Critical state problems which incorporate more than one component for the magnetization vector of hard superconductors are investigated. The theory is based on the minimization of a cost functional ${\cal C}[\vec{H}(\vec{x})]$ which weighs the changes of the magnetic field vector within the sample. We show that Bean's simplest prescription of choosing the correct sign for the critical current density $J_c$ in one dimensional problems is just a particular case of finding the components of the vector $\vec{J}_c$. $\vec{J}_c$ is determined by minimizing ${\cal C}$ under the constraint $\vec{J}\in\Delta (\vec{H},\vec{x})$, with $\Delta$ a bounded set. Upon the selection of different sets $\Delta$ we discuss existing crossed field measurements and predict new observable features. It is shown that a complex behavior in the magnetization curves may be controlled by a single external parameter, i.e.: the maximum value of the applied magnetic field $H_m$.Comment: 10 pages, 9 figures, accepted in Phys. Rev.

Coarse-grained flux density profiles in type-II superconductors with nonparallel vortex configurations are obtained by a proposed phenomenological least action principle. We introduce a functional C[ H] which is minimized under a constraint of the kind J ∈ ∆( H, x), where ∆ is a bounded set.In particular, we choose the isotropic case | J | ≤ J c (H), for which the field penetration profiles H( x, t) are derived when a changing external excitation is applied. Faraday's law, and the principle of minimum entropy production rate for stationary thermodynamic processes dictate the evolution of the system.Calculations based on the model can reproduce the physical phenomena of flux transport and consumption, and the striking effect of magnetization collapse in crossed field measurements. PACS number(s): 41.20. Gz,74.60.Jg, 74.60.Ge, 02.30.Xx Typeset using REVT E X 1

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A comparison of several solution syntheses with a solid-state route to the lead-containing high Tc phase of the B i -S r -C a -C u -0 system has been performed using DSC, TGA, x-ray diffraction, electron microscopy, magnetic ac susceptibility, and critical-current measurements. A novel polymer solution synthesis route is shown to yield an increased percentage of the 2223 high Tc phase when sintering is performed at the low temperature end of this phase's stability range. Under the best preparative conditions given in the literature, however, the properties of samples obtained with the different synthetic methods described in the present study are shown to be similar. Samples derived from solution syntheses have been found to contain higher amounts of carbon precipitates, while samples derived from conventional solid-state synthesis contain CuO precipitates, according to energy dispersive spectroscopy analyses.

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