The effect of eletric currents on superconductivity

Louisiana State University, Baton Rouge LA

Investigators

Abstract

This grant supports the research program of the Principal Investigator on mathematical models of superconductivity and the behavior of the solutions of these models. Superconductors are metals that at a sufficiently low temperature exhibit two important properties: they lose entirely their electrical resistivity, and the magnetic field is excluded from the superconducting area. Superconductors have great technological potential for applications ranging from magnetic sensors, through generators of large magnetic fields, to high power transmitters. Even for low temperatures, a sufficiently strong electric current would revert the superconductor to the state of a normal metal. The Principal Investigator will study the transition of superconducting materials from the normal state to the superconducting one and vice versa, with either increasing or decreasing current. Of particular interest is the disparity between experimental measurements of the critical current and theoretical predictions of the critical current in the absence of magnetic fields, and the maximal amount of current that can flow through a sample before the superconducting state loses its stability. The project will shed light on both the nucleation of superconductivity for decreasing currents and on the loss of superconducting properties when the electric current increases. The results are expected to have an effect on other areas of Applied Mathematics, such as hydrodynamic stability, magnetic resonance imaging, and more. The research will address the Ginzburg-Landau model of superconductivity in the presence of electric currents. The Principal Investigator will study several fundamental theoretical problems related to this model. Most of the project will involve analytical work to be performed by the investigator and his collaborators. The following problems will be studied: (1) the existence and stability of fully superconducting solutions away from the boundary, which is adjacent in part to a normal material from which the current enters and exits the superconducting sample, and solutions will be studied both in the presence and in the absence of a magnetic field, (2) analysis of the behavior of solutions with decreasing current density below the critical current where the normal state loses its stability, (3) generalization of some recent results on the local and global stability of the normal state in the presence of strong electric currents, both in the presence and the absence of magnetic fields.