteresis losses from the total measured losses.

Transport AC loss measurements have been made on YBCO-coated conductors prepared on two different substrate templates—RABiTS (rolling-assisted biaxially textured substrate) and IBAD (ion-beam-assisted deposition). RABiTS samples show higher losses compared with the theoretical values obtained from the critical state model, with constant critical current density, at currents lower than the critical current. An origin of this extra AC loss was demonstrated experimentally by comparison of the AC loss of two samples with different I–V curves. Despite a difference in I–V curves and in the critical currents, their measured losses, as well as the normalized losses, were practically the same. However, the functional dependence of the losses was affected by the ferromagnetic substrate. An influence of the presence of a ferromagnetic substrate on transport AC losses in YBCO film was calculated numerically by the finite element method. The presence of a ferromagnetic substrate increases transport AC losses in YBCO films depending on its relative magnetic permeability. The two loss contributions—transport AC loss in YBCO films and ferromagnetic loss in the substrate—cannot be considered as mutually independent.