Modeling of Vortex Paths in HTS

Abstract

A random walk model of the vortex paths in high temperature superconductors is investigated for different relative densities of -axis, -plane and point pinning defects. The model suggests an origin for some of the more unusual features seen in the field angle dependence of the critical current. It also predicts greater noise in critical currents for fields parallel to the plane of the dominant pinning defects and anomalous behavior of -values. The random walk model also suggests an alternative form for the expected field angle dependence of the upper critical fields in disordered layered superconductors.

Maximum Entropy Distributions Describing Critical Currents in Superconductors

“…It is difficult to foresee how a deterministic model would ever predict a J c peak which is not aligned with the direction of correlated pinning, but this comes quite naturally from Equation (3b). Further examples of the use of these equations to explain J c () from complex pinning structures are given in [7][8][9][10]26,27]. Table 1.…”

“…In earlier publications we derived Equations (3) by directly modeling the shape of the vortex path as a directed random walk [7,8]. That is for a peak centered in the y-direction, we modeled an arbitrarily chosen vortex as a finite set of m steps in the y-direction, giving say,…”

“…The weakness of a direct statistical model of the vortex such as described in [7,8] is it is difficult to understand how or if the model should be altered to take into account oblique defects or other additional forms of disorder. The maximum entropy approach relieves us of this burden as we can properly argue that if our distributions, derived from moments of z y / , accurately describe the data then adding further information to the model is unnecessary.…”

“…That is, there is no reliable methodology to sum the effects of all the defects distributed throughout a material in order to find p F  . We have shown previously [7][8][9][10] how by adopting a maximum entropy approach we can model J c while avoiding the need to construct a model of p F  . Although we do not solve the pinning summation problem in the sense of making direct predictions of the magnitude of J c we do gain insight into how nature averages over all defects and interactions and what information is available from any experiment.…”

The Vortex Path Model Analysis of the Field Angle Dependence of the Critical Current Density in Nanocomposite YBa2Cu3 O 7−x – BaZrO3 Films Obtained by Low Fluorine Chemical Solution Deposition

“…It has been demonstrated that BZO nanoparticle inclusions are able to create a more isotropic J c (θ ) profile [16]. In this paper, we investigate the role of the BZO nanoinclusions on the J c (θ ) dependencies by interpreting the respective data within the framework of the vortex path model [17][18][19]. In this statistical mechanical approach, the J c (θ ) curves may be decomposed into a set of distinct contributions that may be traced back to the particular microstructural features of the sample.…”