Chaotic electron motion caused by sidebands in free electron lasers

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Abstract
The electron dynamics in a free electron laser (FEL) is studied in the case when the radiation field contains many modes. This situation arises when unstable modes (sidebands) are excited during operation. It is observed that when the strength of these sidebands exceeds certain levels the electron motion becomes chaotic. This may lead to extensive particle detrapping and loss of amplification for the FEL signal. The threshold for the onset of stochastic electron motion is computed. The evolution of the trapped electron distribution exhibits a diffusive behavior. The rate of particle detrapping is parametrized by the diffusion coefficient D in action space. The e‐folding length for the number of trapped electrons is parametrized by J2s/D, where Js is the action at the separatrix. It is found that the diffusion rates are related to the type of the sideband spectrum. The diffusion coefficient is always proportional to the ratio of the sideband power in all frequencies to the power of the carrier signal. The coefficient of the proportionality, however, scales differently on the FEL parameters for each of the three spectral categories: a narrow, a broad discrete, and a broad continuous spectrum. The diffusion coefficient is computed analytically for the last two cases and is in good agreement with numerical results. The narrow spectrum yields the highest and the broad continuous the lowest diffusion rates under constant sideband power. It is also found that, in all cases, the diffusion length, measured in wiggler periods, is independent of the electron energy γ.