A. Segreto

Free electron laser saturation: An analytical description

An analytical description of the free electron laser (FEL) strong‐signal regime is developed by means of simple formulas obtained using the theory of Pade approximants. The analysis includes inhomogeneous broadening effects and its validity is tested with two different numerical procedures. The dependence of the saturation intensity on the detuning parameter and on the e‐beam relative energy spread is also analyzed.

Free electron laser gain: Approximant forms and inclusion of inhomogeneous broadening contributions

The free electron laser gain formulae for low‐, intermediate‐, and high‐gain domains are parametrized by means of a simple expression reproducing linear and exponential regimes. The proposed reformulation provides a useful tool of analysis because of its remarkable simplicity and because it offers the possibility of deriving comparably simple gain formulae that include inhomogeneous broadening effects.

Symmetric-split-operator techniques and finite-difference methods for the solution of classical and quantum evolution problems

SummaryWe show that the symmetrically split-operator technique provides a useful method to study evolution problems in classical and quantum mechanics. It is shown that it leads to a finite-difference scheme naturally preserving the symplectic nature of the problem in classical mechanics and the unitarity in quantum mechanics. We also prove its usefulness for the solution of Liouville and Fokker-Planck equations. The link with other difference schemes (Bender-Sharp, Moncrief, Vazquez) is finally discussed.

FEL dynamics, electron-beam bunching and prebunching

Abstract We discuss how a prebunched beam may modify the dynamical behavior of a free-electron laser. We show that the lowest-order coefficients b 1,2 , modify the small signal dynamics, while the saturated regime is affected by the higher-order coefficients. We also present an analysis of the interplay between bunching, saturation and higher harmonic emission during the FEL evolution.

The high-gain free-electron laser equation: exact, perturbative, and approximated solutions

SummaryWe use the Laplace-transform technique for a general analysis of the integral equation that describes the Free-Electron Laser (FEL) small-signal evolution. We include both pulse propagation effects and inhomogeneous broadening contributions. The solutions are obtained in exact form and by using perturbative expansions. It is also shown that these solutions can be approximated with elementary functions and that most of the FEL high-gain evolution can be handled with almost negligible computational effort. The analysis is extended to includee-beam pre-bunching effects, and a generalization of the Madey theorem is proved.

Wave-guide free electron laser: gain inhomogeneous broadening and saturation

Abstract We discuss wave-guide Free Electron Laser gain formulae including inhomogeneous broadening and saturation effects. The analysis is not limited to the low gain regime. It is also proven that, after a proper redefinition, most of the “empirical” formulae exploited for the free space case can be utilised to model the wave-guide evolution.

The pulse propagation problem in free electron lasers: Gain parametrization formulae

The pulse propagation in free electron lasers is treated analytically. A general gain formula including finite pulse effects, high gain corrections, inhomogeneous broadening contributions and the detuning parameter is derived. It is shown that it contains, as particular cases, the already known gain parametrization formulae.

Analytical treatment of transverse-mode evolution in free electron lasers

The problem of the small-signal transverse-mode evolution in free electron lasers is discussed within the framework of an analytical treatment. The analysis is based on the formalism of the amplitude approximants and includes the effect of high gain and inhomogeneous broadening contributions. Mode distortion and focusing effects are derived fairly straightforwardly. We comment on the possibility of including the pulse propagation mechanism.

Evolution of transverse modes in FEL and the method of approximants

Abstract The FEL paraxial wave equation is investigated within the context of the method of the approximants, which has been successfully applied to the one-dimensional FEL dynamics including high gain, inhomogeneous broadening and saturation effects. The method is effective in confining the transverse mode dynamics into a simple analytical model, which is amenable for a fast and reliable numerical procedure, appropriate to small computers. The case of uniform e-beam current profile is considered in some details. Numerical results are presented and compared with those from more sophisticated codes.

Free electron laser dynamics, evolution of the bunching coefficients, and coherent harmonic generation

Free electron laser dynamics is characterized by the interplay between bunching and emission processes. The first mechanism can be quantitatively specified in terms of the so‐called bunching coefficients, which determine the degree of the bunching at the fundamental and higher harmonics. We numerically solve the Liouville equation, which rules the longitudinal phase‐space dynamics, and evaluate the bunching coefficients and associated harmonic generation. We develop a semianalytical method to study the harmonic generation and evolution in free electron laser oscillators.