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

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

Three Dimensional Distorted Black Holes: Initial Data and Evolution

We present a new class of 3D black hole initial data sets for numerical relativity. These data sets go beyond the axisymmetric, ``gravity wave plus rotating black hole'' single black hole data sets by creating a dynamic, distorted hole with adjustable distortion parameters in 3D. These data sets extend our existing test beds for 3D numerical relativity, representing the late stages of binary black hole collisions resulting from on-axis collision or 3D spiralling coalescence, and should provide insight into the physics of such systems. We describe the construction of these sets, the properties for a number of example cases, and report on progress evolving them.Comment: 3 pages, 2 postscript figures, LaTeX, uses mprocl.sty (available at http://shemesh.fiz.huji.ac.il/MG8/submission.html) To appear in the proceedings of the Marcel Grossmann 8 (Jerusalem, 1997

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

Current density inhomogeneity throughout the thickness of superconducting films and its effect on their irreversible magnetic properties

We calculate the distribution of the current density $j$ in superconducting films along the direction of an external field applied perpendicular to the film plane. Our analysis reveals that in the presence of bulk pinning $j$ is inhomogeneous on a length scale of order the inter vortex distance. This inhomogeneity is significantly enhanced in the presence of surface pinning. We introduce new critical state model, which takes into account the current density variations throughout the film thickness, and show how these variations give rise to the experimentally observed thickness dependence of $$ and magnetic relaxation rate.Comment: RevTex, 9 PS figures. To appear in Phys. Rev.

Anisotropic superconducting strip in an oblique magnetic field

The critical state of a thin superconducting strip in an oblique applied magnetic field H_a is analyzed without any restrictions on the dependence of the critical current density j_c on the local magnetic induction {\bf B}. In such a strip, j_c is not constant across the thickness of the sample and differs from J_c/d, where J_c is the critical sheet current. It is shown that in contrast to the case of {\bf B}-independent j_c, the profiles H_z(x) of the magnetic-field component perpendicular to the strip plane generally depend on the in-plane component H_{ax} of the applied magnetic field H_a, and on how H_a is switched on. On the basis of this analysis, we explain how and under what conditions one can extract j_c({\bf B}) from the magnetic-field profiles H_z(x) measured by magneto-optical imaging or by Hall-sensor arrays at the upper surface of the strip.Comment: 7 pages with 4 figure

Hysteretic characteristics of a double stripline in the critical state

Analytical investigations of the critical state are carried out for a superconducting stripline consisting of two individual coplanar strips with an arbitrary distance between them. Two different cases are considered: a stripline with transport current and strips exposed to a perpendicular magnetic field. In the second case, the obtained solutions correspond to "fieldlike" (for unclosed strips) and "currentlike" (for a long rectangular superconducting loop) states in an isolated strip to which both a transport current and a magnetic field are applied with constant ratio.Comment: 8 pages, 6 figures. accepted by SS

Thermal one- and two-graviton Green's functions in the temporal gauge

The thermal one- and two-graviton Green's function are computed using a temporal gauge. In order to handle the extra poles which are present in the propagator, we employ an ambiguity-free technique in the imaginary-time formalism. For temperatures T high compared with the external momentum, we obtain the leading T^4 as well as the subleading T^2 and log(T) contributions to the graviton self-energy. The gauge fixing independence of the leading T^4 terms as well as the Ward identity relating the self-energy with the one-point function are explicitly verified. We also verify the 't Hooft identities for the subleading T^2 terms and show that the logarithmic part has the same structure as the residue of the ultraviolet pole of the zero temperature graviton self-energy. We explicitly compute the extra terms generated by the prescription poles and verify that they do not change the behavior of the leading and sub-leading contributions from the hard thermal loop region. We discuss the modification of the solutions of the dispersion relations in the graviton plasma induced by the subleading T^2 contributions.Comment: 17 pages, 5 figures. Revised version to be published in Phys. Rev.

Buckling instability in type-II superconductors with strong pinning

We predict a novel buckling instability in the critical state of thin type-II superconductors with strong pinning. This elastic instability appears in high perpendicular magnetic fields and may cause an almost periodic series of flux jumps visible in the magnetization curve. As an illustration we apply the obtained criteria to a long rectangular strip.Comment: Submitted to Phys. Rev. Let