Mathematical model of penetration of cylindrical electromagnetic fields with axial symmetry through the plane screen from permalloy

Abstract

The method for solving the boundary-value problem of penetration of monochromatic electromagnetic fields with axial symmetry through the plane screen made from the permalloy is developed. The boundary-value problem is based on the use of differential Maxwell equations and complementary nonlinear differential equation for the field of magnetization, characterizing the permalloy. Classical boundary conditions of continuity of the tangential components of the fields and complementary boundary conditions for the field of magnetization on the face surfaces of the shield are used. For solution simplification of the boundary-value problem as a result of exclusion value the entering in nonlinear equation second-order infinitesimal, nonlinear task is transformed into linear task. Roots (wave numbers) of a dispersion algebraic equations of four order, which characterizing electromagnetic fields with axial symmetry in layer made from the permalloy, is constructed. The sequences of four forward and four backward counter-propagating electromagnetic waves with axial symmetry in the layer of permalloy is formed. Two-sided boundary conditions connecting electromagnetic fields with axial symmetry on both sides of the screen is constructed. The amplitudes of reflected and transient through the shield electromagnetic fields are calculated.