Microbunching-instability-induced sidebands in a seeded free-electron laser

Measurements of the multishot-averaged, soft x-ray, self-seeding spectrum at the LCLS free-electron laser often have a pedestal-like distribution around the seeded wavelength, which limits the spectral purity and can negatively affect some user applications not employing a post-undulator monochromator. In this paper, we study the origins of such pedestals, focusing on longitudinal phase space modulations produced by the microbunching instability upstream of the free-electron laser (FEL) undulator. We show from theory and numerical simulation that both energy and density modulations can induce sidebands in a high-gain, seeded FEL whose fractional strength typically grows as the square of the undulator length. The results place a tight constraint on the longitudinal phase space uniformity of the electron beam for a seeded FEL, possibly requiring the amplitude of long-wavelength modulations to be much smaller than the typical incoherent energy spread if the output sideband power is to remain only a couple percent or less of the amplified seed power.

Figure 1

The total normalized field amplitude $a$ and bunching factor $b_1$ along the undulator for various energy modulation amplitudes $\widehat{A}$. The modulation wavelength is $8\mu \mathrm{m}$, corresponding to $|\mathrm{\Delta }\nu /2\rho |\approx 0.16$ The inset displays the same quantities on a logarithm scale.

Figure 2

Spectra along the undulator length to illustrate the growth of the sideband power. The spectra are normalized by the amplified seed intensity $a_1(\widehat{z})$ and the spectral unit is photon energy ($\mathrm{\Delta }E=\hslash {\omega }_s$). The electron beam energy modulation wavelength is $8\mu \mathrm{m}$ while the normalized modulation amplitude $\widehat{A}=0.13$.

Figure 3

The predicted power ratio of the lower sideband to the seed along the undulator for different energy modulation amplitudes in 1D simulations (squares). The energy modulation wavelength is $8\mu \mathrm{m}$ and the corresponding $\mathrm{\Delta }\nu /2\rho =-0.16$. All dashed lines are theory predictions from Eq. (25).

Figure 4

The power ratio of the lower (top) and upper (middle) sidebands, and their sum (bottom) to the amplified seed along the undulator for different detunings (electron beam energy modulation wavelengths) according to 1D numerical simulations (solid lines). All dashed lines are the theory predictions of Eq. (24). The initial normalized energy modulation amplitude is $\widehat{A}=0.13$.

Figure 5

The power ratio of the lower sideband to the amplified seed along the undulator for different modulation amplitude as predicted in 3D Genesis simulations. The inset plots the power ratio versus the square of the undulator length.