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Language: 
Russian
Heading: 
Innovations in applied physics
Article type: 
Article
UDC: 
530.182
DOI: 
10.18500/0869-6632-003103
EDN: 
MXUNCA

Spectral approach with iterative clarification of a radiation boundary conditions for modeling of quasimodes of a gyrotrons open cavities

Autors: 
Rozhnev Andrej Georgievich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Melnikova Marija Mihajlovna, Saratov State University
Ryskin Nikita Mikhailovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Abstract: 

Purpose. The article presents a new method for numerical simulation of quasi-eigenmode oscillations in open resonators of gyrotrons — powerful vacuum generators of electromagnetic waves in the millimeter and submillimeter ranges. The gyrotron cavity has the shape of a weakly inhomogeneous hollow circular metal waveguide.

Methods. The proposed approach uses the inhomogeneous string equation with radiation boundary conditions to formulate a nonlinear spectral boundary value problem describing oscillations in a resonator, neglecting the couplings of waves with different radial indices. By linearizing with respect to frequency the radiation boundary conditions, the boundary value problem is reduced to a linear boundary value problem. To discretize this boundary value problem, the finite difference method is used and a linear generalized matrix eigenvalue problem is formulated. This problem is solved by the Arnoldi method with eigenvalues calculation in a shift-invert mode. An iterative algorithm is proposed that makes it possible to sequentially calculate a given number of frequencies and quality factors of quasi-eigenmodes of oscillations.

Results. The computer program was developed written in the Wolfram Language and Fortran using the algorithms proposed in the work. The results of test calculations for real gyrotron resonators are presented, which demonstrate the high accuracy of the obtained values of frequencies, quality factors and field distributions of quasi-eigenmode oscillations in the studied resonators.

Conclusion. The methods, algorithms and created program proposed in the article can significantly facilitate the process of developing gyrotrons intended for various practical applications and operating in new frequency ranges. The method of iterative refinement of boundary conditions can be generalized to the case of equations of the linear theory of a gyrotron and used to develop new methods for analyzing the starting conditions for the soft self-excitation in gyrotrons — generators.

Key words: 
Gyrotron
open cavity
high order axial modes
radiation boundary condition
finite difference method
generalized matrix eigenvalue problem
Arnoldi method
Acknowledgments: 
This study was performed within the framework of a state order to the Kotelnikov Institute of Radio Engineering and Electronics of the Russian Academy of Sciences
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Received: 
30.11.2023
Accepted: 
25.12.2023
Available online: 
10.04.2024
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