Modeling and multidimensional optimization of a tapered free electron laser

Abstract

Energy extraction efficiency of a free electron laser (FEL) can be greatly increased using a tapered undulator and self-seeding. However, the extraction rate is limited by various effects that eventually lead to saturation of the peak intensity and power. To better understand these effects, we develop a model extending the Kroll-Morton-Rosenbluth, one-dimensional theory to include the physics of diffraction, optical guiding, and radially resolved particle trapping. The predictions of the model agree well with that of the GENESIS single-frequency numerical simulations. In particular, we discuss the evolution of the electron-radiation interaction along the tapered undulator and show that the decreasing of refractive guiding is the major cause of the efficiency reduction, particle detrapping, and then saturation of the radiation power. With this understanding, we develop a multidimensional optimization scheme based on GENESIS simulations to increase the energy extraction efficiency via an improved taper profile and variation in electron beam radius. We present optimization results for hard x-ray tapered FELs, and the dependence of the maximum extractable radiation power on various parameters of the initial electron beam, radiation field, and the undulator system. We also study the effect of the sideband growth in a tapered FEL. Such growth induces increased particle detrapping and thus decreased refractive guiding that together strongly limit the overall energy extraction efficiency.

Terawatt x-ray free-electron-laser optimization by transverse electron distribution shaping

“…More recent work has shown that seeding or self-seeding an FEL amplifier leads to much larger output power [11]. In light of these promising results many recent efforts have been devoted to optimize the tapered section of a self-seeded X-FEL to reach power levels of one TW or larger [12].…”

Sideband instability analysis based on a one-dimensional high-gain free electron laser model

“…Here we only consider the K-tapering and assume λ u is constant. The maximized energy extraction roughly corresponds to a quadratic taper profile along the undulator axis, i.e., ΔK=K ∝ z 2 [4,5,7]. In the beam rest frame, the near-resonant electrons are trapped in the so-called ponderomotive potential well, in which these electrons execute a synchrotron motion around a synchronous particle.…”

“…Though undulator tapering had been proposed since the 1980s, recently there has been a renewed interest in tapering to achieve enhanced energy conversion efficiency, improved spectral purity, or for polarization control (see, for example, Refs. [4][5][6][7][8][9]). With undulator tapering, the efficiency can be improved and the power can be further increased in the postsaturation regime (however, at a lower rate compared with the exponential growth in the linear regime) but eventually will reach a so-called second saturation and the radiation then approaches another equilibrium.…”

Few-femtosecond time-resolved measurements of X-ray free-electron lasers

“…This requirement is at least one order of magnitude higher than achievable at existing FEL facilities. Tapering the undulator strength after FEL saturation is a well-known method for achieving higher FEL power (see, for example, refs [45][46][47]. The FEL resonant wavelength is l r ¼ l u ð1 þ K 2 =2Þ=2g 2 , where l u is the undulator period, K is the normalized undulator strength parameter and g is the electron energy in units of the rest energy mc 2 .…”