Efficiency enhancement of a two-beam free-electron laser using a nonlinearly tapered wiggler

A nonlinear and non-averaged model of a two-beam free-electron laser(FEL) wiggler that is tapered nonlinearly in the absence of slippage is presented.The two beams are assumed to have different energies,and the fundamental resonance of the higher energy beam is at the third harmonic of the lower energy beam.By using Maxwell’s equations and the full Lorentz force equation of motion for the electron beams,coupled differential equations are derived and solved numerically by the fourth-order Runge-Kutta method.The amplitude of the wiggler field is assumed to decrease nonlinearly when the saturation of the third harmonic occurs.By simulation,the optimum starting point of the tapering and the slopes for reducing the wiggler amplitude are found.This technique can be applied to substantially improve the efficiency of the two-beam FEL in the XUV and X-ray regions.The effect of tapering on the dynamical stability of the fast electron beam is also studied.     

Theoretical studies of the ion-hose instability in a plasma-focusedfree-electron laser

An `ion-focused' relativistic electron beam traversing a magnetic wiggler is subject to a transverse two-steam or `in-hose' instability, resulting from the coupling of transverse displacements of the beam centroid to the `slosh' motion of the (beam-focused) nonneutral ion plasma, and driven by the `V×B' deflection in the wiggler field. The equations of motion are resolved into an inhomogeneous `beam breakup' equation, and asymptotic growth is computed in the limit of linear focusing. The effect of nonlinearities is assessed numerically with a `distributed-mass' model. As examples, ion-hose growth is considered in a UV FEL and a microwave FEL two-beam accelerator     

Electron acceleration in the inverse free electron laser with a helical wiggler by axial magnetic field and ion-channel guiding

Electron acceleration in the inverse free electron laser (IFEL) with a helical wiggler in the presence of ion-channel guiding and axial magnetic field is investigated in this article. The effects of tapering wiggler amplitude and axial magnetic field are calculated for the electron acceleration. In free electron lasers, electron beams lose energy through radiation while in IFEL electron beams gain energy from the laser. The equation of electron motion and the equation of energy exchange between a single electron and electromagnetic waves are derived and then solved numerically using the fourth order Runge-Kutta method. The tapering effects of a wiggler magnetic field on electron acceleration are investigated and the results show that the electron acceleration increases in the case of a tapered wiggler magnetic field with a proper taper constant.     

Chaotic electron trajectories in electromagnetic wiggler free-electron laser with a guide magnetic field

Summary The Hamiltonian for an electron travelling through a large-amplitude backward electromagnetic wave, an axial guide magnetic field and radiation field is formulated. Poincaré surface-of-section plots show that this Hamiltonian is non-integrable, and leads to chaotic trajectories. Equilibrium conditions are derived in the limit where the radiation field approaches zero. Compared to conventional FEL, the total energy of the system at pondermotive resonanceE _c is large, while the electron's critical energy γ_c is low for electromagnetic wiggler FEL. Moreover, the threshold wave amplitude (A _r=A _c) of beam chaoticity is found at lower values of the radiation field amplitude compared to magnetostatic wiggler FEL. Previous features confirmed that electromagnetic wiggler FEL can operate more coherently and more efficiently at moderated particle's energy compared to magnetostatic wiggler FEL.     

磁场逐渐增强的摇摆器

研究了用磁场增强摇摆器来提高自由电子激光器效率的机制．采用KMR方程，考虑空间电荷效应，模拟计算发现自由电子激光器的效率有了很大的提高，而且电子束能散度越大，对提高自由电子激光器效率越有帮助．因此采用磁场增强摇摆器能充分利用加速器的能量来莸得更高的自由电子激光器能量 关键词：     

Effect of normalized plasma frequency on electron phase-space orbits in a free-electron laser

Irregular phase-space orbits of the electrons are harmful to the electron-beam transport quality and hence deteriorate the performance of a free-electron laser （FEL）. In previous literature, it was demonstrated that the irregularity of the electron phase-space orbits could be caused in several ways, such as varying the wiggler amplitude and inducing sidebands. Based on a Hamiltonian model with a set of self-consistent differential equations, it is shown in this paper that the electron- beam normalized plasma frequency functions not only couple the electron motion with the FEL wave, which results in the evolution of the FEL wave field and a possible power saturation at a large beam current, but also cause the irregularity of the electron phase-space orbits when the normalized plasma frequency has a sufficiently large value, even if the initial energy of the electron is equal to the synchronous energy or the FEL wave does not reach power saturation.     

