The magnetic field penetrates into these superconductors in the form of superconductive electron current vortices around the extremely thin. A nite element analysis of critical state models for type. Introduction to superconductivity, magnetooptical imaging. Superconductivity is a phenomenon in the solid state physics that occurs under a certain critical temperature often referred to as tc in some materials. In particular, the temperature dependence of the critical magnetic. A finiteelement analysis of criticalstate models for typeii. Scattering of electrons from the lattice atoms require a change of state of electron. On the bean criticalstate model in superconductivity cambridge. In fact, the superconducting state is now known to be a special quantum. In the superconductive state the current carrying species is the electron pair. Beans criticalstate model as a consequence of the circuit model of. There is a depletion of what we shall describe as the superconducting order parameter. Type ii superconductors, on the other hand, respond differently to an applied magnetic field, as shown in figure 5.
Bean in 1962, gives a macroscopic explanation of the irreversible magnetization behavior hysteresis of hard typeii superconductors. We will mostly focus on conventional superconductors, where the cooper pairs. This equation determines the value of the bound state energy e. For the cooper pair to scatter it would have to change its state like an electron in normal metal. On the bean criticalstate model in superconductivity bgu math. Solid state physics part iv superconducting properties. Pdf we show that the criticalstate problem in typeii superconductivity is equivalent to an evolutionary quasivariational inequality. Bean, a model for magnetic instabilities in hard superconductors. The specimen is in a vortex state between hc1 and hc2, but has super conducting electrical properties up to h c2. Especially we are interested in analyzing the situation where a bulk super. We explain the essential features of the theory of supercon ductivity with the.
Lecture notes on superconductivity a work in progress. However, till now, only beans critical state model is. An increasing field from zero results in two critical fields, bc1 and bc2. On the bean criticalstate model in superconductivity. Pdf on the bean criticalstate model in superconductivity. Most of the pure elements in figure 2 tend to be type i superconductors. Meissner e ect and the distinction between a perfect conductor and a super conductor an electric eld ein a normal conductor causes a curwhich, in a steady state, is related to the electric eld by the equation j. In this paper we propose a nite element method to analyze critical state problems for typeii super conductivity numerically. Introduction to the theory of superconductivity pdf 82p this note covers the following topics. Free superconductivity books download ebooks online. The fact that the resistance is zero has been demonstrated by sustaining currents in superconducting lead rings for many years.