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We show here how the application of the critical state model allows one to determine the magnetic flux density B in each point of a superconducting cylinder with an arbitrary cross section subjected to axial magnetic fields Hz; the B = 0 boundaries of the regions occupied by the vortices are so defined. We successively consider the cases where the critical current density Jc is either isotropic (constant or an arbitrary function of B) or tensorial, which means, for our problem, the use of two components Jcx and Jcy (either constant or depending on B but Jcx/Jcy remaining constant).

Investigations of the mechanics of metal fibres capable of carrying very high currents are presented. The role played by the Laplace force is emphasized. This force appears whenever a fibre carrying a current is subjected to a magnetic field whose direction is different from that of the fibre. The role played by the coefficient of friction is also taken into account. An exact non-linear differential equation is used to describe the problem, i.e. no assumptions are made about the magnitudes of the deflections. When the normal force exerted on the track by the fibre is an increasing function of the Laplace force, it is found that the maximum stress within the fibre has a non-linear dependence on the Laplace force. When the same normal force is a decreasing function of the Laplace force, it is shown that the normal force vanishes for a critical value of the Laplace force. A perturbation method is used to explain the behaviour of the fibre.

Via a cellular model of the mixed state we study the spreading of a vortex normal to a superconducting boundary. For any value of the induction in the superconductor we derive the expressions of the magnetic microscopic field near the surface and of the extra energy added by the boundary. This energy could be responsible for a decrease inHc2, but our calculations show that this is unlikely to occur except for very thin films.

Resume Le deplacement des vortex engendre un champ electrique qui, agissant sur les electrons normaux, provoque des pertes. A l'aide d'un modele nous calculons les pertes relatives a l'exterieur du coeur des vortex.

The concept of a flux jump is now well known and several authors1–4 have reported experimental results on values of H fj (the lowest magnetic field for which a flux jump can occur). Theoretical calculations, using various hypotheses about the orders of magnitude of D th and D m (thermal and magnetic diffusivities) were also made4–7 and gave rather similar expressions for H fj.