Onset of Superconductivity and Hysteresis in Magnetic Field for a Long Cylinder as Obtained from a Self-Consistent Solution of the Ginzburg–Landau Equations

Abstract

Based on the self-consistent solution of a nonlinear system of one-dimensional GL-equations, the onset and destruction of superconductivity, the phase transitions and hysteresis phenomena are discussed for a cylinder (radius R) in the axial magnetic field (H) for arbitrary R, κ, H, m (κ is the GL-parameter, m is the total vorticity of the system). The edge-suppressed solutions (which correspond to the jumps of the magnetization in the states with fixed vorticity m), the depressed solutions (which are responsible for the hysteresis in type-II superconductors), and the precursor solutions (which describe the onset of superconductivity in type-I superconductors) are also studied. The limits of applicability of the linear equation approximation are discussed.