, , Helmholtz equations of electromagnetic waves in hyperbolic the magnetized gyrotropic elliptic wave guides // BSU bulletin. Mathematics, Informatics. - 2016. №2. . - С. 85-90.

Helmholtz equations of electromagnetic waves in hyperbolic the magnetized gyrotropic elliptic wave guides

The generalized equations of Helmholtz of electromagnetic waves in the regular wave guides with orthogonal forms of a transverse section filled with the magnetized ferrite (the gyrotropic environment) are received. One of two cases of cross magnetization of ferrite when the direction distribution of elec- tromagnetic wave and the direction of the outside magnetizing constant mag- netic field are perpendicular is considered, namely – normal magnetization. A mathematical basis is the modified method of invariant conversions allowing to realize easily transition to any regular wave guide with the rectilinear and cur- vilinear orthogonal form of a transverse section: rectangular, round, elliptic. On the basis of the received expressions Helmholtz equations for the least probed gyrotropic elliptic wave guides for the first time are removed in case of normal (hyperbolic) magnetization. The provided Helmholtz equations allow to deliver and solve a boundary value problem of an elliptic wave guide in case of hyperbolic magnetization with further receiving the dispersing equation.

the arbitrary magnetization, tensor of magnetic conductivity of

ferrite, cross components of an electromagnetic wave, coefficients of Lame, symbols of Christoffel.

проницаемости феррита, поперечные компоненты электромагнитной волны, коэффициенты Ламэ, символы Кристоффеля.

ferrite, cross components of an electromagnetic wave, coefficients of Lame, symbols of Christoffel.

проницаемости феррита, поперечные компоненты электромагнитной волны, коэффициенты Ламэ, символы Кристоффеля.

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2. Gurevich A. G., Melkov G. A. Magnetic of fluctuation and waves. — M.: Fizmatlit, 1994. — 464 s.

3. Rajevski S. B., Sedakov A. Yu., Titarenko A. A. Electrodynamic method of calculating the rectangular closed waveguides with arbitrary anisotropic filling // Physics of wave processes and radio engineering systems. — 2012. — T. 15, No. 3. — S. 14 – 21.

4. Itigilov G. B. Mathematical model operation of propagation of electromagnetic waves in restricted gyrotropic areas of the arbitrary form // Disserta- tion for the degree of candidate of technical sciences. — Buryat State Univer- sity. — Ulan-Ude, 2014. — 146 p.

5. Neganov V. A., Nefedov E. I., Yarovoi G. P. Modern methods of designing of lines of transfers and resonators microwave and optical frequencies. — M.: Pedagogika-Press, 1998. — 328 s.