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2015-10-05 Presentation at the International Symposium “Mathematics of XXI Century & Natural Science, St. Petersburg, September 29 – October 3, 2015 21 P. The main object for analysis of chaos in radiation of charged particles moving in non-one-dimensional periodical structures is Volume Free Electron Laser (VFEL). It is one of different types of vacuum electronic devices. The main principle of VFEL operation is the radiation of bunches of charged particles moving through the slow-wave structure (resonator) with simultaneous fulfillment of synchronism and diffraction conditions. Due to diffraction some strong coupled electromagnetic waves appear in the system. Multi-wave volume distributed feedback provides coupling between electromagnetic field and particles and is the main origin of
chaotic oscillations here. VFEL principles are valid for all wavelength ranges regardless the spontaneous radiation mechanism. The VFEL resonator should be a non-one-dimensional periodical structure -- either natural crystal for X-ray range or artificial photonic crystal for other wave-length from optical till THz ranges.
Mathematical model, numerical methods as well as physical features of VFEL operation obtained numerically
are considered in this work.
Different types of VFEL chaotic dynamics and their explanation are given. Particular attention is paid to the effect of suppressing parasitic modes of electromagnetic waves in VFEL that is one of its main physical characteristics. Download:
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