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

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, (kappa), H, m ((kappa) is the GL-parameter, m is the total vorticity of the system). The edgesuppressed 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.