Foundations of Meissner superconductor magnet mechanismus engineering

Abstract

It has long been known that a repulsive force arises between a magnetic field (generated, for instance, by a permanent magnet PM) and a superconductor –Sc (Arkadiev, 1947). This force is due to the repulsion of the magnetic field away from the superconductor – the Meissner effect. Type I superconductors only can be in the Meissner state, which means that a magnetic field will be always expelled from the superconductor, independently of its poles orientation. Nevertheless, type II superconductors may be in two different states: first, provided the magnetic field is low enough, they are at a Meissner state similar to type I superconductors. In this Meissner state they absolutely expel the magnetic field and prevalent repulsive forces appear. Second, for magnetic fields larger than the so-called First Critical Field HC1, the magnetic flux penetrates the superconductor creating a magnetization which contributes to an attractive resulting force. This second state is known as mixed state. In 1953 Simon first tried to make a superconducting bearing (Simon, 1953) using superconductors in the mixed state.The first engine using a superconducting bearing was made in 1958 (Buchhold, 1960). After the discovery of high critical temperature superconductors (Bednorz & Muller, 1986), the Meissner repulsive force has become a popular way of demonstrating superconducting properties (Early et al., 1988).For calculating forces between a magnet and a superconductor it is necessary to have models that describe both the flux penetration state and the Meissner state repulsion. The first one can be solved by using conventional methods to compute forces between magnetic elements and magnetized volumes. However, for the Meissner state the question has remained open until these last years. Several models using the method of images to calculate superconducting repulsion forces (Lin, 2006; Yang & Zheng, 2007) have been proposed. However, this method of images is limited to a few geometrical configurations that can be solved exactly, and the physical interpretation of the method is under discussion (Giaro et al., 1990; Perez-Diaz & GarciaPrada, 2007). Furthermore, some discrepancies within experiments still exist (Hull, 2000). A general local model based on London’s and Maxwell’s equations has been developed to describe the mechanics of the superconductor-permanent magnet system (Perez-Diaz et al., 2008). Due to its differential form, this expression can be easily implemented in a finite elements analysis (FEA) and is consequently appliable to any shape of superconductor in pure Meissner state (Diez-Jimenez et al. 2010).