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。     

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.     

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.     

Gain of a free-electron laser in the Magneto-Compton regime

The gain of a free-electron laser in the presence of a guide magnetic field is calculated for the Raman and Compton regimes. It is found that the external magnetic field enhances the gains, and that for non-monoenergetic relativistic electron beams with a guide magnetic field the Compton process can become important.     

Effect of the Electron‐Beam Self‐Fields on Gain in an Optical Wiggler Pumped Free‐Electron Laser

The effects of self fields on gain for a free‐electron lasers (FELs) with electromagnetic‐wave wiggler and an axial guide magnetic field is presented. The relativistic equation of motion for a single electron for all relevant fields, including wiggler, self‐fields and axial guide magnetic field has been solved. Two classes of possible single‐particle trajectories in this configuration are found. Result of the numerical calculation shown that the relativistic part of group I (group II) orbits decreases (increases) monotonically with the axial field. The gain equations for the FEL configuration by adding the effect of self‐fields have been derived. The numerical calculation has been employed to analysis the gain induced by the effects of the self‐fields. It is shown that, for group I orbits the gain decreases in the presence of self‐fields and the gain decrement increases with increasing axial guide magnetic field, while for group II orbits the self‐fields enhances the gain. The gain decrement and enhancement are due to diamagnetic and paramagnetic effects of the self‐magnetic field, respectively. The comparison of the gain for electromagnetic‐wave wiggler with the gain in helical wiggler has been done (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Self-field effects on small-signal gain in two-stage free-electron lasers

Self-field effects, induced by charge and current densities of the electron beam, on gain in two-stage free-electron laser with nonuniform guide magnetic field is presented. The gain equation for small-signal has been derived analytically. The results of numerical calculations show a gain decrement for group I orbits and a gain enhancement for group II orbits, due to the self-field effects. The wiggler-induced self-magnetic field has a diamagnetic effect for group I orbits, whereas for group II, it has a paramagnetic effect. It is also found that using a nonuniform guide field, rather than a uniform one, causes the gain to increase.     

不用导引磁场的虚火花束源拉曼自由电子激光器的数值计算

采用非线笥模型对拉曼自由电子激光器进行数值模拟,发现虚火花束源自由电子激光器苛以去掉导引磁场,用小周期摇摆器,实现器件的小型化和高功率。     

Posibilities of Channelling Radiation as γ-Laser

In this paper the electron axial channeling radiation has been compared with a free electron laser (FEL),and the possibility of reforming this type of radiation as γ–laser has been discussed.introducing equivalent magnetic field to describe ~electron’s motion,the pendulum equation and energy gain of the electron longitudial motion have been obtained using interaction of the electron with the radiation field. it shows that the channeling radiation is very similar to fel, if there exists standing wave field in the crystal.     

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.     

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.     

基于激光等离子体加速的自由电子激光研究新进展

激光等离子体加速器能够在cm尺度内产生GeV量级的高品质电子束,为研制台式化自由电子激光提供驱动源。但是受限于激光等离子体加速中的难点和现有技术发展,电子束的品质难以达到自由电子激光的需求,尤其在稳定性、发散角和能散等方面,阻碍了台式化自由电子激光的研制。介绍了基于激光等离子体加速器的自由电子激光的最新进展,整理了目前高增益自由电子激光实验过程中存在的主要挑战和对应的解决方案与实验进展,并展望未来的发展方向。最近的研究结果证明,通过控制和优化激光等离子体加速器的注入和加速过程产生的高品质电子束可以在指数增益区域实现自发辐射放大,产生高增益的辐射,这也推动基于激光等离子体加速器的自由电子激光研究进入了一个新的阶段。     

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.     

Investigation of mechanism of free electron laser through spontaneous radiation spectrum

In this paper, the mechanism of free electron laser with a guide magnetic field is investigated by analyzing spontaneous radiation spectrum of electrons. The physical relation between spontaneous radiation and stimulated radiation in FEL with a guide magnetic field is studied. It is found that this relation in FEL is similar to that in quantum lasers. The spontaneous radiation spectrum is discrete. The frequency of stimulated radiation in FEL is oneselected and amplified in the radiation spectrum.     

