15,352 research outputs found
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
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
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
Absolute value preconditioning for symmetric indefinite linear systems
We introduce a novel strategy for constructing symmetric positive definite
(SPD) preconditioners for linear systems with symmetric indefinite matrices.
The strategy, called absolute value preconditioning, is motivated by the
observation that the preconditioned minimal residual method with the inverse of
the absolute value of the matrix as a preconditioner converges to the exact
solution of the system in at most two steps. Neither the exact absolute value
of the matrix nor its exact inverse are computationally feasible to construct
in general. However, we provide a practical example of an SPD preconditioner
that is based on the suggested approach. In this example we consider a model
problem with a shifted discrete negative Laplacian, and suggest a geometric
multigrid (MG) preconditioner, where the inverse of the matrix absolute value
appears only on the coarse grid, while operations on finer grids are based on
the Laplacian. Our numerical tests demonstrate practical effectiveness of the
new MG preconditioner, which leads to a robust iterative scheme with minimalist
memory requirements
Motion of Vacancies in a Pinned Vortex Lattice: Origin of the Hall Anomaly
Physical arguments are presented to show that the Hall anomaly is an effect
of the vortex many-body correlation rather than that of an individual vortex.
Quantitatively, the characteristic energy scale in the problem, the vortex
vacancy formation energy, is obtained for thin films. At low temperatures a
scaling relation between the Hall and longitudinal resistivities is found, with
the power depending on sample details. Near the superconducting transition
temperature and for small magnetic fields the Hall conductivity is found to be
proportional to the inverse of the magnetic field and to the quadratic of the
difference between the measured and the transition temperatures.Comment: minor change
An effective lowest Landau level treatment of demagnetization in superconducting mesoscopic disks
Demagnetization, which is inherently present in the magnetic response of
small finite-size superconductors, can be accounted for by an effective
within a two-dimensional lowest Landau level approximation of the
Ginzburg-Landau functional. We show this by comparing the equilibrium
magnetization of superconducting mesoscopic disks obtained from the numerical
solution of the three-dimensional Ginzburg-Landau equations with that obtained
in the ``effective'' LLL approximation.Comment: 5 pages, 4 figures, submitted to Phys. Rev.
A model for the interaction of high-energy particles in straight and bent crystals implemented in Geant4
A model for the simulation of orientational effects in straight and bent
periodic atomic structures is presented. The continuum potential approximation
has been adopted.The model allows the manipulation of particle trajectories by
means of straight and bent crystals and the scaling of the cross sections of
hadronic and electromagnetic processes for channeled particles. Based on such a
model, an extension of the Geant4 toolkit has been developed. The code has been
validated against data from channeling experiments carried out at CERN
Symmetry of the remanent state flux distribution in superconducting thin strips: Probing the critical state
The critical-state in a thin strip of YBaCuO is studied by magneto-optical
imaging. The distribution of magnetic flux density is shown to have a specific
symmetry in the remanent state after a large applied field. The symmetry was
predicted [PRL 82, 2947 (1999)] for any Jc(B), and is therefore suggested as a
simple tool to verify the applicability of the critical-state model. At large
temperatures we find deviations from this symmetry, which demonstrates
departure from the critical-state behavior. The observed deviations can be
attributed to an explicit coordinate dependence of since both a surface
barrier, and flux creep would break the symmetry in a different way.Comment: 5 pages including 5 eps figures, submitted to PR
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