Brownian motion and the superconducting surface sheath

19780123 We give an explicit solution for the mean velocity of a Brownian particle that is subject simultaneously to a spatially sinusoidal and a constant force. An application is made to the superconducting surface sheath of lead, wherein the fluxoids are represented by Brownian particles. When Brownian mean velocity curves are fitted to experimental voltage-current curves, we find that the parameter values are physically reasonable provided that interactions among the fluxoids are taken into account. The fluxoids move, in effect, as collections of about 100 fluxoids.     

Resistive behavior of the superconducting surface sheath of alloys

Measurements are reported of the surface resistance of dirty type-II superconductors driven into the surface-sheath regime by a static magnetic field,H ₀ parallel or nearly parallel to the sample surfaces and transverse to the microwave current, in which condition the latter can excite fluctuations of the order parameter. A recent calculation by Maki has suggested that the surface resistance would be influenced by the presence of Kulik's vortex state even when the sample surface is polished and is as nearly as possible parallel toH ₀. It is therefore proposed that the sample surface should be decomposed into elements which make different angles withH ₀, and the distribution of these angles described by a Gaussian. ₂ (t) is deduced from the surface-resistance measurements nearH _c3, so interpreted, and a temperature variation, ₂ (t)/₂(1), is found which agrees reasonably with theory and with magnetization data, [₂(1)=lim_{t 1} (₂)]. It is suggested that the anomalously large variation of ₂ (t) reported by Fischer and Maki may have resulted from failure to take Kulik's vortices into account. In magnitude, present ₂(1) data agree with theory but not with magnetization data.     

Electromagnetic response of surface superconducting sheath in an inclined magnetic field

The microwave response of the superconducting surface sheath in an inclined magnetic field is studied theoretically. Due to the vortex structure in the surface sheath in the present configuration, the low-frequency electromagnetic response is dominated by the flux-flow mechanism. Limiting ourselves to the dirty limit, the surface impedance is calculated explicitly. We find, in particular, that the surface resistance has a sharp minimum at =0, where is the angle between the dc magnetic field and the sample surface.     

On the threshold pinning force in type II superconducting films

The maximum pinning force of a two-dimensional vortex lattice in a random potential is calculated. A connection is established between this threshold pinning force and the potential energy discontinuities due to elastic and plastic instabilities of the vortex lattice. Inspired by recent computer simulations, we assume that the fluctuations in the commensurability between the random potential and the vortex potential breaks the vortex system up into a set of flowing channels in between trapped regions. Two instability mechanisms and their contribution to the threshold force are discussed within this channel-flow picture. We find that three different regimes exist depending on, w, the width of the channels;w=,a ₀w=a ₀ , wherea ₀ is the vortex lattice spacing. Weak pinning superconductors can pass through all three regimes as the reduced magnetic field is varied from 0 to 1, whereas strong pinning compounds can remain in the saturated region (w=a ₀ ) for all values of the field. We compare the expression for the threshold force with experimental results for both strong and weak pinning samples. A satisfactory qualitative agreement is obtained between theory and experiment.     

Vortex-antivortex lattices in superconducting films with magnetic pinning arrays

We found a rich variety of vortex structures when a thin superconducting film (SC) is covered with a lattice of out-of-plane magnetized magnetic dots (MDs). The vortices are confined to the MD regions, and antivortices nucleate into regular lattices which relax through several second order transitions towards single-dot vortex-antivortex configurations with increasing period of the magnetic array. Creation of vortex-antivortex pairs with increasing MD-magnetization is controlled by a single quantity—the superfluid velocity. We demonstrate that due to the vortex-antivortex pairs and the supercurrents induced by the MDs, the critical current in the sample actually increases if exposed to a homogeneous external magnetic field, contrary to conventional SC behavior. We explain further experimental implications, such as the magnetic field-induced-superconductivity.     

