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Register a new userTheory of flux cutting and flux transport at the critical current of a type-II superconducting cylindrical wire
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John R. Clem
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I introduce a critical-state theory incorporating both flux cutting and flux transport to calculate the magnetic-field and current-density distributions inside a type-II superconducting cylinder at its critical current in a longitudinal applied magnetic field. The theory is an extension of the elliptic critical-state model introduced by Romero-Salazar and Perez-Rodriguez. The vortex dynamics depend in detail upon two nonlinear effective resistivities for flux cutting (rho_parallel) and flux flow (rho_perp), and their ratio r = rho_parallel/rho_perp. When r < 1, the low relative efficiency of flux cutting in reducing the magnitude of the internal magnetic-flux density leads to a paramagnetic longitudinal magnetic moment. As a model for understanding the experimentally observed interrelationship between the critical currents for flux cutting and depinning, I calculate the forces on a helical vortex arc stretched between two pinning centers when the vortex is subjected to a current density of arbitrary angle phi. Simultaneous initiation of flux cutting and flux transport occurs at the critical current density J_c(phi) that makes the vortex arc unstable.
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We discuss predictions of five proposed theories for the critical state of type-II superconductors accounting for both flux cutting and flux transport (depinning). The theories predict different behaviours for the ratio $E_y/E_z$ of the transverse and parallel components of the in-plane electric field produced just above the critical current of a type-II superconducting slab as a function of the angle of an in-plane applied magnetic field. We present experimental results measured using an epitaxially grown YBCO thin film favoring one of the five theories: the extended elliptic critical-state model. We conclude that when the current density $bm J$ is neither parallel nor perpendicular to the local magnetic flux density $bm B$, both flux cutting and flux transport occur simultaneously when $J$ exceeds the critical current density $J_c$, indicating an intimate relationship between flux cutting and depinning. We also conclude that the dynamical properties of the superconductor when $J$ exceeds $J_c$ depend in detail upon two nonlinear effective resistivities for flux cutting ($rho_c$) and flux flow ($rho_f$) and their ratio $r= rho_c/rho_f$.
The current distribution across the thickness of a current-carrying rectangular film in the Meissner state was established long ago by the London brothers. The distribution across the width is more complicated but was later shown to be highly non-uniform, diverging at the edges. Accordingly, the standard view for type II superconductors is that vortices enter at the edges and, with increasing current, are driven inwards until they self-annihilate at the centre, causing dissipation. This condition is presumed to define the critical current. However we have shown that, under self-field (no external field), the transport critical current is a London surface current where the surface current density equals the critical field divided by {lambda}, across the entire width. The critical current distribution must therefore be uniform. Here we report studies of the current and field distribution across commercial YBa2Cu3O7 conductors and confirm the accepted non-uniform distribution at low current but demonstrate a radical crossover to a uniform distribution at critical current. This crossover ends discontinuously at a singularity and calculations quantitatively confirm these results in detail. The onset of self-field dissipation is, unexpectedly, thermodynamic in character and the implied vortex-free critical state seems to require new physics.
Doping of MgB2 by nano-SiC and its potential for improvement of flux pinning was studied for MgB2-x(SiC)x/2 with x = 0, 0.2 and 0.3 and a 10wt% nano-SiC doped MgB2 samples. Co-substitution of B by Si and C counterbalanced the effects of single-element doping, decreasing Tc by only 1.5K, introducing pinning centres effective at high fields and temperatures and enhancing Jc and Hirr significantly. Compared to the non-doped sample, Jc for the 10wt% doped sample increased by a factor of 32 at 5K and 8T, 42 at 20K and 5T, and 14 at 30K and 2T. At 20K, which is considered to be a benchmark operating temperature for MgB2, the best Jc for the doped sample was 2.4x10^5A/cm2 at 2T, which is comparable to Jc of the best Ag/Bi-2223 tapes. At 20K and 4T, Jc was 36,000A/cm2, which was twice as high as for the best MgB2 thin films and an order of magnitude higher than for the best Fe/MgB2 tapes. Because of such high performance, it is anticipated that the future MgB2 conductors will be made using the formula of MgBxSiyCz instead of the pure MgB2.
The order of the vortex state in La_{1.9} Sr_{0.1} CuO_{4} is probed using muon spin rotation and small-angle neutron scattering. A transition from a Bragg glass to a vortex glass is observed, where the latter is composed of disordered vortex lines. In the vicinity of the transition the microscopic behavior reflects a delicate interplay of thermally-induced and pinning-induced disorder.
To address unsolved fundamental problems of the intermediate state (IS), the equilibrium magnetic flux structure and the critical field in a high purity type-I superconductor (indium film) are investigated using magneto-optical imaging with a 3D vector magnet and electrical transport measurements. The least expected observation is that the critical field in the IS can be as small as nearly 40% of the thermodynamic critical field $H_c$. This indicates that the flux density in the textit{bulk} of normal domains can be textit{considerably} less than $H_c$, in apparent contradiction with the long established paradigm, stating that the normal phase is unstable below $H_c$. Here we present a novel theoretical model consistently describing this and textit{all} other properties of the IS. Moreover, our model, based the rigorous thermodynamic treatment of observed laminar flux structure in a tilted field, allows for a textit{quantitative} determination of the domain-wall parameter and the coherence length, and provides new insight into the properties of all superconductors.
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