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

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

Finiteness of 2D Topological BF-Theory with Matter Coupling

We study the ultraviolet and the infrared behavior of 2D topological BF-Theory coupled to vector and scalar fields. This model is equivalent to 2D gravity coupled to topological matter. Using techniques of the algebraic renormalization program we show that this model is anomaly free and ultraviolet as well as infrared finite at all orders of perturbation theory.Comment: 17 pages, Late

Etching of High Purity Zinc

A method of etching high purity zinc to reveal various etch figures on {101¯0} planes is presented in this paper. Etch figures are formed by polishing in a dichromic acid solution after the introduction of mercury to the crystal surface. No measurable aging time is required to form etch figures at newly formed dislocation sites when mercury is on the surface prior to deformation. The mercury concentrates at the sites where etch figures form and may be removed by vacuum distillation and chemical polishing before it appreciably affects the purity of the bulk of the crystal

Transition (LINER/HII) nuclei as evolved Composite (Seyfert 2/Starburst) nuclei

We compare the circumnuclear stellar population and environmental properies of Seyfert and Composite (Seyfert + Starburst) nuclei with those of LINERs and LINER/HII transition galaxies (TOs), and discuss evidences for evolution from Seyfert/Composite to LINER/TO nuclei.Comment: 2 pages, 1 figure; to appear in the Proceedings of IAU Symp. No. 222: The Interplay among Black Holes, Stars and ISM in Galactic Nuclei, CUP, eds. T. Storchi-Bergmann, L. Ho and H. R. Schmit

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

Dislocations and etch figures in high purity zinc

A method of etching high purity zinc single crystals to reveal various etch figures on {1010} planes is presented in the preceding paper. The procedure involves the introduction of mercury to the crystal surface prior to a chemical polish with dichromic acid. The mercury was found to be concentrated at the etch figures. This paper presents the results of several experiments which support the conclusion that there exists a one-to-one correspondence between etch figures and dislocations. Some observations of slip on (0001) basal planes and {1212} pyramidal planes, and of twinning in zinc are also presented

The structure of the graviton self-energy at finite temperature

We study the graviton self-energy function in a general gauge, using a hard thermal loop expansion which includes terms proportional to T^4, T^2 and log(T). We verify explicitly the gauge independence of the leading T^4 term and obtain a compact expression for the sub-leading T^2 contribution. It is shown that the logarithmic term has the same structure as the ultraviolet pole part of the T=0 self-energy function. We argue that the gauge-dependent part of the T^2 contribution is effectively canceled in the dispersion relations of the graviton plasma, and present the solutions of these equations.Comment: 27 pages, 6 figure