Theory of Type-II Superconductors with Finite London Penetration Depth

Previous continuum theory of type-II superconductors of various shapes with and without vortex pinning in an applied magnetic field and with transport current, is generalized to account for a finite London penetration depth lambda. This extension is particularly important at low inductions B, where the transition to the Meissner state is now described correctly, and for films with thickness comparable to or smaller than lambda. The finite width of the surface layer with screening currents and the correct dc and ac responses in various geometries follow naturally from an equation of motion for the current density in which the integral kernel now accounts for finite lambda. New geometries considered here are thick and thin strips with applied current, and `washers', i.e. thin film squares with a slot and central hole as used for SQUIDs.Comment: 14 pages, including 15 high-resolution figure

Critical State in Thin Anisotropic Superconductors of Arbitrary Shape

A thin flat superconductor of arbitrary shape and with arbitrary in-plane and out-of-plane anisotropy of flux-line pinning is considered, in an external magnetic field normal to its plane. It is shown that the general three-dimensional critical state problem for this superconductor reduces to the two-dimensional problem of an infinitely thin sample of the same shape but with a modified induction dependence of the critical sheet current. The methods of solving the latter problem are well known. This finding thus enables one to study the critical states in realistic samples of high-Tc superconductors with various types of anisotropic flux-line pinning. As examples, we investigate the critical states of long strips and rectangular platelets of high-Tc superconductors with pinning either by the ab-planes or by extended defects aligned with the c-axis.Comment: 13 pages including 13 figure files in the tex

Meissner-London currents in superconductors with rectangular cross section

Exact analytic solutions are presented for the magnetic moment and screening currents in the Meissner state of superconductor strips with rectangular cross section in a perpendicular magnetic field and/or with transport current. The extension to finite London penetration is achieved by an elegant numerical method which works also for disks. The surface current in the specimen corners diverges as l^(-1/3) where l is the distance from the corner. This enhancement reduces the barrier for vortex penetration and should increase the nonlinear Meissner effect in d-wave superconductors

Turbulent channel flow of dense suspensions of neutrally-buoyant spheres

Dense particle suspensions are widely encountered in many applications and in environmental flows. While many previous studies investigate their rheological properties in laminar flows, little is known on the behaviour of these suspensions in the turbulent/inertial regime. The present study aims to fill this gap by investigating the turbulent flow of a Newtonian fluid laden with solid neutrally-buoyant spheres at relatively high volume fractions in a plane channel. Direct Numerical Simulation are performed in the range of volume fractions Phi=0-0.2 with an Immersed Boundary Method used to account for the dispersed phase. The results show that the mean velocity profiles are significantly altered by the presence of a solid phase with a decrease of the von Karman constant in the log-law. The overall drag is found to increase with the volume fraction, more than one would expect just considering the increase of the system viscosity due to the presence of the particles. At the highest volume fraction here investigated, Phi=0.2, the velocity fluctuation intensities and the Reynolds shear stress are found to decrease. The analysis of the mean momentum balance shows that the particle-induced stresses govern the dynamics at high Phi and are the main responsible of the overall drag increase. In the dense limit, we therefore find a decrease of the turbulence activity and a growth of the particle induced stress, where the latter dominates for the Reynolds numbers considered here.Comment: Journal of Fluid Mechanics, 201

Analytic Solution for the Critical State in Superconducting Elliptic Films

A thin superconductor platelet with elliptic shape in a perpendicular magnetic field is considered. Using a method originally applied to circular disks, we obtain an approximate analytic solution for the two-dimensional critical state of this ellipse. In the limits of the circular disk and the long strip this solution is exact, i.e. the current density is constant in the region penetrated by flux. For ellipses with arbitrary axis ratio the obtained current density is constant to typically 0.001, and the magnetic moment deviates by less than 0.001 from the exact value. This analytic solution is thus very accurate. In increasing applied magnetic field, the penetrating flux fronts are approximately concentric ellipses whose axis ratio b/a < 1 decreases and shrinks to zero when the flux front reaches the center, the long axis staying finite in the fully penetrated state. Analytic expressions for these axes, the sheet current, the magnetic moment, and the perpendicular magnetic field are presented and discussed. This solution applies also to superconductors with anisotropic critical current if the anisotropy has a particular, rather realistic form.Comment: Revtex file and 13 postscript figures, gives 10 pages of text with figures built i

Charge profile in vortices

The electric charge density in the vortex lattice of superconductors is studied within the Ginzburg-Landau theory. We show that the electrostatic potential $\phi$ is proportional to the GL function, $\phi\propto|\psi|^2-|\psi_\infty|^2$. Numerical results for the triangular vortex lattice are presented.Comment: 4 pages with 2 figure

Properties of the Ideal Ginzburg-Landau Vortex Lattice

The magnetization curves M(H) for ideal type-II superconductors and the maximum, minimum, and saddle point magnetic fields of the vortex lattice are calculated from Ginzburg-Landau theory for the entire ranges of applied magnetic fields Hc1 <= H < Hc2 or inductions 0 <= B < Hc2 and Ginzburg-Landau parameters sqrt(1/2) <= kappa <= 1000. Results for the triangular and square flux-line lattices are compared with the results of the circular cell approximation. The exact magnetic field B(x,y) and magnetization M(H, kappa) are compared with often used approximate expressions, some of which deviate considerably or have limited validity. Useful limiting expressions and analytical interpolation formulas are presented.Comment: 11 pages, 8 figure