Critical current anisotropy in high temperature superconductors

After nearly 15 years of research effort, High Temperature Superconductors (HTS) are finding a wide range of practical applications. A clear understanding of the factors controlling the current carrying capacity of these materials is a prerequisite to their successful technological development. The critical current density (Jc) in HTS is directly dependent on the structure and pinning of the Flux Line Lattice (FLL) in these materials. This thesis presents an investigation of the Jc anisotropy in HTS. The use of thin films grown on off c-axis (vicinal) substrates allowed the effect of current directions outside the cuprate planes to be studied. With this experimental geometry Berghuis, et al. (Phys. Rev. Lett. 79, 12, pg. 2332) observed a striking flux channelling effect in vicinal YBa2Cu3O7-δ (YBCO) films. By confirming, and extending, this observation, it is demonstrated that this is an intrinsic effect. The results obtained, appear to fit well with the predictions of a field angle dependent cross-over from a three dimensional rectilinear FLL to a kinked lattice of strings and pancakes. The pinning force density for movement of strings inside the cuprate planes is considerably less than that on vortex pancake elements. When the FLL is entirely string-like this reduced pinning leads to the observed channelling minima. It is observed that anti-phase boundaries enhance the Jc in vicinal YBCO films by strongly pinning vortex strings. The effect on the FLL structure cross-over of increasing anisotropy has been elucidated using de-oxygenated vicinal YBCO films. Intriguingly, the counter intuitive prediction that the range of applied field angle for which the kinked lattice is fully developed reduces with increasing anisotropy, appears to be confirmed. Although vortex channelling cannot be observed in c-axis YBCO films, the pinning force density for vortex string channelling has been extracted by observing string dragging. By studying the effect of rotating the applied field at a constant angle to the cuprate planes, it is possible to observe the cross-over into the string pancake regime in c-axis films. In the 3D region, the observed behaviour is well explained by the anisotropic Ginzburg-Landau model. Measurements were also made on thin films of the much more anisotropic Bi 2Sr2CaCu2O8+x material, grown on vicinal substrates. The absence of any flux channelling effect and clear adherence to the expected Kes-Law behaviour in the observed Jc characteristics does not provide evidence for the existence of the predicted ‘crossing lattice’ in Bi 2Sr2CaCu2O8+x .

Global modes with multiple saddle points

Significant progress has been made towards understanding the global stability of slowly-developing shear flows. The WKBJ theory developed by Patrick Huerre and his co-authors has proved absolutely central, with the result that both the linear and the nonlinear stability of a wide range of flows can now be understood in terms of their local absolute/convective instability properties. In many situations, the local absolute frequency possesses a single dominant saddle point in complex X-space (where X is the slow streamwise coordinate of the base flow), which then acts as a single wavemaker driving the entire global linear dynamics. In this paper we consider the more complicated case in which multiple saddles may act as the wavemaker for different values of some control parameter. We derive a frequency selection criterion in the general case, which is then validated against numerical results for the linearized third-order Ginzburg-Landau equation (which possesses two saddle points). We believe that this theory may be relevant to a number of flows, including the boundary layer on a rotating disk and the eccentric Taylor-Couette-Poiseuille flow. © 2014 Elsevier Masson SAS. All rights reserved.