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Transition Effects of THz Helical Undulator Radiation in a Waveguide

“…For this reason, its frequency distribution is characterized by sharp peaks at frequencies determined by equation 𝑓𝑓(𝑗𝑗 𝑛𝑛𝑛𝑛 ) = 0. Thus, the resonant frequencies remain the same as in the stationary motion of a particle in an infinite waveguide [7]. Obtained formula (31) describes narrow-directed and narrow-band radiation.…”

“…Except for works [2,3], to date, the focus has been on the cases of stationary helical motion of a particle in infinite rectangular [4][5][6] and circular waveguides [1,[7][8][9][10][11]. Meanwhile, there is an injection process in real undulators, i.e., the introduction of a bunch into an undulator, which is equivalent to the gradual appearance of bunch particles in an undulator.…”

“…The integrand of 𝑋𝑋 𝑁𝑁 (0) (𝑡𝑡) is an analytic function on the entire complex plane 𝑗𝑗 and, with the exception of points 𝑗𝑗 = 𝑗𝑗 1 and 𝑗𝑗 = 𝑗𝑗 2 , corresponding to two simple poles lying on the real axis. Its value (in the sense of the principal value) is determined by the residues of these poles in the usual way [7]. The integrand of 𝑋𝑋 𝑁𝑁 (1) (𝑡𝑡) has the same poles, but it is not an analytic function.…”