Stability of a free-electron-laser spectrum in the continuous-beam limit

Abstract

A multifrequency model is developed for a Compton free-electron laser and is solved to investigate the continuous-electron-beam limit. Both numerical simulations and perturbation expansions allow us to exhibit a mechanism leading to the broadening of the spectrum. Then, the nonlinear asymptotic behavior of the spectrum is analyzed.PACS numbers: 42.55.Tb, 52.35.Mw One of the most challenging questions in freeelectron-laser (FEL) physics is related to the nonlinear evolution of the spectrum, including the sideband instability 1_3 and mode competition (MC). 4 New nonlinear effects can alter the further evolution of a FEL spectrum, especially in the asymptotic regime which corresponds to a large number of round trips for an oscillator. Of course, optical elements can select a single frequency, 5 but we are concerned here with the natural physical evolution of the spectrum in the absence of frequency discrimination. Moreover, we focus on the limit of a continuous electron beam, which means that finite-pulse issues, such as the natural Fourier spread or temporal overlap effects, are disregarded.In the continuous-beam limit (CBL), our numerical simulations exhibit the following essential property: Any spectral pattern, for instance, two frequencies with the same amplitude, can duplicate itself. We confirm this numerical prediction by expanding the multifrequency model with two different perturbation theories. Then, the nonlinear evolution of the spectrum is investigated by means of computer simulations. We observe some expected results, such as the transition between narrow and broad spectra depending upon the electronic current or the cavity losses. A more challenging numerical prediction in the saturation regime is a scaling law between the spectral width and the extracted efficiency.To investigate the FEL spectral dynamics, we use a specific model for the CBL which is appropriate for electronic pulses much longer than the slippage distance. 6 To work out this model, we expand the laser field A L as the product of rapid phases and slowly varying envelopes S"iz): S"(z)where k n =(\+n/N)kL is a wave number close to the central mode /cz, = 27rAz,. Each complex laser field S" J satisfies a paraxial equation: n/N)k H w z G n -^Q--a w e 2Kwhere a w and k w are the normalized amplitude and the wave number of the magnetic field. The longitudinal electronic distribution g(z,y/,y) satisfies the associated Vlasov equations:[3 z + v8 vr +r(8 y -l/y)]g(z,^y)-0, v-k w -(k L /2Y 2 Hl+ ja£) , F= J a w \m 2 &me(3) dy/J dyg(z,y/,y)mc=p e , 2TTNJOwhere p e is the electron number per unit of volume. The electron phase space is characterized x by the resonant phase y/^ikL + k^z -co L t and the kinetic energy y normalized to the electronic mass m. The variable y/ depends on the central frequency cot^ckL, but Eqs. (l)-(3) are invariant under the choice of co L when we consider the limit of the continuous Fourier expansion in , -i(\+n/N)y 2y(2)Eq. (1). Indeed, the phase (\+n/N)y/-(n/N)k w z, in Eqs. (2) and (3), is precisely the resonant ...

Two-frequency wiggler for better control of free-electron-laser dynamics

“…The code written for this purpose works in the continuous-beam limit from noise up to saturation. For a standard wiggler, simulations of that type have shown that a high-power FEL presents a large spectrum equilibrium with a relative width roughly equal to the extracted efficiency [3], A TFU can lead to large efficiencies despite complex electron trajectories which induce nontrivial modification in the sideband generation and, then, in the spectral evolution. To investigate this point, we have performed a systematic mapping in the (e a ,£f) plane for e/ ranging from 0 to 4% and e a from 0 to 30%.…”

“…Such devices require a simple phase-space structure [2] which is not consistent with a large-spectrum FEL. As high-power FEL's are characterized by strong spectral broadenings [3], adiabatic taperings may then become inefficient. To investigate a larger class of tapering function j8, we consider a first generalization provided by the possibility to introduce a second frequency in the wiggler magnetic field.…”

Jean-Luc Ferrer (1964–2020): structural biologist, beamline instrumentation innovator and entrepreneur

“…After obtaining a Diplô me d'Etudes Approfondies (DEA) in Physical Chemistry from Université Paris VI, Jean-Luc Ferrer undertook a doctoral thesis in physics on the dynamics of the spectrum of a free-electron laser at the Bruyè res-le-châ tel research centre of the CEA (Commissariat à l'Energie Atomique). This work enabled him to obtain a doctorate degree from Université Paris XI in 1990 (Iracane & Ferrer, 1991). At the end of the same year, Jean-Luc was recruited by the Direction des Science du Vivant (DSV) at the CEA in Grenoble and joined the Laboratoire de Cristallographie et Cristallogenè se des Proté ines (LCCP).…”

<title>Narrow high-power microwave pulses from a free-electron laser</title>

“…Furthermore, in the operation of a EEL oscillator, experiment [4] as well as numerical theory which carries the analysis well into the nonlinear regime [5], shows that the FEL can operate in a mode characterized by low efficiency together with a narrow spectrum, or in a mode that has higher efficiency and a wide spectrum. The latter has to do with the sideband instability [6] which has been observed experimentally [7,8] and which is also found in connection with superradiant spiking studies [9-13] since both [14] arise from slippage.…”