Interaction of a relativistic dense electron beam with a laser wiggler in a vacuum: self‐field effects on the electron orbits and free‐electron laser gain

Employing laser wigglers and accelerators provides the potential to dramatically cut the size and cost of X‐ray light sources. Owing to recent technological developments in the production of high‐brilliance electron beams and high‐power laser pulses, it is now conceivable to make steps toward the practical realisation of laser‐pumped X‐ray free‐electron lasers (FELs). In this regard, here the head‐on collision of a relativistic dense electron beam with a linearly polarized laser pulse as a wiggler is studied, in which the laser wiggler can be realised using a conventional quantum laser. In addition, an external guide magnetic field is employed to confine the electron beam against self‐fields, therefore improving the FEL operation. Conditions allowing such an operating regime are presented and its relevant validity checked using a set of general scaling formulae. Rigorous analytical solutions of the dynamic equations are provided. These solutions are verified by performing calculations using the derived solutions and well known Runge–Kutta procedure to simulate the electron trajectories. The effects of self‐fields on the FEL gain in this configuration are estimated. Numerical calculations indicate that in the presence of self‐fields the sensitivity of the gain increases in the vicinity of resonance regions. Besides, diamagnetic and paramagnetic effects of the wiggler‐induced self‐magnetic field cause gain decrement and enhancement for different electron orbits, while these diamagnetic and paramagnetic effects increase with increasing beam density. The results are compared with findings of planar magnetostatic wiggler FELs.     

Three-dimensional simulation of long-wavelength free-electron lasers with helical wiggler and ion-channel guiding

A three-dimensional simulation of a steady-state amplifier model of a long-wavelength free-electron laser (FEL) with realizable helical wiggler and ion-channel guiding is presented. The set of coupled nonlinear differential equations for electron orbits and fields of TE 11 mode in a cylindrical waveguide are solved numerically by the Runge-Kutta algorithm with averages calculated by the Gaussian quadrature technique. Self-fields and space-charge effects are neglected, and the electron beam is assumed to be cold and slippage is ignored. The parameters correspond to the Compton regime. Evolution of the radiation power and growth rate along the wiggler is studied. Ion-channel density is chosen to obtain optimum efficiency. Simulations are preformed for the FEL operating in the neighborhood of 35 GHz and 16.5 GHz for the electron beam energies of 250 keV and 400 keV, respectively. The result of the saturated efficiency was found to be in good agreement with the simple estimation based on the phase-trapping model.     

CAEP远红外100 μm FEL自发辐射谱的实验研究

在FEL实验中,电子束通过摇摆器,一方面由于周期性磁场作用,电子束轨迹要周期性的摆动,另一方面还要辐射同FEL辐射波长一致的自发辐射,该辐射谱反映电子束、摇摆器集成后的参数。在CAEP(Institute of China Academic Engineering Physics)远红外100 μm FEL实验中,自发辐射谱通过Ge∶Ga低温探头和远红外100 μm光栅谱仪测量。文章侧重从实际摇摆器磁场分析了远红外100 μm FEL的自发辐射谱。     

Gain enhancement in two-stream free electron laser with a planar wiggler and an axial guide magnetic field

The theory for a two-stream free electron laser (FEL) consisting of a relativistic electron beam transported along the axis of a planar wiggler in the presence of an axial guiding magnetic field is proposed and investigated. The electron trajectories and the small signal gain are derived. The characteristic of the linear gain and the normalized maximum gain are studied numerically. The result shows that the normalized maximum gain is considerably enhanced in comparison with that of the single stream. The effect of the difference between the energies of the two beams in this configuration of FEL is also considered, and we find that the gain is affected by the energy differences between groups 1 and 2.     

Gain enhancement in two-stream free electron laser with planar wiggler and axial guide magnetic field

The theory for the two-stream free electron laser (FEL) consisting of a relativistic electron beam transported along the axis of a planar wiggler in the presence of an axial guiding magnetic field is proposed and investigated. The electron trajectories and the small signal gain are derived. The characteristic of the linear gain and the normalized maximum gain are studied numerically. The result shows that the normalized maximum gain is considerably enhanced in comparison with that of the single stream. The effect of the difference between the energies of the two beams in this configuration of FEL is also considered, and we find that the gain is affected by the energy differences between groups 1 and 2.     

Two-stream instability in free electron lasers

The analysis of the interaction between electromagnetic waves and electron beams in semi-infinite wigglers is presented. The beam is assumed to include two cold streams of electrons; hence, its space-charge waves may be unstable (two-stream instability). In the wiggler, this instability is shown to yield much larger growth rates (up to seven times greater) than in the conventional one-stream free electron laser (FEL). Accordingly, the gain per pass is enhanced by orders of magnitude. The enhancement of the two-stream instability is shown to be most effective for short-period wigglers     

An analysis of the Transverse Optical Klystron (TOK) and the Free Electron Laser (FEL) through the exact solution of their evolution equation

We give the exact analytical solution of the evolution equation of an electron beam interacting in a wiggler with an electromagnetic wave. The initial energy distribution is assumed both monochromatic and gaussian. Furthermore, the evolution in a drift space is considered. Some basic characteristics of the FEL and TOK are derived from the mathematical properties of the solution.     

