Vector magnetic hysteresis of hard superconductors

Details Vector magnetic hysteresis of hard superconductors Vector magnetic hysteresis of hard superconductors

2001-12-15

arxiv.org/abs/cond-mat/0112284v1

Physics

Condensed Matter

Superconductivity

10 pages, 9 figures, accepted in Phys. Rev. B

Scientific paper

10.1103/PhysRevB.65.104514

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 $H_m$.

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