Lumped-Element Dynamic Electro-Thermal model of a superconducting magnet

Modeling accurately electro-thermal transients occurring in a superconducting magnet is challenging. The behavior of the magnet is the result of complex phenomena occurring in distinct physical domains (electrical, magnetic and thermal) at very different spatial and time scales. Combined multi-domain effects significantly affect the dynamic behavior of the system and are to be taken into account in a coherent and consistent model.A new methodology for developing a Lumped-Element Dynamic Electro-Thermal (LEDET) model of a superconducting magnet is presented. This model includes non-linear dynamic effects such as the dependence of the magnet’s differential self-inductance on the presence of inter-filament and inter-strand coupling currents in the conductor. These effects are usually not taken into account because superconducting magnets are primarily operated in stationary conditions. However, they often have significant impact on magnet performance, particularly when the magnet is subject to high ramp rates.Following the LEDET method, the complex interdependence between the electro-magnetic and thermal domains can be modeled with three sub-networks of lumped-elements, reproducing the electrical transient in the main magnet circuit, the thermal transient in the coil cross-section, and the electro-magnetic transient of the inter-filament and inter-strand coupling currents in the superconductor. The same simulation environment can simultaneously model macroscopic electrical transients and phenomena at the level of superconducting strands.The model developed is a very useful tool for reproducing and predicting the performance of conventional quench protection systems based on energy extraction and quench heaters, and of the innovative CLIQ protection system as well.     

Fluxoid pinning by vanadium carbide precipitates in superconducting vanadium

Vanadium carbide precipitates were formed in pure, annealed vanadium foils by the introduction of carbon in the specimens. Thin, disk-shaped precipitates resulted with mean diameters in the range 100–2600 Å and with number densities from 3 × 10¹⁵ to 4 × 10¹⁷ particles/cm³. The macroscopic, pinning-force density for magnetic fluxoids was measured at temperatures from 2 to 5 K and for magnetic fields from 0 to H _c2(T). Peak pinning-force densities in the range of 3 × 10 to 3 × 10⁶ dyn/cm³ for T=0K were realized in the 30 specimens studied. The pinning force density was found to obey a scaling law for specimens meeting certain requirements with respect to precipitate particle size and number density. These requirements correlate with the temperature-dependent, superconducting coherence length (T). Many specimens obeyed the scaling law at temperatures T < T _c except near T _c, where (T) is large in comparison with the precipitate size.Part of this work was supported by the Applied Research Laboratory of The Pennsylvania State University, under contract with the U.S. Naval Sea Systems Command.     

Embedding of nanoparticles as flux pinning sites in superconducting samples

Crystallographic orientations of thin films and bulk, melt-textured YBa₂Cu₃O_x high-T_c superconductors with embedded Y₂Ba₄CuMO_x (M = Nb, Zr, Ag) nanoparticles are studied by electron backscatter diffraction. The Y₂BaCuO₅ particles exhibit no preferred orientation but have a strong negative influence on the matrix orientation. In contrast, the nanoparticles are not disturbing the texture of the YBCO matrix. For the bulk samples, depending on the preparation route, a different particle orientation with respect to the matrix is obtained. Untextured M-2411 nanoparticles are formed by solid state reaction during the melt process by adding oxides (Nb₂O₅ or Y₂O₃) to the precursor powder. Pre-formed Y₂Ba₄CuMO_x particles added to the precursor in the form of pre-reacted nanopowder, exhibit a dominant single orientation related to the surrounding YBCO matrix. In the case of thin films prepared using laser ablation with a bulk YBCO sample with embedded nanoparticles as a target, the nanoparticles are transferred into the thin film, but the transferred M-2411 particles are found to be randomly oriented. Nevertheless, these films exhibit increased flux pinning properties.     