远红外自由电子激光器的带宽扩展

本文研究了波导尺寸、电子束能量、摇摆器周期及磁场强度对波导型自由电子激光带宽的扩展作用，文中给了带宽约４００μｍ的远红外（工作波长６００－１０００μｍ）自由电子激光振荡器的设计参数，并对有关工程问题进行了讨论。     

自由电子激光的单粒子理论及其应用

本文建立了圆极化摇摆场自由电子激光的单粒子理论,导出了电子未扰轨道及其稳定性判据和自由电子激光单程增益的表达式。单程增益由三项构成,其中第一项即自由电子激光不稳定性的增益与动力学理论得到的指数增益相符。第二项和和三项表明存在一对新的不稳定性——正不稳定性和负不稳定性。该理论没有对电子未扰轨道纵向速度作任何假设,不仅可以更合理地用于常规自由电子激光的研究,而且可以用于短周期摇摆器弱相对论自由电子激光研究。后者由于电子未扰轨道纵向速度比较低,已有的单粒子理论中所作的电子纵向速度约等于光速的假设不再成立。借助数值分析,我们发现:(1)稳定轨道Ⅱ的弱导引场区域也出现了动力学理论描述过的与自由电子激光互作用机理相悖的现象。(2)正不稳定性和负不稳定性在稳定轨道Ⅰ的导引磁场临界值附近可能严重影响自由电子激光的工作。(3)可以使用较弱的短周期摇摆场和较强的导引场产生高频率高增益相干受激辐射。     

Three-dimensional simulation analysis of a 3 cm wavelengthfree-electron laser afterburner

We have simulated a 3 cm wavelength free-electron laser afterburner (FEL Afterburner) using two sets of parameters: one is for a 3-cm period wiggler and the other is for a 5.4 cm period wiggler. For the 3 cm period wiggler, the input beam energy is 112.5 keV, and for the 5.3 cm period wiggler the beam energy is increased to 290 keV to make the FEL Afterburner operate at the same frequency. It is found, from the simulations, that the FEL Afterburner with a longer period wiggler has a higher power conversion efficiency: larger than 16% $ for the 5.4 cm wiggler while only about 9% for the 3 cm wiggler. It is also shown that to enhance the interaction efficiency in the slow wave cavity, the slow wave number should be a little larger than the sum of the fast wave number and the wiggler wave number     

Self-field effects on electron dynamics in a three-dimensional helical wiggler free-electron laser with axial magnetic field

An analytic linear theory of the electron dynamics in a three-dimensional helical wiggler free electron laser (FEL) with axial magnetic field is presented. Orbits are obtained by perturbing the steady state-trajectories in order to determine the characteristic frequencies Ω_± of the FEL. The effect of the self-fields on electron dynamics is studied and modified steady-state orbits and their stabilities have been analysed considering variation of electron energy and density. Among the features encountered is that in both group-I and group-II, one of the characteristic frequencies may have either signs affecting then the stability of the motion, while in group-II operation a repulsion of the frequencies at a pseudocrossing leads to highly perturbed trajectories when the wiggler frequency is approximately half the cyclotron frequency. Self-fields effects can significantly impair the stability of the electron orbits. For group-I orbits, they are more important for higher wiggler frequencies and lower beam energies. For group-II orbits, they remain less important for higher wiggler frequencies and lower beam energies before reaching the inversion zone, then they behave as for group-I orbits. It should be remarked that self-fields shift the inversion zone towards higher cyclotron frequencies the thing that is obtained by either decreasing the wiggler frequency or increasing the beam energy. It is shown that the axial velocity-induced self-magnetic field has a diamagnetic effect for both groups orbits, while the wiggler-induced self-magnetic field has a diamagnetic effect for group-I orbits and a paramagnetic effect for group-II orbits. The paramagnetic and diamagnetic effects are more important for higher beam energies and densities.     

Mode-selective amplification in a waveguide free electron laserwith a two-sectioned wiggler

One important issue in waveguide free electron lasers (FELs) involves an interaction of the electron beam with one waveguide mode at two different resonant frequencies. Since the low-frequency mode often has a higher pain, the usually preferred high-frequency mode is suppressed as a result of mode competition. In this paper, possible control of this mode competition is considered using a nonstandard wiggler magnet consisting of two cascaded wiggler sections with different periods and field strengths. It is demonstrated that with an appropriate differentiation between the two wiggler sections the high-frequency mode may be amplified preferentially. This mode-selective amplification may be used to suppress the low-frequency mode. A small signal gain formulation is developed for a waveguide FEL with such a two-sectioned wiggler arrangement and numerical examples are used to demonstrate its applicability to mode control in waveguide FELs. Effects of wiggler field errors and electron energy spread are also considered. It is shown that the requirement for wiggler field errors and electron energy spread in the two-sectioned wiggler arrangement is similar to that in the usual straight wiggler configuration     

Three dimensional gain analysis of free electron laser with focusing permanent magnet wiggler

A three dimensional simulation software system developed to estimate a free electron laser (FEL) gain has been applied to FEL using a standard plane polarized wiggler and an alternately shifted magnet wiggler. It is seen for the latter wiggler that a large filling factor could be selected and each maximum gain corresponding to each orbit of electron beam concentrates at a certain frequency region of FEL radiation. It is, therefore, implied that a proper shift between the adjacent magnets in the wiggler produces the improvement of the FEL gain.