Characterisation of microbunching instability with 2D Fourier analysis

Abstract

The optimal performance of high-brightness free-electron lasers (FELs) is limited by the microbunching instability, which can cause variations in both the slice energy spread and longitudinal profile of electron beams. In this paper, we perform 2D Fourier analysis of the full bunch longitudinal phase space, such that modulations in both planes can be studied simultaneously. Unlike the standard 1D analysis, this method is able to reveal modulations in a folded phase space, which would otherwise remain uncovered. Additionally, the plasma oscillation between energy and density modulations is also revealed by this method. The damping of the microbunching instability, through the use of a laser heater, is also analysed with this technique. We confirm a mitigation of the amplitude of modulation and a red-shift of the microbunching frequency as the energy spread added increases. As an outcome of this work, a systematic experimental comparison of the development of the instability in the presence of different compression schemes is here presented for the first time.

Microbunching instability characterization via temporally modulated laser pulses

“…II), the LSC forces within the bunch can cause a plasma oscillation between microbunching in energy and longitudinal density over a sufficiently long distance. This manifests itself as a rotation of the microbunches in longitudinal phase space [35]. This process of rotation is further enhanced by bunch compression, which causes a shearing in the phase space.…”

“…Previous experimental studies of the microbunching instability have analysed the structure along the longitudinal plane of the bunch [2]; here, we use the procedure introduced in Ref. [35] to analyse the bunching in both time and energy. An example of the significance of the second of these parameters is in a freeelectron laser: if there are discrete energy bands in an electron bunch upon its entrance to the undulator, this may result in the generation of multicolour photon pulses.…”

“…where N is the number of particles, and k and m describe, respectively, the frequency modulation in the temporal and energy planes [35].…”

“…Through the use of 2D Fourier analysis, it is possible to measure the bunching factor along both axes of the longitudinal phase space simultaneously. This method has the added benefit of providing a measurement of the plasma oscillation phase of the microbunches as they transition between energy and den-sity modulations [35]. The variation in modulation frequency and bunching factor as a function of laser heater energy can be quantified by analysing the 2D Fourier transform of the longitudinal phase space.…”

“…In this paper we study the effect of imposing such a modulated laser pulse on the electron beam in the Fermi laser heater for three bunch compression scenarios, and for a range of laser pulse modulation frequencies and laser pulse energies. By analysis of the full longitudinal phase space, rather than only the current density, a more detailed picture of the microbunching instability can be obtained, as the evolution of the microbunching instability through the oscillation between energy and density modulations can be investigated in full [35].…”