Superconducting tape coils and Roebel cables are often modeled as stacks of parallel superconducting tapes carrying the same transport current. We solved, in the infinitely thin approximation, the transport current and magnetization problems for such stacks using an efficient numerical scheme based on a variational formulation of the Kim critical-state model. We also refined the anisotropic bulk approximation, introduced by Clem et al. in order to simplify AC loss estimates for densely packed stacks of many tapes; this was achieved by removing the simplifying a priory assumptions on the current sheet density in the subcritical zone and the shape of this zone boundary. Finally, we studied convergence of stack problem solutions to the solution of the modified bulk problem. It was shown that, due to the fast convergence to the anisotropic bulk limit, accurate AC loss estimates for stacks of hundreds of tapes can usually be obtained also using a properly rescaled model of a stack containing only ten-twenty tapes.

Design, parameters, and application areas of a superconducting fault current limiter (FCL) are analyzed on the basis of the requirements of power systems. The comparison of resistive and inductive designs is carried out. An example of the effective application of FCLs in distribution substations is considered and the gain from the FCL installation is discussed. It is shown that an FCL not only limits a fault current but also increases the dynamic stability of the synchronous operation of electric machines. The calculation procedure of the parameters of an inductive FCL for a specific application case is described.Index Terms-Fault current limiter (FCL), high-temperature superconductor (HTS), power system.

Superconductors are considered in view of applications to atom chip devices. The main features of magnetic traps based on superconducting wires in the Meissner and mixed states are discussed. The former state may mainly be interesting for improved atom optics, while in the latter, cold atoms may provide a probe of superconductor phenomena. The properties of a magnetic side guide based on a single superconducting strip wire placed in an external magnetic field are calculated analytically and numerically. In the mixed state of type II superconductors, inhomogeneous trapped magnetic flux, relaxation processes and noise caused by vortex motion are posing specific challenges for atom trapping. PACS: 37.10.Gh Atom traps and guides 85.25.Am Superconducting device characterization, design, and modeling Progress towards this goal demands the control and reduction of magnetic noise produced by the metallic components of the atom chip. Randomly fluctuating magnetic fields are generated by thermal current noise in the conducting chip elements and reduce the number of trapped atoms (losses), increase their temperature (heating) and lead to a phase uncertainty in the atom's state (decoherence) -see, for example, [1, 2, 3] and references therein. Theoretical analysis of the magnetic noise generated by a normal metal [4,5,6,7] predicts a fast reduction of the lifetime with the decrease of the distance z t between the trapped atom and the metal surface (trap height); this is in excellent agreement with lifetime measurements [8,9,10]. At a trap height less than 10 ÷ 20 µm, thermal magnetic noise exceeds all other harmful influences on the atom cloud (technical noise due to the current supply instability, residual gas collisions, stray magnetic fields) and provides the dominant limit for the lifetime [1,3]. In the last few years, the application of superconducting materials to atom chips has been widely discussed as a perspective to extend the lifetime of cold atoms [7,11,12,13,14]. A recent theoretical estimate [13] of the magnetic noise caused by a superconductor in the Meissner state showed that the lifetime of atoms trapped above a superconducting layer would be, at least, six orders of magnitude longer than above a normal metal in the same geometry. The analysis presented in [14] predicts an atom lifetime of 5000 s at a trap height of 1 µm. For comparison, at the same height in a normal metal trap the lifetime is less than 0.1 s [9]. At larger heights, the lifetime in a superconducting niobium chip can be much larger (up to 10 11 s at temperature T = 4.2 K).Two first realizations of atom chips with superconducting elements have been reported in Refs. [15] and [16]. In both setups, the trapped atoms were 87 Rb. In the experiment by Nirrengarten et al. [15], the current-carrying wires (in "U" and "Z" shape) were made of niobium and operated at about 4.2 K. The obtained atom spin relaxation time was estimated as 115 s. This value is comparable to the best one achieved for atoms trapped near normal-metal wires [17]. In the second ...

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