ANALYTICAL SOLUTION OF THE GINZBURG-LANDAU EQUATIONS FOR THE ABRIKOSOV VORTEX IN SUPERCONDUCTORS WITH AN ARBITRARY VALUE OF THE PARAMETER æ > 0.707

Until now, there is no exact analytical solution to the equations of the Ginzburg-Landau theory of superconductivity for any value of the parameter æ > 0.707, satisfying the boundary conditions for the Abrikosov vortex and the magnetic flux quantization condition, as well as the classical asymptotics (for the value æ >> 1) of the London and Abrikosov formulas. In this regard, the goal of this computational and analytical research was to find a satisfactorily accurate analytical solution to the equation of the Ginzburg-Landau theory for the Abrikosov vortex in superconductors with an arbitrary value æ > 0.707. By analytically solving the equations of the phenomenological theory of Ginzburg-Landau superconductivity for a single Abrikosov vortex in a massive type II superconductor with an arbitrary value of the parameter æ, we found: magnetic field strength h (ρ), current density j (ρ) and order parameter f (ρ), satisfying the boundary conditions, the quantization condition and the classical asymptotics of London and Abrikosov. The first critical magnetic field Hc1 and the ratio of absolute values Hc1/Hc2 in superconductors with æ > 0.707 are determined.