Flux Lines In Type Research Articles

Scaling behaviors and novel creep motion of ac-driven flux lines in type II superconductor with random point pins

We performed Langevin dynamics simulations for the ac-driven flux lines in a type II superconductor with random point-like pinning centers. Scaling properties of flux-line velocity with respect to an instantaneous driving force of small frequency and around the critical dc depinning force are revealed successfully, which provides precise estimates on dynamic critical exponents. From the scaling function, we derive a creep law associated with activation by regular shaking. The effective energy barrier vanishes at the critical dc depinning point in a square-root way when the instantaneous driving force increases. The frequency plays a similar role to temperature in conventional creep motions, but in a nontrivial way governed by the critical exponents. We have also performed systematic finite-size scaling analysis for flux-line velocity in transient processes with dc driving, which provide estimates on critical exponents in good agreement with those derived with ac driving. The scaling law is checked successfully.

Deblocking of interacting particle assemblies: from pinning to jamming

A wide variety of interacting particle assemblies driven by an external force are characterized by a transition between a blocked and a moving phase. The origin of this deblocking transition can be traced back to the presence of either external quenched disorder, or of internal constraints. The first case belongs to the realm of the depinning transition, which, for example, is relevant for flux-lines in type II superconductors and other elastic systems moving in a random medium. The second case is usually included within the so-called jamming scenario observed, for instance, in many glassy materials as well as in plastically deforming crystals. Here we review some aspects of the rich phenomenology observed in interacting particle models. In particular, we discuss front depinning, observed when particles are injected inside a random medium from the boundary, elastic and plastic depinning in particle assemblies driven by external forces, and the rheology of systems close to the jamming transition. We emphasize similarities and differences in these phenomena.

Exact solution of a lattice model of flux lines in superconductors

We consider a statistical mechanical model describing flux lines in type II superconductors by embedding the flux lines on a lattice wound on torus. The lines are nonintersecting and each loop of lines is associated with a fugacity z = −1. It is shown that the exact solution of this model leads to a second-order transition between the Meissner and the superconducting states as well as a first-order transition between the superconducting and the normal states.

Determination, by neutron diffraction, of basic interaction forces for flux pinning in superconductors

Abstract A new method has been developed for the determination of the basic interaction force exerted on the flux lines in type II superconductors. From neutron diffraction by flux line lattices in the two-phase system Nb with Nb2N precipitates of a well defined metallurgical structure, it is observed that the flux lines are bent due to the presence of pinning centres. A measure for the bending is the width of the rocking curve which is rather directly related to the mean basic interaction force ⟨f 2⟩1/2. For four specimens with different number densities of precipitates from 1·3 × 1017 to 1·3 × 1018 m−3 the force ⟨f 2⟩1/2 has been evaluated as a function of the flux density B from the angular widths of the measured rocking curves. These widths ranged from 6’ to 4°. The basic interaction forces were independent of the number density; at B/B c2=0·5 a value ⟨f 2⟩1/2=2 × 10−10 N was obtained. The maximum interaction force K 0 obtained from the pinning force densities for one sample agreed well with ⟨f 2⟩1/2....

Statistical theory of pinning on point defects

The statistical treatment of pinning on point defects is given including the correlations of the number of defects in neighbouring volumes (the interaction of these volumes with the fluxoid is taken as the elementary interaction causing the pinning). For higher defect densities, the agreement with the experiments on niobium is better than with the previous theory. This method of correlations seemed suitable for study the effect of “cutting-off” the small elementary interactions and for the replacement of the Gauss distribution function by the Poisson distribution function for the number of defects in the elementary volumes. Both these efforts give negative results with respect to the experiments; so far we are therefore not able to explain quantitatively the large increase of the pinning force at small defect densities and small magnetic fields, as well as its decrease to zero always for fields smaller thanH c2 . The attractive interaction between the flux lines in type II superconductors with small Ginzburg-Landau parameter could give a qualitative explanation of the enhancement of the pinning at small defect densities.

On the existence of several-quanta flux lines in type II superconductors

The existence of several-quanta flux lines is shown to be possible in the surface vicinity of type II superconductors.

The direct observation of individual flux lines in type II superconductors

Triangular flux line lattices have been observed by electron microscopy on Pb-4at% In and niobium specimens in the remanent state. These lattices contain various kinds of defects.

Pinning forces and hysteresis in type II superconductors

Flux lines in type II superconductors experience pinning forces due to material defects. Under critical-current conditions it is assumed that the forces are proportional to |H|n, where H is the local magnetic field and n is an arbitrary constant. On this basis, the magnetic flux distribution in an infinite superconducting slab is calculated as a function of time, when a sinusoidal magnetic field, Ho=Hm sinωt, is applied parallel to the slab surface. Hence, the instantaneous rate at which flux penetrates into the superconductor is evaluated. The results lead to the hysteresis loop of the material, which implies power dissipation proportional to Hm3−n for n ≤1. It is shown that the Bean-London and Kim-Anderson models of hysteresis in type II superconductors appear as special cases of the above theory.

Mesure directe par resonance magnetique nucleaire de la distribution du champ magnetique dans un supraconducteur de deuxieme espece

The nuclear magnetic resonance of 93Nb nuclei in the superconductive state (type II) near HC 2 has been observed directly in pure powdered niobium metal as a function of the external magnetic field. Theoretical calculations of line shape and width have been made using the assumption of a triangular or square lattice of flux lines in type II superconductors. The observed line shape and width are in numerical agreement with the calculations for a triangular lattice. The saturation of the line was studied, in the situation where the flux lines broadening becomes greater than the line width observed in the normal state.

The motion of flux lines in type II superconductors

Abstract The motion of a flux line in a clean superconductor of extreme type II (λ≫ζ) at zero temperature is discussed in detail. It is shown that the vortex core is subject to a Magnus force identical to that found in liquid helium. The Magnus force balances the friction force exerted by the lattice on the core. The nature of this friction force is discussed, particularly in the light of a recent paper by Bardeen and Stephen. Different possible forms of the force are discussed and compared with experiment.

The behaviour of type II superconductors

Abstract By treating the flux lines in a type II superconductor as a compressible fluid Friedel et al. (1963) have shown that, for a non-uniform distribution of lines, the force per unit length acting on one line is (φ04π). dH(B)/dx. Here B is the induction at x and H(B) the external field which would be in equilibrium with B if the material were reversible. The flux lines in an irreversible type II superconductor in the critical state of Kim et al. (1963) are in virtual equilibrium under the forces due to the flux concentration gradient and a pinning force F. F arises from the interaction between the flux lines and structural defects in the material. It follows that F = (φ0/4π)(dH/dB) a(dB/dx) s, where (dH/dB) a is the gradient of the reversible B/H curve and (dB/dx) s the field gradient in the specimen.