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Application of dispersion relations to the problem of calculating the radiation field of a particle moving along a helical trajectory in a multilayer cylindrical waveguide.
M.I, Ivanyan 1*, B. A. Grigoryan1, A. H. Grigoryan1,2, K. Floettmann3, L. Anjo1, L. V. Aslyan1, M. Z. Karalyan1, V.G. Khachatryan1
1CANDLE Synchrotron Radiation Institute, 31 Acharyan Street, Yerevan, Armenia, 0040
2Yerevan State University, 1 Alex Manoogyan Street, Yerevan, Armenia, 0025,
3Deutsches Elektronen-Synchrotron DESY, Notkestraße 85, 22607 Hamburg, Germany
A new approach to solving the problem of the radiation field of a particle moving along a helical trajectory in a cylindrical waveguide with a multilayer wall is proposed. The solution for forced electromagnetic oscillations (caused by charges and currents generated by the particle's motion) in the waveguide's interior is represented as a superposition of elementary solutions of inhomogeneous Helmholtz equations containing uncertain transverse eigenvalues. The latter are determined from the dispersion relations for the same elementary inhomogeneous modes of the multilayer waveguide. As a result, frequency distributions of the expansion weight coefficients for an arbitrary mode are determined, each characterized by pronounced resonances describing forward and backward radiation, respectively.
One advantage of the resulting solution is the ability to fill the waveguide's interior with an arbitrary dispersive medium (e.g., plasma), which may expand the scope of application of the structure. Another advantage is the visual form of the solution, which represents the direct transformation of the charge’s own field under the influence of the multilayer structure surrounding the charge’s trajectory.
Keywords: multilayer waveguide, helical motion, dispersion relations, Helmholtz equation, forced oscillations
The work was supported by the Science Committee of RA, in the frame of the research project № 25RG-1C177.