One-body electron dynamics in a free electron laser

The free electron laser is analyzed by solving the one-body classical Lorentz force equation in the presence of periodic magnetic field and a plane electromagnetic wave. Phase space paths for electrons are related to those of a simple pendulum and describe laser gain, saturation, and coherent electron beam modulation.     

Hamiltonian model of a free electron laser including high-density effects

Both the Compton and the Raman regimes of a free electron laser are described by a relativistic Hamiltonian which originates the evolution equations for 2N+2 canonically conjugate electron and field variables, with the space coordinate as the independent variable. Space charge and field contribution to electron transverse velocity are included.     

Chaotic electron trajectories in a circular free electron laser

The motion of a relativistic electron is analyzed in the field configuration consisting of a circular wiggler magnetic field, an axial magnetic field, and the equilibrium self-electric and self-magnetic fields produced by the non-neutral electron ring. By generating Poincare surface-of-section maps, it is shown that when the equilibrium self-fields is strong enough, the electron motions become chaotic. Although the realistic circular wiggler magnetic field destroys the integrability of the electron motion as the equilibrium self-fields do, the role the latter plays to make the motions become chaotic is stronger than the former. In addition, the axial magnetic field can restrain the occurrence of the chaoticity.     

Chaotic dynamics in a storage-ring free electron laser

The temporal dynamics of a storage-ring Free Electron Laser is here investigated with particular attention to the case in which an external modulation is applied to the laser-electron beam detuning. The system is shown to produce bifurcations as well as chaotic regimes. The peculiarities of this phenomenon with respect to the analogous behaviour displayed by conventional laser sources are pointed out. Theoretical results, obtained by means of a phenomenological model reproducing the evolution of the main statistical parameters of the system, are shown to be in a good agreement with experiments carried out on the Super-ACO Free Electron Laser. Received 27 March 2002 / Received in final form 17 July 2002 Published online 21 January 2003 RID="a" ID="a"Present address: Sincrotone Trieste, 34012 Trieste, Italy. RID="b" ID="b"e-mail: fanelli@nada.kth.se     

Quantum theory of a free electron laser

Spontaneous emission by electrons moving in a magnetic field constant in time and periodic in space (with circular polarization) is calculated using exact solutions of the corresponding Dirac equation. In addition to the known transitions we find two harmonics connected with spin flip processes, which are, however, strongly suppressed. The gain of the free electron laser is recalculated from the rate for spontaneous emission. The results obtained by classical methods are corroborated.Supported in part by Deutsche Forschungsgemeinschaft     

Coherent states of a free electron laser

We define electron-field coherent quasi-classical states of a free electron laser. In these states both the photon number and the electron momentum are given by a Poisson distribution centered on the classical trajectories.     

Betatron-synchrotron resonance in free electron laser

In terms of Bogoliubov's nonlinear theory, the first five betatron-synchrotron resonances of _s=(p q)2K, p/q=1/2, 1, 3/2, 1/3, 2/3 which may occur during laser satulation establishing process have been generally examined. Contrast to previous studies we found that the most dangerous resonance does not take place in the vicinity of _s=2k, but in that of _s=k. The width of region of _s=k is proportional to with (k _w ² /k) remittance, the passing time over the region due to the laser field being amplified is only one pass over the undulator at most and depends on the gain, and the increment of synchrotron amplitude in passing time is proportional to .In summary we conclude that the betatron-synchrotron resonances do not have any significant effect for detrapping off-axis electrons in a practical case.     

Chaos in free electron laser oscillators

The chaotic nature of a storage-ring free electron laser (FEL) is investigated. The derivation of a low embedding dimension for the dynamics allows the low-dimensionality of this complex system to be observed, whereas its unpredictability is demonstrated, in some ranges of parameters, by a positive Lyapounov exponent. The route to chaos is then explored by tuning a single control parameter, and a period-doubling cascade is evidenced, as well as intermittence.     

Equations for pulse propagation in a free electron laser

The equations for pulse propagation in a free electron laser are derived. The equations are valid in a reference frame, moving with a relativistic velocity with respect to the laboratory frame, chosen in such a way that the carrier frequency of the pulse equals the pseudoradiation (wiggler) field frequency. In this reference frame the equations assume a simple non relativistic form.     

