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ISSN Печать: 0040-2508
ISSN Онлайн: 1943-6009
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Renormalized Resonant Conditions for a Hybrid Weakly-Relativistic Waveguide Free-Electron Laser
Краткое описание
We propose an analytical technique of twofold perturbation expansion to solve the nonlinear equations of motion of weakly-relativistic electrons moving in the magnetostatic pump field of a hybrid planar free-electron laser and apply it to obtain linear corrections to the electron trajectories caused by interaction with given propagating modes of a circular waveguide. In the nonlinear part of the problem, existing trajectory resonances are studied and their accessibility is numerically investigated. In a single-particle approximation the conditions of the most efficient interaction between an electron beam and propagating modes of a circular waveguide (resonant conditions) are derived analytically using small-signal theory in the microwave field. These conditions contain 'renormalization' multipliers, which are responsible for enforcement of energy conservation conditions if the microwave field is neglected.