Mathematical model of shielding monochromatic electromagnetic fields by means of plane screens made of permalloy

A method for solving a boundary-value problem of penetration of plane monochromatic electromagnetic fields through the plane screen made of permalloy is developed. Setting the boundary-value problem is based on the use of differential Maxwell equations and complementary nonlinear differential equation for the field of magnetization, characterizing permalloy. The classical boundary conditions of continuity of the tangential components of the fields and complementary boundary conditions for the field of magnetization on the front surfaces of the screen are used. To simplify the solution of the boundary-value problem as a result of exclusion of the values of the second infinitesimal order, included in nonlinear equation, the nonlinear task is transformed into linear one. The roots (wave numbers) of dispersion algebraic equation of a fourth-order, characterizing the electromagnetic fields in the layer made of permalloy, are constructed. A complete system of four forward and four backward counter-propagating electromagnetic waves in the permalloy layer is formed. The two-sided boundary conditions connecting electromagnetic fields on both sides of the screen are obtained. An analytical solution of the boundary-value problem with two-sided boundary conditions is performed. The amplitudes of reflected and transmitted through the screen electromagnetic fields are analytically calculated.

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