Resumen
One hundred years ago Meissner discovered that, in the presence of a magnetic field, superconductors create a current that induces a magnetic field directly opposite the applied field. This effect is now being used with high temperature superconductors to levitate trains (maglev), to screen magnetic fields in medical instruments and in many other applications. It is then particularly important to understand how such a material reacts to an external magnetic field.
The basic unit of magnetic flux is the magnetic vortex, it has a typical size $10^{-6} m$. These vortices are described by the Ginzburg-Landau equations for the vector potential and the superconducting density. I will show how Maxwell’s equations can be coupled with these equations leading to a Maxwell-Ginzburg-Landau model. In particular we considered how a magnetic pulse scatters on a superconducting layer inducing vortices inside it.
The above description is correct for small samples ($10^{-4} m$). When the sample is larger, there are too many vortices and a macroscopic approach is necessary. It involves Maxwell’s equations and a phenomenological constitutive equation $E(J)$ relating the current density $J$ to the electric field $E$. This equation involves the critical current density $J_c$ which depends on the magnetic field $B$ and the temperature $T$. We will analyze mathematically this model which consists in a nonlinear convection-diffusion equation for $B$ coupled to a diffusion equation for $T$.
Actividad presencial con transmisión a través de Zoom.
Inscripción previa: https://shorturl.at/jq1Ak
Informes:
luis.lopez@aries.iimas.unam.mx
calleja@mym.iimas.unam.mx
Ponente:
Dr. Jean-Guy Caputo, Institut national des sciences appliquées de Rouen, France