The free-electron laser: Status and perspectives

Bizzarri, U.; Ciocci, P.; Dattoli, G.; Angelis, A. De; Fiorentino, E.; Gallerano, G.P.; Letardi, T.; Marino, A.; Messina, Giovanni; Renieri, A.; Sabia, E.; Vignati, A.

doi:10.1007/bf02739979

Cited by 28 publications

(4 citation statements)

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“…This means that odd powers of the functions sinw and cosw vanish, and the functions sin 2 w and cos 2 w are replaced by their average value 0.5. As a consequence, we obtain the following linear differential equations for the slowly varying functions x s z ðÞand y s z ðÞ , see [10][11][12]]:…”

Section: Smoothed (Focusing) Approximation For Electron Trajectoriesmentioning

confidence: 99%

“…It is correct to suppose that these numerically simulated trajectories are highly accurate results. The checking of these numerically simulated trajectories was made against analytically calculated trajectories, obtained by using the oscillation-averaging method (focusing approximation) [10][11][12]. This comparison has been demonstrated in a conclusive way that in most cases the numerically simulated trajectories differ significantly from those calculated by using the analytical formulas derived in focusing approximation.…”

Section: Introductionmentioning

confidence: 97%

“…Electron long-wave anharmonic betatron oscillations in very long undulator magnetic fields were considered in [9]. The action of the focusing properties of undulators on the operation of free-electron lasers was studied in [10][11][12]. In addition, a configuration of an undulator with a parabolic shape of the magnetic-pole surface was also proposed in [10].…”

Section: Introductionmentioning

confidence: 99%

“…The formulas derived in this manner are very complicated since they include all terms of the cubic power of small quantities. However, these formulas give a higher approximation to electron trajectories in the undulator field than those derived in the smoothed (focusing) approximation [10][11][12]. Analysis of these highly accurate expressions shows that electron motion in undulator magnetic field is very sophisticated and cannot be reduced to the standard focusing effects.…”

Section: Introductionmentioning

confidence: 99%

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Motion of Electrons in Planar Ideal Undulator

Smolyakov¹

2018

Accelerator Physics - Radiation Safety and Applications

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This chapter describes the motion of relativistic electrons in three-dimensional ideal undulator magnetic field. The undulator magnetic field satisfies the stationary Maxwell equations. Usually, the differential equations of electron motion in three-dimensional sinusoidal magnetic field are analysed by averaging over the fast electron oscillations. This averaging method was applied in a number of previously published papers. In this study, the nonlinear differential equations for electron motion were solved analytically by using the perturbation theory. The analytic expressions for trajectories obtained by this method describe the electron trajectories more accurately as compared with the formulas, which were obtained within the framework of the averaging method. An analysis of these expressions shows that the behaviour of electrons in such a three-dimensional field of the undulator is much more complicated than it follows from the equations obtained by the averaging method. In particular, it turns out that the electron trajectories in a planar undulator are cross-dependent. A comparison of the trajectories, calculated using these new analytical expressions with the numerically calculated trajectories using the RungeKutta method, demonstrated their high accuracy.

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Section: Smoothed (Focusing) Approximation For Electron Trajectoriesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%