Theoretical Model and Experimental Observation of Resonance Generation of Free Electron Laser

Yefimov, B. P.; Ilyenko, K.; Yatsenko, Tetyana; Goryashko, Vitaliy

doi:10.1615/telecomradeng.v61.i3.50

Cited by 6 publications

(6 citation statements)

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“…Analytical linear in the microwave field theory of beamwave interaction for a hybrid planar FEL amplifier can be constructed along the same lines as the highly successful theory of gyrotron provided analytical expressions for singleparticle trajectories of electrons in the combined pump magnetostatic field are known [3][4][5] . Solutions to the corresponding nonlinear equations are found numerically.…”

Section: Resultsmentioning

confidence: 99%

Free-electron laser with resonant pumping

Ilyenko

Goryashko

Opanasenko

2008

2008 33rd International Conference on Infrared, Millimeter and Terahertz Waves

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We find the boundaries of regular and chaotic dynamics zones around the magnetoresonance for a hybrid planar free-electron laser amplifier. For the zones of regular dynamics the maximal magnetoresonant gain is calculated analytically and is shown to be in a good agreement with non-linear numerical simulations. It is also analytically demonstrated that in the vicinity of magnetoresonance the gain is independent of the spatial amplitude of undulator magnetic field. Moreover, we find that in the zone of regular dynamics above the magnetoresonance the efficiency of amplification achieves its maximal value and is less prone to the influence of space-charge effects.

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Section: Resultsmentioning

confidence: 99%

Free-electron laser with resonant pumping

Ilyenko

Goryashko

Opanasenko

2008

2008 33rd International Conference on Infrared, Millimeter and Terahertz Waves

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“…6 below). In the zone of regular dynamics, a solution to system (5) can be obtained by the use of a method of Lindshtedt [34,35] of asymptotic expansion of trajectory and frequencies in the small parameter " (see [19] for a detailed exposition of the method). To the order oð" 3 Þ, the velocity components read…”

Section: Magnetostatic Resonance: Energy Transfer and Dynamical mentioning

confidence: 99%

“…430-439): under what conditions motion of an individual test electron becomes chaotic in the presence of the guide magnetic field; what does influence the width of dynamical chaos zone around the magnetoresonant value (the undulator frequency is approximately equal to the cyclotron frequency) of the guide magnetic field; what does define the maximal value of the gain under the conditions of the magnetoresonance; and, finally, how do beam initial parameters spread and space-charge effects impact microwave amplification ? We focus our attention on the operation of FEM around the magnetoresonant regime caused by the guide magnetic field usually used in FEM setups to enhance the efficiency of beam-microwave interaction and provide transverse confinement of the electron beam. The study is based upon analytical asymptotically exact expressions for electron trajectories developed recently [19] as well as on the use of numerical simulations. More specifically, in the adopted approach we highlight the fundamental role of the nonlinear dynamical system describing motion of electrons in the combined magnetostatic spatially periodic (undulator) and uniform guide magnetic field.…”

Section: Introductionmentioning

confidence: 99%

Hybrid planar free-electron maser in the magnetoresonance regime

Goryashko

Ilyenko

Opanasenko

2009

Phys. Rev. ST Accel. Beams

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We study the operation regime of a hybrid planar free-electron maser (FEM) amplifier near the magnetoresonant value of the uniform longitudinal (guide) magnetic field. Using analytical expressions for individual test electron trajectories and normal frequencies of their three-dimensional oscillations in the magnetostatic field of the hybrid planar FEM, an analytical condition of chaotization of motion is established and shown to be given by the Chirikov resonance-overlap criterion applied to the normal undulator and cyclotron frequencies with respect to the coupling induced by the undulator magnetic field. It is also shown analytically that, in spite of the well-known drop for the exact magnetoresonance, the gain attains its maximal value in the zone of regular dynamics slightly above the magnetoresonant value of the guide magnetic field. Under the condition of undulator resonance, it is practically independent of the amplitude of the undulator magnetic field and the wavelength of amplified signal. To account for spacecharge effects, we propose a theoretical model of a weakly relativistic FEM, which accommodates not only potential but also rotational parts of the nonradiated electromagnetic field of a moving charged particle. It turns out that the rotational part of nonradiated field diminishes the defocusing influence of the potential part on the beam bunching. Numeric simulation of the nonlinear stage of amplification is fulfilled, taking into consideration adiabatic entrance of the electron beam to the interaction region and initial electron velocity spread. We find that nonradiated field and initial electron velocity spread do not influence essentially the efficiency of hybrid planar FEM amplification if parameters of the beammicrowave interaction correspond to the operational regime in the zone of regular dynamics near the magnetoresonance.

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“…It should be noted that out of six quantities λ w , B ⊥ , B , V , V x and V y only four their dimensionless combinations ε = ω ⊥ /ω 0 ≡ cK/(γ 0 V ) (K is the conventional undulator parameter), σ 0 = ω /ω 0 , V x /V and V y /V define the behavior of nonlinear dynamic system (6). Solution to system (6) can be obtained by the use of a method of Lindshtedt [27,28] of asymptotic expansion of trajectory and frequencies in the small parameter ε (see [17] for a detailed exposition of the method in the case V x = V y = 0). To the order o(ε 2 ) the velocity components read:…”

Section: Magnetostatic Resonance: Energy Transfer and Dynamical Chaosmentioning

confidence: 99%

“…We focus our attention on the operation of FEM around the magnetoresonant regime caused by the guide magnetic field usually used in FEM setups to enhance the efficiency of beam-microwave interaction and provide transverse confinement of electron beam. The study is based upon analytical asymptotically exact expressions for electron trajectories developed recently [17,18] as well as on the use of direct numerical simulations. More specifically, in the adopted approach we highlight the fundamental role of nonlinear dynamical system describing motion of electrons in the combined magnetostatic spatially periodic (undulator) and uniform guide magnetic field.…”

Section: Introductionmentioning

confidence: 99%

Hybrid Planar FEM in Magnetoresonance Regime: Control of Dynamical Chaos

Goryashko,

Ilyenko,

Opanasenko

2008

Preprint

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We establish the influence of nonlinear electron dynamics in the magnetostatic field of a hybrid planar free-electron maser on its gain and interaction efficiency. Even for the 'ideal' undulator magnetic field the presence of uniform longitudinal (guide) magnetic field potentially leads to the existence of chaotic zone around certain (magnetoresonant) value of the guide magnetic field. The width of the chaotic zone is given by the Chirikov resonance-overlap criterion applied to the normal undulator and cyclotron frequencies with respect to the coupling induced by the undulator magnetic field. Using analytical asymptotically exact solutions for trajectories of individual test electrons, we show that the magnetoresonant multiplier in electron trajectories is also present in the expression for the gain. The same Chirikov resonance-overlap criterion allows us to estimate analytically the maximal magnetoresonant gain of a hybrid planar free-electron maser showing that, in spite of the well-known drop in the gain for the exact magnetoresonance, the operation regime in the zone of regular dynamics slightly above the magnetoresonant value of the guide magnetic field is the preferable one.

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Theoretical Model and Experimental Observation of Resonance Generation of Free Electron Laser

Cited by 6 publications

References 0 publications

Free-electron laser with resonant pumping

Free-electron laser with resonant pumping

Hybrid planar free-electron maser in the magnetoresonance regime

Hybrid Planar FEM in Magnetoresonance Regime: Control of Dynamical Chaos

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