On the Possibility of Controlling the Second Harmonic Radiation of the Free Electron Laser Using the Second Harmonic of the Undulator Field

The Influence of Increased Electron Energy Spread on the Radiation of the Second Harmonic in Free Electron Lasers

“…The values from ( 16) exceed the measurements for most FELs by an order of magnitude, so we suggested in [82] a correction factor of Θ ~0.01, which restored the agreement with most measured FEL data. Huang also estimated the second harmonic saturated power [69], which reasonably agreed with reported experimental data; we reformulated the result of Huang in terms of the Fresnel number Γ = 4πσ 2 x,y /Nλ u λ 1 in [58]. In this form, we get an explicit account for the radiation wavelength λ, the undulator length Nλ u , the beam section σ x,y and the bunching values b 1,2 as follows:…”

“…In what follows, we perform an analytical study of the generation and radiation of FEL harmonics with the goal to find a way to reduce even FEL harmonics on the axis and maintain the fundamental at the same time. It has been recently proposed in [58] to use a bi-harmonic undulator with a second harmonic of the undulator field to regulate the radiation of the second FEL harmonic. In [58], it was analytically shown that a second field harmonic with an amplitude ~10% of the main undulator field and opposite to its phase reduces the power of the second FEL harmonic by an order of magnitude.…”

“…It has been recently proposed in [58] to use a bi-harmonic undulator with a second harmonic of the undulator field to regulate the radiation of the second FEL harmonic. In [58], it was analytically shown that a second field harmonic with an amplitude ~10% of the main undulator field and opposite to its phase reduces the power of the second FEL harmonic by an order of magnitude. Studies were conducted for the third field harmonic and its influence on the radiation of the third UR and FEL harmonics.…”