Radial solutions for the Ginzburg-Landau equation with applied magnetic field

The purpose of this work is a systematic study of symmetric vortices for the Ginzburg-Landau model of superconductivity along a cylinder, with applied magnetic field parallel to its axis. The Ginzburg-Landau constant kappa of the material and the degree d of the vortex are fixed. For any given parameters (r) over bar (the radius of the cylinder) and h (the intensity of the applied magnetic field), one can find a symmetric vortex (Psi, A) which satisfies the boundary conditions Psi(\phiB (r) over bar)=e(idtheta) and curl(A)(\phiB (r) over bar)=he(3). It is then shown that symmetric vortices form a family depending continuously on two real parameters alpha and c which describe the behaviour at the center of the vortex. As the boundary conditions depend smoothly on those parameters, one can distinguish two main connected domains of vortices: the first one, defined by the boundary conditions Psi(\phiB (r) over bar)=e(idtheta) and \rA(r)\ (\phiB (r) over bar) < d, is a zone of stability where \Psi\ remains increasing; the second one, defined by the boundary conditions Psi(\phiB (r) over bar) =e(idtheta) and \rA(r)\(\phiB (r) over bar) > d, is a zone where some instability can occur. Attention is focused on the smooth branch of vortices which separates those two domains: it is indexed by the parameter a running from some L > 0 to + infinity, and the limit as alpha decreases to L corresponds to a Berger and Chen type vortex. (C) 2003 Elsevier Ltd. All rights reserved.