Effects of self-fields on electron trajectory and gain in two-stream electromagnetically pumped free-electron laser with ion channel guiding

A theory for the two-stream free-electron laser with an electromagnetic wiggler (EMW) and an ion channel guiding is developed.In the analysis,the effects of self-fields have been taken into account.The electron trajectories and the small signal gain are derived.The stability of the trajectories,the characteristics of the linear gain and the normalized maximum gain are studied numerically.The dependence of the normalized frequency ω corresponding to the maximum gain on the ion-channel frequency is presented.The results show that there are seven groups of orbits in the presence of the self-fields,which are similar to those reported in the absence of the self-fields.It is also shown that the normalized gains of 2 groups decrease while the rest increase with the increasing normalized ion-channel frequency.Furthermore,it is found that the two-stream instability and the self-field lead to a decrease in the maximum gain except for group 4.     

Effects of self-fields on gain in two-stream free electron laser with helical wiggler and an axial guiding magnetic field

The theory for the two-stream free electron laser （FEL） consisting of a relativistic electron beam transporting along the axis of a helical wiggler in the presence of an axial guiding magnetic field is proposed and investigated. In the analysis, the effects of self-fields are taken into account. The electron trajectories and the small signal gain are derived. The characteristics of the linear-gain and the normalized maximum gain are studied numerically. The results show that there are seven stable groups of orbits in the presence of self-fields instead of two groups reported in the absence of the self-fields. It is also shown that the normalized gains of three groups decrease while the rest increase with the increasing of normalized cyclotron frequency g20. Furthermore, it is found that the two-stream instability and the self-field lead to a decrease in the maximum gain except for group 3. The results show that the normalized maximum gain is enhanced in comparison with that of the single stream.     

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.     

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.     

The effects of self-fields on the electron trajectory and gain in a two-stream electromagnetically pumped free-electronlaser with axial guiding field

A theory of a two-stream free-electron laser in a combined electromagnetic wiggler (EMW) is developed, in which we use an axial-guide magnetic field and take into account the effects of the self-fields. The electron trajectories and the small signal gain are derived. The stability of the trajectories, the characteristics of the linear-gain, and the normalised maximum gain are studied numerically. The results show that there are nine stable groups of orbits in the presence of self-fields instead of seven groups reported in the absence of the self-field. It is also shown that the normalised gains of four groups of the orbits are decreasing and those for the rest of them are increasing with growing \barΩ₀. Furthermore, it is found that the two-stream laser with self-field enhances the maximum gain in comparison with the single stream case.     

The effects of self-fields on the electron trajectory in a two-stream free electron laser with a helical wiggler and an axial guiding magnetic field

A theory for the two-stream free-electron laser(TSFEL) with a helical wiggler and an axial guide magnetic field is developed.In the analysis,the effects of self-fields are taken into account.An analysis of the two-stream steady-state electron trajectories is given by solving the equation of motion.Numerical calculations show that there are seven groups of orbits in the presence of self-fields instead of two groups reported in the absence of self-fields.The stability of the trajectories is studied numerically.     

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.     

Effects of self-fields on dispersion relation and growth rate in two-stream electromagnetically pumped free electron laser with axial guide magnetic field

A theory for a two-stream free-electron laser （FEL） with an electromagnetic wiggler （EMW） and axial guide magnetic field is developed. In the analysis, the effects of self-fields are taken into account. The growth rate is derived. The characteristics of the growth rate are studied numerically. The dependence of the normalized wave number, which corresponds to the maximum growth rate, on the cyclotron frequency is presented. The comparisons between the normalized maximum growth rate and its corresponding wave number normalized by employing the axial magnetic field, for the cases with and without self-fields in the two-stream FEL are studied numerically.     

波荡器入口区绝热压缩磁场分布对自由电子激光输出功率和效率的影响

本文对波荡器(Wiggler)入口区绝热压缩磁场分布对自由电子激光输出功率、增益、效率的影响,进行了非线性计算机模拟.结果表明:磁场幅值沿轴向接立方函数分布,比通常采用的正弦平方函数和平方函数这两种分布更好,更接近实验值.     

