A kinetic small signal gain analysis of a planar wiggler FEL, operating in the high harmonic (strong wiggler) regime

E. Jerby*, A. Gover

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


A kinetic linear analysis of a strong planar wiggler FEL operating at the fundamental or odd harmonic frequencies is presented in this paper. The gain dispersion equation in the high harmonic regime is shown to be an extension of the known general FEL equation, and converges to it in the weak pump limit. In the low gain, cold, tenuous beam regime we get the known gain expression with the Bessel function correction term. A similar term also appears in the gain expression of the high gain strong pump limit. When space charge effects are significant (Raman regime), the strong pump gain dispersion relation is more complicated than the corresponding weak pump relation. In the cold beam limit it leads to a quintic polynomial dispersion relation instead of the known cubic equation. This brings about gain curve dependences on the detuning parameter which are double humped and with a relatively high bandwidth. The higher the order of the harmonic frequency, the stronger is the effect of the axial velocity spread on the gain and the tighter are the beam acceptance parameters. The analytical model permits an arbitrary axial velocity distribution. The gain damping effect is computed, both with a simple model of a Gaussian electron velocity distribution and with a more accurate model, taking into account an analytical expression for the asymmetrical skewed velocity distribution produced by the combined finite emittance and energy spread effects.

Original languageEnglish
Pages (from-to)192-202
Number of pages11
JournalNuclear Instruments and Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors and Associated Equipment
Issue number1-2
StatePublished - 1 Sep 1986


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