2024 , Volume 29, № 4, p.24-40

The research addresses finding of the electromagnetic part for the problem of calculating the thickness and shape of a liquid film resulted from the floating zone melting of the silicon sample of large radius (5–10 cm) in a magnetic field. The applied approach relies on the analytical transformations of electromagnetic field equations and the method of complex amplitudes for description of harmonic oscillations in time of the sought values. The explicit analytical formulas have been obtained for calculating the vector potential of the magnetic field, its strength, electric current density, ponderomotive force and density of Joule heat sources for the case of axisymmetric formulation. The estimate of the film thickness is given and model calculations are performed for a simple film geometry and the discrete set of thickness values of the film. The method for determining the parameters of an electromagnetic field in a three-layer medium, namely, the air space between the inductor and the liquid film, the film itself, and the solid phase of the silicon sample, has been developed. The method allows performing calculations for a film thickness comparable to the thickness of the skin layer in a liquid phase.