Spectrum Phase and Constraints on THz-Optical klystron

Abstract

Optical klystrons provide an efficient mechanism for enhancing coherent radiation through laser-induced microbunching and dispersive amplification. In the terahertz (THz) regime and at low beam energy, however, the radiation wavelength becomes comparable to the characteristic wavelengths of longitudinal space-charge (LSC) and coherent synchrotron radiation (CSR) driven microbunching. In this work, we analyze the impact of electron-beam microbunching on the spectral amplitude and phase of a seeded optical klystron operating in the THz regime. Using a phase-space formalism, incoherent energy modulations generated by collective effects are shown to enter the bunching spectrum as a stochastic longitudinal phase, producing local wavenumber jitter and spectral broadening. An explicit connection between the microbunching-induced energy modulation and LSC/CSR gain is established for low-energy beams, demonstrating that the overlap between collective-effect wavelengths and the optical-klystron radiation wavelength leads to strong spectral phase distortion. These effects impose fundamental constraints on the achievable harmonic bunching and spectral purity and stability of THz optical klystrons and must be considered in the design and optimization of next-generation low-energy THz FEL facilities.

Figures (6)

• Figure 1: Microbunching gain at the exit of the beamline section upstream of the dispersive element.
• Figure 2: The calculated relative energy modulation $p(k_{\mu})$ due to microbunching instability at the modulator exit
• Figure 3: Normalized seed-induced energy modulation amplitude $A=\Delta E/E$ as a function of the seed laser power for three seed wavelengths, $\lambda = 100~\mu$m, $50~\mu$m, and $10~\mu$m, calculated using the DALI beam parameters in eq.(\ref{['eq:seed_energy_modulation']}). Longer seed wavelengths lead to a stronger energy modulation at a given seed power. Calculations are performed for a beam energy $E_{0}=50$ MeV ($\gamma_{0}\simeq98.9$), rms energy spread $\sigma_{E}=100$ keV, undulator length $L_{u}=1$ m with $N_{u}=10$ periods, and rms transverse seed beam size $\sigma_{r}=2$ mm.
• Figure 4: Fundamental bunching amplitude as a function of the normalized seed-induced energy modulation $A$. The blue solid curve corresponds to the ideal case without microbunching instability (MBI), calculated using Eq. (\ref{['eq:ok_bunching_factor']}), while the red dashed curve includes the effect of MBI-induced energy spread according to Eq. (\ref{['eq:ok_bunching_factorMBI']}). The presence of MBI leads to a systematic reduction of the achievable bunching amplitude over the entire parameter range.
• Figure 5: Excess rms spectral bandwidth $\Delta\sigma_k$ induced by microbunching instability as a function of the normalized seed-induced energy modulation amplitude $A$. The quantity $\Delta\sigma_k$ is obtained from the second term of Eq. (\ref{['eq:sigk_OK_simple']}) and represents the contribution beyond the transform-limited bandwidth set by the electron bunch length.