Enhanced harmonic generation in terahertz FELs: influence of pre-bunching and undulator geometry on spectral and angular emission

Both theoretical and numerical analyses are conducted to investigate terahertz (THz) radiation emission from free-electron lasers. The angular and spectral characteristics of radiation are analytically evaluated leveraging Liénard–Wiechert field formalism. The analysis spanned across varying beam profiles and undulator parameters, including harmonic order, magnetic strength, period, and electron energy. The Fourier analysis of the electric field reveals strong sensitivity of spectral content to the underlying beam dynamics and undulator structure. Planar undulators tend to generate radiation with more prominent sidelobes, especially at higher harmonics, while helical undulators produce narrower, more focused emission profiles. Importantly, the polarization and forward-directed nature of radiation are governed primarily by the resonant conditions and beam dynamics, rather than the undulator geometry itself. Building on these analytical insights, GENESIS simulations are employed to quantify the evolution of the bunching factor and radiation intensity under varying energy spread and plasma dispersion. The results show that increased undulator periods enhance radiation coherence, while transitions to wiggler regimes (at high magnetic parameters) lead to angular broadening and lateral lobe formation. Among all beam profiles studied—Gaussian, Lorentzian, bi-Gaussian, and pre-bunched—the pre-bunched configuration demonstrates superior harmonic generation capabilities, albeit with high sensitivity to energy spread and plasma effects.