G.B. Itigilov1, D.Sh. Shirapov2, V.A. Kravchenko3

1–3 East Siberia State University of Technology and Management (Ulan-Ude, Russia)

1 gablz@mail.ru, 2 shir48@mail.ru, 3 krawyach@mail.ru

It is known that the electrical conductivity of ferrite is not zero, therefore, in gyrotropic waveguides, depending on the filling material, there may be significant heat losses affecting the main parameters of the waveguides, as well as the characteristics of electromagnetic waves propagating in them. The effect of heat loss in gyrotropic waveguides should be investigated. To carry out such studies, it is necessary to have partial Helmholtz equations of hybrid NON- and NON-electromagnetic waves for gyrotropic waveguides with specific cross-sectional shapes (rectangular, circular and elliptical) at certain magnetizations (longitudinal, normal and tangential) taking into account heat losses. Then determine the boundary conditions for the partial Helmholtz equations, followed by the formulation of the corresponding boundary value problem and its solution. The objective of this article is to draw consistent conclusions: 1) generalized Helmholtz equations of hybrid NON- and EH-electromagnetic waves for gyrotropic waveguides with orthogonally curved cross-section shapes under arbitrary magnetization, taking into account thermal losses; 2) general Helmholtz equations of hybrid NON- and EH-electromagnetic waves for gyrotropic waveguides with orthogonally curved cross-section shapes under longitudinal magnetization, taking into account thermal losses; 3) partial Helmholtz equations of hybrid NON- and EH-electromagnetic waves for gyrotropic longitudinally magnetized waveguides with rectangular, round and elliptical cross-sections, taking into account heat losses.

To solve this problem, generalized Helmholtz equations of hybrid NON- and EH-waves for gyrotropic waveguides with orthogonally curved cross-section shapes with arbitrary magnetization are obtained from a system of Maxwell differential equations containing tensor magnetic and complex dielectric permittivity using tensor analysis apparatus, taking into account heat losses, from which the general Helmholtz equations of hybrid NON- and EH-waves are sequentially derived.- and EH- waves for gyrotropic waveguides with orthogonally curved cross-section shapes under longitudinal magnetization and Helmholtz partial equations of hybrid NON- and EH-electromagnetic waves for gyrotropic longitudinally magnetized waveguides with rectangular, round and elliptical cross-section shapes, taking into account heat losses.

Itigilov G.B., Shirapov D.Sh., Kravchenko V.A. Generalized, general and particular equations of gyrotropic waveguide Helmholtz taking into account heat losses. Radiotekhnika. 2023. V. 87. № 12. P. 137−148. DOI: https://doi.org/10.18127/j00338486-202312-15 (In Russian)

1. Artemov M.L., Afanas'ev O.V., Slichenko M.P. Napravlenie sovershenstvovanija harakteristik perspektivnyh antennyh system. Radiotehnika. 2023. T. 86. № 5. S. 184-198. DOI: https://doi.org/10.18127/j00338486-202305-19. (in Russian).
2. Mikajeljan A.L. Teorija i primenenie ferritov na sverhvysokih chastotah. L.: Gosjenergoizdat. 1963. 664 s. (in Russian).
3. Gurevich A.G., Melkov G.A. Magnitnye kolebanija i volny. M.: Fizmatlit. 1994. 464 s. (in Russian).
4. Ustinov A., Kochemasov V., Has'janova E. Ferritovye materialy dlja ustrojstv SVCh-jelektroniki. Osnovnye kriterii vybora. SVCh-jelektronika. 2015. № 8. S. 86-92 (in Russian).
5. Laks B., Batton K. Sverhvysochastotnye ferrity i ferrimagnetiki. M.: Mir. 1965. 676 s. (in Russian).
6. Raevskij S.B., Sedakov A.Ju., Titarenko A.A. Metod jelektrodinamicheskogo rascheta prjamougol'nyh zakrytyh volnovodov s proizvol'nym anizotropnym zapolneniem. Fizika volnovyh processov i radiotehnicheskie sistemy. 2012. T. 15. № 3. S. 14-21 (in Russian).
7. Vajnshtejn L.A. Jelektromagnitnye volny. M.: Radio i svjaz'. 1988. 440 s. (in Russian).
8. Vinogradova M.B., Rudenko O.V., Suhorukov A.P. Teorija voln. Moskva: Lenand. 2019. 432 s. (in Russian).
9. Ango A. Matematika dlja jelektro- i radioinzhenerov. M.: Nauka. 1967. 780 s. (in Russian).
10. Korn G., Korn T. Spravochnik po matematike dlja nauchnyh rabotnikov i inzhenerov. M.: Nauka. 1973. 832 s. (in Russian).
11. Nikol'skij V.V. Jelektrodinamika i rasprostranenie radiovoln. M.: Nauka. 1973. 607 s. (in Russian).
12. Shirapov D.Sh., Itigilov G.B. Obobshhennye uravnenija Gel'mgol'ca girotropnyh volnovodov proizvol'noj formy poperechnogo sechenija. Materialy II Vseross. nauch. konf. «Sovremennye problemy distancionnogo zondirovanija, radiolokacii, rasprostranenija i difrakcii voln» (g. Murom. 26-28 ijunja 2018 g.). S. 209-219 (in Russian).