A slow wave free-electron laser in a longitudinal wiggler field

Linearized Vlasov-Maxwell equations are solved to obtain the growth rate of free electron laser instability from a tenuous relativistic electron beam propagating in a partially dielectric loaded waveguide immersed in combined axial and longitudinal wiggler magnetic fields. The instability appears via cyclotron resonance interactions for wave perturbations very close to w-kV_z-w_c=nk ₀V_Z where n is the general harmonic number. For n=0, the gain is similar to a slow wave cyclotron amplifier. For n⩾1, the growth rate is substantially larger than the standard slow wave free electron laser scheme utilizing a transverse wiggler field     

Plasma-aided radiation guiding in a free-electron laser

The introduction of a plasma in a free-electron laser (FEL) helps radiation guiding via nonlinear refraction. At high-radiation power density, when oscillatory electron velocity is comparable to the electron thermal velocity, the radiation pushes plasma radially out, forming a depleted plasma duct and guiding the radiation. The radius of the self-trapped laser is ~c/ω_po, where ω_po is the unperturbed plasma frequency and c is the velocity of light in vacuum     

A free-electron laser amplifier with a spatially varying wiggler

We discuss the dynamics of the free-electron laser in the high gain Compton regime with a linearly decreasing wiggler wave-length, and give evidence for the possibility of a much greater amplification of an input signal with the selected wiggler geometry over the more traditional uniform wiggler configuration. In addition, our numerical results suggest the existence of an interesting transition in the FEL dynamical evolution.     

小周期波荡器自由电子激光器：数值模拟与实用化设计

采用三维自洽非线性理论计算方法,针对小周期波荡器自由电子激光器进行了数值模拟计算研究.结果表明,在我所现有脉冲线加速器基础上,采用周期为10mm的波荡器,可获得输出功率为20MW,波长为1.7mm的自由电子激光.最后给出实用化总体实验设计方案.     

Laser wiggler beat wave in a plasma

It is shown that by combining a laser wave and an electron beam propagating through a plasma inside a wiggler: (i) Electrons can be accelerated to high energies. For usual laser frequencies and wiggler wavelengths, plasma densities are in the range 10¹⁵–10¹⁶ cm^-3. The plasma density fluctuation in the longitudinal wave suffices to obtain electron energies of several hundred MeV over short distances. (ii) High frequency radiation can be amplified.     

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.     

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.     

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.     

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.     

On the beam transport of a helical coaxial wiggler for a free-electron laser

Dynamics of an electron beam in a helical coaxial wiggler is studied. It is observed that the electrons perform betatron oscillation in a potential well that reflects the effective radiation pressure of the wiggler field and a centrifugal force due to an average azimuthal drift.     

A slow wave free-electron laser

A simple calculation of a free-electron laser in the Compton regime that uses a dielectric-lined waveguide is presented. The introduction of a dielectric lining in a free-electron laser considerably reduces the requirements on beam voltage for generating a given frequency ω₁=k₀c/(1 - v_b η/c), where k₀ is the wiggler wave period η is the effective index of refraction (1<η<√ϵ) and ϵ is the permittivity. The system supports electromagnetic waves whose Poynting flux is largely concentrated in the dielectric; hence the electron beam is required to propagate close to the dielectric lining. The mode structure and dispersion behavior of the guiding system without the beam are discussed. a thin annular beam is introduced, and a perturbation theory is used to obtain the frequency and growth rate of radiation     

The effects of the guide field and tapered wiggler in free-electron laser

The interaction between electromagnetic field and electron beam was investigated numerically in a free-electron laser, using a new simulation code which consist of the three-dimensional electron motion, amplitude and phase of emitted radiation. The maintenance of the quality and stability of electron beam and the resonance condition through the wiggler is important to obtain the high gain and the high efficiency. But the electron orbits diverge and become unstable, and the resonance condition is not preserved because of the three-dimensional effects on the off-axis electron and the conversion of electron energy to electromagnetic field. To prevent those defects and improve the efficiency compared with the conventional case, we used the new methods such as the axial-guide field and tapered wiggler.     

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.     

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 orbit in a combined plasma wave wiggler and an axial guidemagnetic field free electron laser near magnetoresonance

The nonlinear electron orbit dynamics is presented for a combined electrostatic plasma wave wiggler and an axial guide magnetic field free electron laser near magnetoresonance. The perpendicular orbit equation is derived and simplified identical to the wave-driven nonlinear oscillator equation but with different expressions of parameters. The nonlinear effect induced by the inclusion of β_⊥² in the relativistic factor γ is dominant in governing the perpendicular wiggling velocity and the orbit excursion even in the case of β_⊥²≪β_∥² , where γ=(1-β₁²-β_∥ ²)^-1/2. The dependence of the maximum perpendicular wiggling velocity and the orbit excursion on the wiggler constant, the wiggler frequency, and the initial parameters of motion is given analytically     

Effects of self-fields on electron trajectory and gain in planar wiggler free-electron lasers with two-stream and ion-channel guiding

The effects of self-fields on electron trajectories and gain in planar wiggler free-electron lasers with two-stream and ion-channel guiding are investigated. An analysis of the two-stream quasi-steady-state electron trajectories is given by solving the equation of motion in the presence of ion-channel guiding and the planar wiggler. The electron trajectories and the gain are derived. The stability of the trajectories, the characteristics of the linear gain, and the normalized maximum gain are studied numerically. The numerical calculations show that there are eight group trajectories rather than the two groups reported in the absence of the self-fields. It is also shown that the normalized gain group seven （G7） decreases while the rest increases with the increase in normalized ion-channel frequency. The two-stream instability and the self-field lead to a decrease in the maximum gain, except for G7.