Dispersion relation and growth rate for a corrugated channel free-electron laser with a helical wiggler pump

The effects of corrugated ion channels on electron trajectories and spatial growth rate for a free-electron laser with a one-dimensional helical wiggler have been investigated. Analysis of the steady-state electron trajectories is performed by solving the equations of motion. Our results show that the presence of a corrugated channel shifts the resonance frequency to smaller values of ion channel frequency. The sixth-order dispersion equation describing the coupling between the electrostatic beam mode and the electromagnetic mode has also been derived. The dispersion relation characteristic is analyzed in detail by numerical solution. Results show that the growth rate of instability in the presence of corrugated ion channels can be greatly enhanced relative to the case of an uniform ion channel.     

Three-dimensional motion of electrons in combined realistic helical wiggler with axial guide field for free-electron laser

3-D motion of electrons with on-axis and off-axis guiding centers in realistic helical wiggler and axial guide field is analysed. It is found that purely helical orbits couldnot exist for the electrons with off-axis guiding centers, except for those with on-axis guiding centers. Perturbation solutions of the electron's velocity and orbit averaged over the cyclotron angle are derived. Our calculations indicate the divergence of the electron orbits near resonance.     

短波长自由电子激光器电子运动特性研究

短波长自由电子激光器的电子束在摇摆器中的传输通道长而狭窄, 须得电子具有良好的运动特性, 避免在传输过程中产生横向发散. 本文研究短波长自由电子激光器中超相对论电子在磁场具有横向分布的平面摇摆器中的三维运动特性, 用逐次逼近法推导相对论运动方程的解析表达式, 非线性数值计算模拟传输过程, 采用科尔莫 戈罗夫熵 方法分析运动的稳定性. 结果表明: 摇摆器磁场除使电子做周期性摇摆运动外, 还迭加了偏离轴线的横向漂移运动, 在没有外置的磁场聚焦系统情况下, 电子将偏离轴线横向发散; 但是, 恰当选取电子的横向初始速度, 可有效地防止电子运动的横向发散, 即使没有外置的磁场聚焦系统, 也能在长达10 m 的摇摆器中顺利传输, 横向位移范围不超过0.09 mm, 而且其运动是稳定的. 关键词： 短波长自由电子激光器 平面摇摆器 超相对论电子运动 运动稳定性     

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.     

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.     

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     

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.     

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.     

Electron trajectories and gain in free electron laser with ionchannel guiding

A detailed analysis of electron trajectories and gain in a helical wiggler free electron laser (FEL) with ion channel focusing using single particle dynamics is presented. Conditions for stability of electron orbit have been obtained and stable regimes have been identified. Gain has been evaluated in the low-gain-per-pass limit with the help of the self-consistent pendulum equation. It is seen that the presence of ion channel leads to significant gain enhancement under appropriate conditions     

Wave growth rate in a cylindrical metal waveguide with ion-channel guiding of a relativistic electron beam

This paper addresses the formulae and numerical issues related to the possibility that fast wave may be grown when a relativistic electron beam through an ion channel in a cylindrical metal waveguide.To derive the dispersion equations of the beam-wave interaction,it solves relativistic Lorentz equation and Maxwell’s equations for appropriate boundary conditions.It has been found in this waveguide structure that the TM 0m modes are the rational operating modes of coupling between the electromagnetic modes and the betatron modes.The interaction of the dispersion curves of the electromagnetic TM 0m modes and the upper betatron modes is studied.The growth rates of the wave are obtained,and the effects of the beam radius,the beam energy,the plasma frequency,and the beam plasma frequency on the wave growth rate are numerically calculated and discussed.     

Collective and single-electron interactions of electron beams with electromagnetic waves,and free-electron lasers

The field of radiation emission from electron beams is reviewed with special reference to work related to free-electron lasers. Different schemes of interaction in periodic structures, electromagnetic slow-wave structures, and in transverse confining force are distinguished. Various effects and devices such as traveling wave amplifiers, Smith-Purcell radiators, Cerenkov and bremsstrahlung-free electron lasers, cyclotron resonance masers, coherent bremsstrahlung and channeling radiation are discussed and the differences and relations among them are explained. A simple comprehensive model is developed to describe electron-beam interaction with an electromagnetic wave in periodic electromagnetic structures. The model is general enough to describe both collective and single-electron modes of interaction and quantum mechanical, classical and Fermi degenerate regimes. Simplified expressions are developed for the gain by stimulated emission of radiation and for gain conditions of the Smith-Purcell-Cerenkov type free-electron lasers under conditions of very thin electron beams and infinite interaction length. This research is supported by the Air Force Office of Scientific Research under contract AFOSR-76-2933