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17Complex Systems of Charged Particles and their Interactions with Electromagnetic Radiation 2018
TO THE PROBLEM OF ELECTROMAGNETIC FIELD ENERGY IN THE MEDIUM
OUTSIDE THE TRANSPARENCY DOMAIN
1 2 S.A. Trigger , A.G.Zagorodny
1 Joint Institute for High Temperatures, Russian Academy of Sciences, Moscow 2 Bogolyubov Institute for Theoretical Physics of the National Academy of Sciences of Ukraine,
Kiev
e-mails: satron@mail.ru; azagorodny@bitp.kiev.ua
The problem of calculation of electromagnetic energy outside the transparency domain is discussed. It is shown that charged particle contribution to the energy of electromagnetic perturbations in the general case can be described in terms of bilinear combination of the dielectric polarization of the medium. The explicit form of such contribution is found. The relations obtained are used to generalize the Planck's formula and Kirchhoffs law to the case of absorptive medium. The purpose of the present contribution is to derive general relation for the energy of electromagnetic perturbation in the medium with temporal and spatial dispersion outside the transparency domain. We use the idea proposed in [1], namely we treat the energy of perturbation as a sum of the electromagnetic energy and the particle energy (both kinetic and potential) which particles acquire in the field. Obtained relations are applied to calculate the fluctuation field energy and to generalize the Planck formula for the case of non-transparent medium with spatial and temporal dispersion. Here, it is necessary to note that quantum field approach was proposed in [2, 3] in order to obtain such generalization. The comparison of the results is also between the goals of the present work. We also use the photon Green function expression for calculation of the equilibrium fluctuations for the vector potential and further for the electric field and magnetic induction. We also underline that the classical approach used for the polarization functions of particles which we use in this work can be generalized for the quantum plasma [4,5]. For the transparent medium we arrive at the generalized Planck distribution [6] if we extract the zero oscillations in the form depending on the particle density.
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