Proposal for a Raman X-ray free electron laser

A scheme for an X-ray free electron laser is proposed, based on a Raman process occurring during the interaction between a moderately relativistic bunch of free electrons, and twin intense short pulse lasers interfering to form a transverse standing wave along the electron trajectories. In the high intensity regime of the Kapitza-Dirac effect, the laser ponderomotive potential forces the electrons into a lateral oscillatory motion, resulting in a Raman scattering process. I show how a parametric process is triggered, resulting in the amplification of the Stokes component of the Raman-scattered photons. Experimental operating parameters and implementations, based both on LINAC and Laser Wakefield Acceleration techniques, are discussed.     

Exact one-particle theory of a free electron laser

From a semiclassical discussion of the one-particle quantized model we demonstrate that the free electron dynamics exhibits a phase transition in correspondence to a threshold value of the wiggler magnetic field. Below threshold the FEL can work as a small gain amplifier and can be described by the well-known pendulum analogy and gain-spread expressions. Above threshold the analogy is broken and the FEL works as a large gain amplifier which goes from spontaneous to stimulated emission regime.     

The effects of slippage and diffraction in long wavelength operation of a free electron laser

The Free-Electron Laser user facility FELIX produces picosecond optical pulses in the wavelength range of 5–110m. The proposed installation of a new undulator with a larger magnetic period would allow extension towards considerably longer wavelengths. This would result in the production of extremely short, far-infrared pulses, with a duration of a single optical period or even less. In order to investigate the pulse propagation for free-electron lasers operating in the long wavelength limit, a three-dimensional simulation code was developed. Using the FELIX parameters, with the addition of a long-period undulator, the effects of slippage, diffraction losses, changes in the filling factor, as well as the effects of the optical cavity geometry were studied for wavelengths up to 300m, with electron pulses in the ps regime. It is shown that slippage effects are less restrictive for long wavelength operation than the increasing losses due to optical beam diffraction.     

Collective instabilities and high-gain regime in a free electron laser

We study the behavior of a free electron laser in the high gain regime, and the conditions for the emergence of a collective instability in the electron beam-undulator-field system. Our equations, in the appropriate limit, yield the traditional small gain formula. In the nonlinear regime, numerical solutions of the coupled equations of motion support the correctness of our proposed empirical estimator for the build-up time of the pulses, and indicate the existence of optimum parameters for the production of high peak-power radiation.     

Proposal for a free electron laser in the X-ray region

It is proposed that a free electron laser can be operated in the X-ray region, in the range 2–3 Å. An analysis is presented of the machine parameters and the characteristics of the mirrors that are required for operation in the Ångstrom region.     

Inhomogeneous broadening effects in high-gain free electron laser operation: A simple parametrization

Summary In this paper we present a simple parametrization of the effects of gain degradation induced in high-current FELs by the inhomogeneous broadenings due to the energy spread and emittances of the electron beam. The parametrization is based on a fitting procedure of the numerical data. The accuracy of the fit is better than 1%.

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Riassunto In questo lavoro si analizzano gli effetti di allargamento inomogeneo in FEL operanti nel regime di alto guadagno. Si presenta una semplice formula che permette di parametrizzare il guadagno in funzione dei parametri inomogenei dovuti allo spread di energia ed alle emittanze. La parametrizzazione è basata su una procedura di interpolazione dei dati numerici. L'accuratezza della interpolazione è migliore dell'1%.

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Резюме В этой работе анлизируется влияние эффектов неоднородного уширения на действие лазера на свободных электронах с высоким усилением. Предлагается простая формула для параметризации коэффициента усиления в зависимости от параметров неоднородного уширения, связанных с разбросом энергии и эмиттанса электронного пучка. Параметризация основана на интерполяции численных данных. Точность интерполяции оказывается лучше 1%.

     

On the coherent states of a free electron laser

The coherence properties of the Free Electron Laser are examined both in the single mode and multimode case.     

Pulse propagation solution for a quantum free electron laser

We calculate the exact solution of the propagation equations describing a quantum free electron laser. The solution is obtained by evaluating the residue in the essential singularities of the Fourier-Laplace transformed optical field, and is expressed as a complete series of special functions. The classical and quantum limits of the solution are discussed and an asymptotic form, valid in the high-gain regime, is obtained.     

A compact free electron laser investigation

An electron beam source based on pseudospark discharge was successful in operation at the beam voltage of 200keV and beam current of 2kA. The detailed design of a compact free electron laser using an electron beam by a pseudospark discharge is described. The compact free electron laser consists of a smaller Marx generator with 6 capacitors and switches, a water capacitance of 6nF and a beam source with a high brightness of 3×10¹¹ A/(m rad)². The computer simulation shows that an output power of 101MW is expected at a frequency of 38GHz with a beam energy of 300keV, a current of 2kA and a beam emittance of 48mm mraa.