On the determination of the parameters that describe a quasistatic electromagnetic field in an electrically conducting shell

Abstract

We state the initial equations and the boundary conditions for determining the parameters that describe a quasistatic electromagnetic field perturbed by the action of external electric currents in a thin nonferromagnetic shell.Consider a thin electrically conducting shell of constant thickness 2h in a region D in which there is no charge or current. The shell is situated in a dielectric medium Do (which we assume to be approximately a vacuum) and subject to the action of a quasistatic electromagnetic field. The field is generated by a system of quasistatic currents flowing in Do (an inductor of time-varying intensity), given by the expressionwhere r is the radius-vector of the point, w is the cyclic frequency, t is time, r is the initial phase, and jA(r, t) j(t)j~r) is the amplitude, which varies only slightly over the period of an electromagnetic wave, f. = 2pi/w, so that the following condition holds:We pose the problem of determining the parameters that describe the electromagnetic field under such an action in the shell-external medium system. We recall that finding these parameters is the first step in computing the thermoelastic state of electrically conducting shells perturbed by an electromagnetic field [1].We shall start from Maxwell's equations for the external medium (a vacuum) and a solid isotropic nonferromagnetic nonpolarized motionless body with constant (averaged over a temperature interval) material characteristics and neglecting the displacement currents [5]. We write the following system of independent equations with complex current density j. = j(t)Re{j(r)ei~t}, electric field intensities E. = j(t)Re {E(r)ei~t}, E (~ = j(t)Re {E(~ and magnetic field intensities H. = j(~)Re {H(r)e~t}, H(. ~ = j(t)Re//(~ in the region D of the body and Do of the surrounding medium, taking account of relations (1) and (2) Here jg~ = f(r)e ~o is the complex amplitude of the given current density in the surrounding medium; E, H, E (~ and H (~ are the complex amplitudes of the intensities of the electric and magnetic fields in the regions D and D O respectively; ~ = eo~., and # = #0#.~o, and #o are the dielectric permittivity and magnetic permeability of the body and the magnetic permeability of the vacuum; a is the electrical conductivity of the body.Equations (3) must be supplemented by the independent coupling conditions of the characteristics of the electromagnetic field at the interface between the body and the surrounding medium:

Mathematical models of thermomechanics of magnetizable and polarizable electrically conducting bodies subject to quasisteady electromagnetic radiation

“…Then the original relations for the quantitative description of the characteristics of the electromagnetic, thermal, and mechanical processes are formulated in two stages. At the first stage the equations for the characteristics of the electromagnetic radiation are written in the quasisteady approximation [8,10,30], as well as the expressions for heat emission and force factors in terms of these characteristics. At the second stage problems of thermomechanics for determining the thermostressed state are stated [10,34,46,47].…”