Phenomenological theory of the local magnetic field in type-II superconductors

It is demonstrated that: 1. Within the framework of the Ginzburg-Landau theory, the procedure of obtaining the local magnetic field by a linear superposition of contributions of individual flux lines is valid for arbitrary kappa and flux-line spacings, provided these contributions are calculated using the correct spatially-dependent magnitude of the order parameter that is appropriate for the given flux-line spacing. 2. The field contribution of an individual flux line can be approximated with a simple model involving two parameters, a core radius parameter which is of the order of the Ginzburg-Landau coherence length and a field-dependent penetration depth which reduces to the weak-field penetration depth at low average flux density B, increases with increasing B, and diverges at the upper critical field. 3. This model gives a good semi-quantitative overall description of the neutron diffraction form factors and the corresponding magnetic field distribution in Nb at 4.2K. (Auth.)