Edge pinning in superconducting thin films in perpendicular magnetic fields

Two-dimensional systems of bosons and fermions are studied at zero temperature by means of variational calculations. When viewed as a function of the quantum parameter = ²/m in the variational context, bosons are found to undergo a second-order liquid-to-gas transition, whereas, contrary to expectations, fermions are found to undergo a first-order transition with a region in which liquid and gaseous phases can coexist. Although these results are qualitatively the same as those in three dimensions, it is emphasized that, for two-dimensional fermions, the underlying physics is quite different. These results are examined critically in view of the special properties of two-dimensional systems. It is found that critical values of are rigorously lower bounds, and it is further argued that the essential features of these results remain valid. Finally, the implications of these results for experiments on submonolayer physisorbed helium and spin-aligned hydrogen systems are discussed.This research was supported, in part, by the National Science Foundation under grants DMR76-14447 and DMR73-02609.This research was performed as part of the NSF Independent Research Program. However, any of the opinions expressed herein are those of the author (LHN) and do not necessarily reflect the views of the NSF.     

On pinning of superconducting flux lines by grain boundaries

A simple model is developed which describes the reduction of the mean free path of conduction electrons in metals near a grain boundary. This leads to a decrease of the self-energy of flux lines in a layer which is considerably thicker than the perturbed zone of the boundary itself. The model yields pinning forces which agree, within an order of magnitude, with recent measurements on niobium bicrystals, and with observed values of grain boundary pinning in Nb₃Sn.Work supported by FAPESP, proc. no. 78/1230, and by the Niobium Project of FTI, Lorena SP, Brazil.On sabbatical leave from Instituto de Física da Universidade Estadual de Campinas (UNICAMP).     

Fluxoid pinning by second phases in a superconducting niobium-zirconium alloy

The effects of second phases on the critical currents of superconducting niobium-zirconium alloys containing a nominal 25 wt % zirconium have been determined by superconducting magnetisation experiments. Heat treatment of annealed and extruded materials in the temperature range 600 to 900° C leads to a cellular decomposition of the high temperature structure into two isostructural phases, one niobium-rich ( _Nb) and the other zirconium rich ( _Zr), with an accompanying increase in critical current (at an average field of 20 kOe) up to twelve times the original value. Heat treatment of quenched tubes at 800 or 900° C produces precipitation on sub-boundaries prior to the cellular reaction, this being accompanied by an increase in critical current to at least thirteen times the original value. In this case, however, prolonged heating leads to a fall in critical current which it is suggested is an overageing effect.     

Flux pinning in superconducting amorphous Zr1−x Co x

The pinning force F_P in amorphous Zr_1–x Co _x (x=0.30; 0.35) is measured as a function of perpendicular field and temperature. The homogeneous samples exhibit a weak flux pinning force of about 10⁴ N/m ³ in the temperature range 2–3 K. The field dependence ofF _P at several temperatures can be explained by a collective pinning model in the Larkin-Ovchinnikov theory in three dimensions. Structural relaxation studies in amorphous ZrCo confirm that bothT _c andF _P are sensitive to a slight isothermal annealing treatment at 220°C for 1 h. The collective flux-pinning characteristics still remain after such a structural relaxation, which allows us to conjecture that these defects are stable against this thermal treatment.     

冷绝缘高温超导电缆模型导体的动态稳定性分析

对两根2.2 m长YBCO涂层导体绕制的冷绝缘高温超导导体模型进行短路实验。实验在77.3 K的液氮环境进行,短路电流25 k A,时长2 s。对电缆温升和恢复进行实验研究,与仿真模拟结果进行比较,实验值和仿真模拟值吻合得很好。     

Resistive transition of superconducting wire networks. Influence of pinning and fluctuations

We have studied the resistive transition of several 2-D superconducting wire networks of various coupling strengths, which we characterize in terms of the Kosterlitz-Thouless transition temperature and the ratio /a of the coherence length to the array period. In the extreme strong coupling limit where the mesh size is of the order of the zero-temperature coherence length, the superconducting behavior is well described by the mean-field properties of the superconducting wave function. Extending to 2-D array, the 1-D phase slippage model explains the dissipative regime observed above the Ginzburg-Landau depairing critical current. On the other hand, when the coupling is weak, phase fluctuations below the Ginzburg-Landau transition and vortex depinning dominate the resistive behavior. An activated dissipation is observed even below the depairing critical current. Results obtained in this regime for critical temperature, magnetoresistance or critical current versus temperature, and magnetic field are shown; their periodic oscillations are discussed in terms of depinning of vortices on the array. A simple periodic pinning potential for a vortex in a wire network is calculated, and compared with the case of pinning in Josephson junction arrays. We show that this model explains qualitatively the experimental results observed for small /a.     

