Abstract
When an untapered high-gain free electron laser (FEL) reaches saturation, the exponential growth ceases and the radiation power starts to oscillate about an equilibrium. The FEL radiation power or efficiency can be increased by undulator tapering. For a high-gain tapered FEL, although the power is enhanced after the first saturation, it is known that there is a so-called second saturation where the FEL power growth stops even with a tapered undulator system. The sideband instability is one of the primary reasons leading to this second saturation. In this paper, we provide a quantitative analysis on how the gradient of undulator tapering can mitigate the sideband growth. The study is carried out semianalytically and compared with one-dimensional numerical simulations. The physical parameters are taken from Linac Coherent Light Source-like electron bunch and undulator systems. The sideband field gain and the evolution of the radiation spectra for different gradients of undulator tapering are examined. It is found that a strong undulator tapering ($\ensuremath{\sim}10%$) provides effective suppression of the sideband instability in the postsaturation regime.
Highlights
It is known that a free electron laser (FEL) is capable of generating coherent high-power radiation over a broad spectrum
In this paper we followed Refs. [23,24] to study the FEL sideband effects based on similar parameters to those of the operating Linac Coherent Light Source (LCLS) X-ray FEL and have investigated the dependence of the sideband instability growth rate on the undulator tapering
We derived the sideband dispersion equation based on 1-D high-gain tapered FEL model in the post-saturation regime, and further examined the approximate expressions for the maximum sideband growth rate
Summary
It is known that a free electron laser (FEL) is capable of generating coherent high-power radiation over a broad spectrum. The stability analyses are usually treated by single-particle or kinetic methods Both approaches may assume small perturbations of electron synchrotron motion and radiation fields from the equilibria. While they may provide practical use to quickly estimate whether the sideband instability will be an issue, most of the previous work assumes constant-parameter undulators [4,10,11], focuses on longer wavelength regime [12,14,15], or addresses oscillator configurations [16,17]. Lindberg [18] and Zhang et al [19] have theoretically investigated the FEL sideband instability induced by initial beam modulations, in which their studies focus on a mechanism in the linear or exponential regime with a constant undulator parameter.
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