Modeling cryo-magnets
Jean-Guy Caputo  1, 2@  , Ionut Danaila  3, *@  , Cyril Tain  4, *@  
1 : Laboratoire de Mathematiques
Université de Rouen - Normandie et INSA de Rouen - Normandie
76801 Saint-Etienne du Rouvray -  France
2 : Laboratoire de Mathématiques de lÍNSA de Rouen Normandie
Institut national des sciences appliquées Rouen Normandie : EA3226, Normandie Université, Institut National des Sciences Appliquées
685 Avenue de lÚniversité, BP 8, 76801 Saint-Étienne-du-Rouvray Cedex -  France
3 : Laboratoire Raphaël Salem
Université de Rouen - Normandie et INSA de Rouen - Normandie
Avenue de l'Université, BP.12 76801 Saint-Étienne-du-Rouvray, France -  France
4 : Laboratoire de Mathématiques Raphaël Salem
Université de Rouen Normandie, Normandie Université, Centre National de la Recherche Scientifique : UMR6085
Avenue de lúniversité BP 12 76801 Saint-Étienne-du-Rouvray -  France
* : Corresponding author

Cryomagnets can be made by applying a pulse of magnetic field to cooled bulk superconductors, resulting in a "trapped field" that can reach several teslas. These easily transportable devices could be used in many applications, in particular magnetic levitation and motors.
We analyze the theoretical models proposed; these are based on Maxwell's equations and a constitutive equation which is usually Bean-Kim. In particular, we show that they cannot yield amplitude dependant effects and this is contrary to the experimental observations of "giant flux jumps". A solution to this is to couple directly Maxwell's equations to the Ginzburg-Landau free energy and derive a Maxwell-Ginzburg-Landau Lagrangian for the vector potential and the order parameter. We discuss this new model and present 1D and 2D simulations.

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