Analysis of electrical coupling parameters in superconducting cables

The analysis of current distribution and re-distribution in superconducting cables requires the knowledge of the electric coupling among strands, and in particular the interstrand resistance and inductance values. In practice both parameters can have wide variations in cables commonly used such as Rutherford cables for accelerators or Cable-in-Conduits for fusion and SMES magnets. In this paper we describe a model of a multi-stage twisted cable with arbitrary geometry that can be used to study the range of interstrand resistances and inductances that is associated with variations of geometry. These variations can be due to cabling or compaction effects. To describe the variations from the nominal geometry we have adopted a cable model that resembles to the physical process of cabling and compaction. The inductance calculation part of the model is validated by comparison to semi-analytical results, showing excellent accuracy and execution speed.     

Modeling of bent vortices and surface pinning

Vortices in superconducting film can be pinned by its surface roughness, which causes them to bend, creating the energy barriers against drift. Here, pinning of a single vortex by a surface ledge is analyzed analytically and numerically. It is found that thermal noise does not significantly lower the critical current.     

Maximum current of a superconducting wire in a transverse magnetic field in the case of weak pinning

A model of weakly pinned flux lines is described, permitting the calculation of the maximum current transverse field characteristic of a superconducting wire in the range of low fields. Studying the penetration of the first flux lines, the initial shape of the maximum current curve is found to be linear, up to a field which depends on the strength of pinning. Beyond this field the calculation of the maximum current requires a determination and investigation of the field distribution inside and outside the wire. This leads, the vortex state being only partially achieved, to a Hilbert problem involving a free boundary.     

Study of flux pinning by torque measurements in superconducting Al - 10% at Ag

The influence of magnetic field and temperature on Abrikosov fluxoid pinning in supersaturated Al-10 at % Ag solid solution is investigated by the torque measurement method. The minimum rotation angle of the magnetic field for the breakaway of fluxoids from pinning centres, logarithmic decrement of oscillation attenuation, and oscillation frequency of elastic suspension with the specimen are determined. The magnetic moment of the specimen is also calculated.It is shown that pinning increases with the decomposition of the alloy leading to the formation of γ¹-phase lamels.     

Artificial vortex pinning arrays in superconducting films deposited on highly ordered anodic alumina templates

A simple procedure is described for creating periodic vortex pinning centers in thin superconducting NbN films. We report on three different strategies which involve the use of highly ordered alumina templates. In this approach, NbN thin films are deposited either on the porous face of the template made of a triangular array of nanoholes or on the triangular array of bumps formed by the barrier layer or even on the top of perpendicularly oriented ferromagnetic nanowire arrays obtained by electrochemical deposition, thus forming superconductor-ferromagnet hybrids. In all cases, the ordered template allows NbN films to form a periodic pinning array during its growth. The interpore (or inter-bump) distance ranged between 50 and 100?nm and adjustable pore (or wire) diameter was varied between 30 and 60?nm. Numerous matching effects have been observed up to 2.5?T and are maintained at low temperature. These fields are considerably higher than those typical for periodic pinning arrays made by lithographic techniques, which reflects the benefits of nanostructuring superconductors by using self-organized growth to enhance vortex pinning in a large field and temperature range.     

Improved surface treatment of the superconducting TESLA cavities

The proposed linear electron–positron collider TESLA is based on $\text{1.3}\text{GHz}$ superconducting niobium cavities for particle acceleration. For a centre-of-mass energy of $\text{500}\text{GeV}$, an accelerating field of $\text{23.4}\text{MV/m}$ is required which is reliably achieved with a niobium surface preparation by chemical etching. An upgrade of the collider to $\text{800}\text{GeV}$ requires an improved cavity preparation technique. In this paper, results are presented on single-cell cavities which demonstrate that fields of up to $\text{40}\text{MV/m}$ are accessible by electrolytic polishing of the inner surface of the cavity.