Effect of betatron oscillations on waveguide free electron laser gain

In this paper we analyse the spontaneous emission and gain spectrum of a waveguide free electron laser with betatron motion included in the analysis. The zero slippage condition and the small signal gain in the waveguide free electron laser is discussed.     

Quantum theory of a free electron laser for strong fields

A quantum mechanical derivation of the gain of the free electron laser is presented which starts from the exact solutions of the Klein-Gordon equation in the presence of the magnetic wiggler field and the stimulating plane wave field. The gain is obtained from the transition amplitude of the electron, which is expressed in terms of the Green's function. For comparatively weak fields the usual small signal gain results, whereas for strong fields saturation behaviour is found.Supported by Deutsche Forschungsgemeinschaft     

Generalized gain-spread expressions for the free electron laser

Starting from a many electron hamiltonian model we derive general expressions for the unsaturated gain and spread of a free electron laser that are valid for arbitrary magnetic field configurations. The general validity of a well known gain-spread relation is demonstrated.     

Three-dimensional numerical investigations of the laser-beam interactions in an undulator

Laser-beam interaction in an undulator is commonly suggested in the development of free electron laser(FEL)schemes. In this paper, a three-dimensional algorithm is developed to assist in laser-beam interaction simulation in an undulator, which is built on the basis of the fundamentals of electrodynamics, i.e.the electron's behavior is determined by the magnetic field and the laser electric field in the time domain. On the basis of the algorithm, the detuning effect in a laser heater, the carrier envelope phase effect of a few-cycle laser in attosecond X-ray FEL schemes and output wavelength tuning in a high gain harmonic generation FEL are numerically discussed.     

拉曼型自由电子激光器中相对论电子运动稳定性的比较研究

拉曼型自由电子激光器作为一种兆瓦级高功率毫米波、太赫兹波辐射源, 其电子的运动稳定性对整体器件的性能至关重要.本文采用科尔莫戈罗夫熵方法, 以典型的麻省理工学院公布的实验数据为例, 比较研究拉曼型正向导引磁场和反向导引磁场两类自由电子激光器中相对论电子的运动稳定性. 结果表明:摇摆器绝热压缩磁场对电子运动的稳定性无实质性影响, 但对电子运动影响大; 电子束自身场在拉曼型正向导引磁场自由电子激光器中使电子运动稳定性变差, 而在拉曼型反向导引磁场自由电子激光器中则可改善电子运动稳定性. 关键词： 拉曼型自由电子激光器 相对论电子运动稳定性 科尔莫戈罗夫熵 电子束自身场     

Optimization of the lattice function in the planar undulator applied for terahertz FEL oscillators

Since the beta function of the electron beam within the undulator has a great influence on the power gain of the free electron laser (FEL), optimization of the undulator lattice becomes important. In this paper, the transfer matrix of the planar undulator is obtained from differential equations of the electron motion. Based on this, the lattice function of the planar undulator in a terahertz FEL oscillator proposed by Huazhong University of Science and Technology (HUST-FEL) is optimized and the expressions of the average beta function are derived. The accuracy of the optimization result was confirmed well by the numerical method. The application range of this analytical method is given as well. At last, the emittance growth in the horizontal direction due to the attenuation of the magnetic field is discussed.     

Multiphoton analysis of the free electron laser

A model of the free electron laser is proposed which is based on the classical current of the electron in the wiggler field interacting with a quantized radiation field. To calculate the gain, the quantum recoil for the processes of n-photon emission and absorption must be put in by hand from kinematical considerations. Apart from a spontaneous emission term the gain agrees essentially with the usual small signal expression, for the radiation field being in either an eigenstate of photon number or in a coherent state. The distribution of the electrons after the interaction is, however, essentially quantum mechanical.