SIMULATION OF THE PROPAGATION OF A PLANE ELECTROMAGNETIC WAVE IN AN INHOMOGENEOUS NONABSORBING MEDIUM
DOI:
https://doi.org/10.20998/2079-0023.2023.02.08Keywords:
electron beam, magnetron gun, electron dynamics, motion direction transformation, gradient magnetic field, control, mathematical modelingAbstract
Analytical solutions of the Ishimaru's parabolic equation for the coherence function of the electromagnetic field, which describe the temporal properties of the pulse at the output of a heterogeneous non-dissipative medium, are considered. A generalization of the approach used in the Ishimaru model to describe the time evolution of a monochromatic electromagnetic pulse enveloping in homogeneous non-dissipative media is obtained for the case of non-homogeneous non-dissipative media. Thus, an attempt was made to take into account the influence of the heterogeneity of the medium on the shape of the resulting pulse. When solving the given problem, the difficulties associated with the calculation of the continuous integral arising in the space of diffusion trajectories were overcome. This made it possible to obtain an explicit expression for the Green's function of the task and to build a computational algorithm based on which a number of numerous experiments were conducted. The analysis of the work was carried out based on the apparatus of quadratic integral functionals based on the solutions of differential stochastic equations. In the paper, the invariant temporal properties of the envelope of monochromatic electromagnetic pulses recorded after passing through a flat layer of a scattering heterogeneous medium, i.e., properties that remain unchanged when the parameters of the medium vary, in particular, the distribution of the concentration of scattering centers. The dynamics of the formation of time plumes of the scattered wave, in which the tail part is located in the peripheral time area, were analyzed. When propagating at the speed of transformation of the wave front, it reflects the appearance of the layers of the scattering region and its longitudinal shape. It is noted that the development of the proposed approximation approach to the processes affecting the time delay of electromagnetic pulses can be the accounting for the attenuation of radiation during its propagation in an inhomogeneous absorbing medium.
References
Ishimaru A. Theory and Application of Wave Propagation and Scattering in Random Media. Proc. IEEE. 1977, vol. 65, pp. 1030–1061.
Ishimaru A. Rasprostranenie i rassejanie voln v sluchayno-neodnorodnych sredah. [Propagation and scattering of waves in randomly inhomogeneous media]. Moscow, Myr Publ., 1981, vol. 1, 280 p.; vol. 2. 317 p.
Flatte S. M. Wave Propagation Through Random Media: Contributions from Ocean Acoustics. Proc. IEEE. 1983, vol. 71, pp. 1267–1294.
Rytov S. M., Kravzov Yu. A., Tatarskiy V. I. Vvedenie v stohasticheskuyu fiziku [Introduction to statistical radiophysics]. Moscow, Nauka Publ., 1966. 404 p.
Helstrom K. Quantovaya teoriya proverki gypotez i ocenivaniya [Quantum theory of hypothesis testing and estimation]. Moscow, Мyr Publ., 1979. 344 p.
Feller V. Vvedenie v teoriyu veroyatnostey i eje prilogeniya [Introduction to Probability Theory and Its Applications]. Moscow, Мyr Publ.,1979. 640 p.
Kolmogorov A. N., Fomin S. V. Elementy teorii funkciy I funkcional'nogo analiza [Elements of the theory of functions and functional analysis]. Moscow, Nauka Publ., 2004. 356 p.
Galuza А. А., Mazmanishvili A. S. Forma impul`sa, rasprostranyayutschegosja c neodnorodnoy nepoglotschayutschey srede [Shape of a pulse propagating in a non-uniform non-absorbing medium]. Radiofizika i Radioastronomiya [Radiophysics and Radio Astronomy]. 1997, vol. 2, pp. 353–358.
Kolmogorov A. N., Fomin S. V. Elementy teorii funkciy i funkcional'nogo analiza [Elements of the theory of functions and functional analysis]. Moscow, Nauka Publ., 2004. 356 p.
Virchenko N. O. Osnovni methoody rozv`yazannya zadach mathematychnoyi fyzyky [Basic methods of solving mathematical physics problems]. Kyiv, Volya Publ., 2006. 332 p.
Pirs Jh. P. Тeoriya i raschet elektronnykh potokov [Theory and calculation of electron currents]. Moscow, Sov. Radio Publ., 1956. 254 p.
Andrunyk V. A., Vysoc`ka V.A., Pasychnyk V. V. Chysel`ny metody v komp`yuternyh naukah [Numerical methods in computer science]. Lviv, Novyi svit-2000 Publ., 2018. 536 p.
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