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 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.     

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.     

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.     

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.     

Instability of Two-stream Free-electron Laser with an Axial Guiding Magnetic Field

A model of two-stream Free-Electron Lasers (FEL) with an axial guiding magnetic field (AGMF) is proposed and investigated in this paper. The dispersion relation is derived employing linear fluid theory. The characteristics of dispersion relation are analyzed in detail by numerical solutions, which show that the growth rate can be considerably enhanced and the operation frequency is significantly broader with the suitable of AGMF, separation velocity and beams’ relative density factor, and the occurrences of two-stream instability in FEL are stronger due to the presence of AGMF.     

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.     

Effect of self-fields on the electron cyclotron maser instability in a dielectric loaded waveguide

The influence of self-fields on the cyclotron maser instability in a hollow electron beam propagating parallel to a uniform axial magnetic field B ₀ ê _z in a dielectric loaded waveguide is investigated. The theoretical analysis is carried out within the framework of linearized Vlasov-Maxwell equations. It is assumed that the beam is thin with the radial thickness much smaller than the beam radius. A new dispersion relation for azimuthally symmetric electromagnetic perturbation is derived and analyzed numerically. The influence of self-fields on the cyclotron maser instability in a dielectric loaded waveguide for different dielectric medium is studied. It is found that unlike the hollow waveguide the growth rate is increased by increasing self-fields. The instability band width decreases due to the increasing self-fields. The maximum growth rate increases gradually as self-fields increase as regards a different dielectric medium.     

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.     

Diamagnetic and Paramagnetic Effects in Free-Electron Lasers

The effect of high-current relativistic electron beams (REB's) on the undulator field amplitude in free-electron lasers (FEL's) is investigated. Two mechanisms of excitation of periodic magnetostatic self-fields by REB are considered: 1) a static mechanism that is realized at stationary motion of REB in the undulator field; and 2) a dynamic mechanism that is realized at signal wave amplification. The static mechanism in the absence of an axial magnetic field leads to a decrease of the total undulator field amplitude (a diamagnetic effect). The dynamic mechanism for low-density beams leads to an increase of the total undulator field amplitude (a paramagnetic effect), with a subsequent increase of electron efficiency. For high-density beams, the effect of the phase shift of the total undulator field is most essential, due to which the growth of the signal wave amplitude is limited by nonlinear mismatch of synchronism.     

Plasma effects in a free electron laser

The introduction of a plasma and a strong guide magnetic field in a free electron laser (FEL) slows down the phase velocity of radiation, significantly reducing the requirements on beam energy for generating frequencies below the electron-cyclotron frequency (ω₁≲ω_c). Around plasma resonance (ω₁~ω_p), the FEL mode couples to two-stream instability (TSI), attaining a large growth rate, comparable to that of the wiggler-free TSI. At plasma densities comparable to beam density, the beam-induced local depression in the electron density of the plasma acts as a waveguide for guiding any high-frequency radiation when the beam current is ≳17 kA     

自由电子激光的计算机模拟

本文使用1(2/2)维电磁相对论粒子程序对自由电子激光进行计算机模拟。在线性段,计算机模拟与用解析理论计算的增长率符合很好。与没有轴向引导磁场的自由电子激光相比,加一弱轴向引导磁场时,Wiggler场的强度可降得较低。加一强轴向引导磁场时,波能量达到饱和水平所需时间较短。     

Growth rate enhancement of free-electron laser by two consecutive wigglers with axial magnetic field

The operative mechanism for a free-electron laser (FEL) with two consecutive helical wigglers having opposite circular polarization in the presence of an axial magnetic field is proposed and analysed. With the help of fluid theory, a tenth-degree polynomial dispersion equation for electromagnetic and space–charge waves is derived. The results are used to illustrate and discuss the dependence of growth rate on different system parameters. Finally, it is shown that for the same system parameters the growth rate of the proposed structure is more than the growth rate of instability in a conventional FEL.     

Dispersion of multi-stream instability in quantum magnetized hot plasmas

Using the quantum hydrodynamic (QHD) equations with magnetic field on the Wigner-Maxwell system, the general dielectric tensor and dispersion equation for quantum plasmas were derived. Dispersion relations of one-, two-stream and beam-plasma instabilities in uniform quantum magnetized plasmas are investigated through the new dielectric tensor. The magnetic field which is parallel to the fluid velocity does not work on stream instabilities. The quantum and thermal effects have remarkable impact on two-stream instability. The critical wave number for beam-plasma instability with quantum effects correction is given too.     

Chaotic electron trajectories in a circular free electron laser

The motion of a relativistic electron is analyzed in the field configuration consisting of a circular wiggler magnetic field, an axial magnetic field, and the equilibrium self-electric and self-magnetic fields produced by the non-neutral electron ring. By generating Poincare surface-of-section maps, it is shown that when the equilibrium self-fields is strong enough, the electron motions become chaotic. Although the realistic circular wiggler magnetic field destroys the integrability of the electron motion as the equilibrium self-fields do, the role the latter plays to make the motions become chaotic is stronger than the former. In addition, the axial magnetic field can restrain the occurrence of the chaoticity.     

Effect of the induced magnetic field on peristaltic flow of a couple stress fluid

We have analyzed the MHD flow of a conducting couple stress fluid in a slit channel with rhythmically contracting walls. In this analysis we are taking into account the induced magnetic field. Analytical expressions for the stream function, the magnetic force function, the axial pressure gradient, the axial induced magnetic field and the distribution of the current density across the channel are obtained using long wavelength approximation. The results for the pressure rise, the frictional force per wave length, the axial induced magnetic field and distribution of the current density across the channel have been computed numerically and the results were studied for various values of the physical parameters of interest, such as the couple stress parameter γ, the Hartmann number M, the magnetic Reynolds number Rm and the time averaged mean flow rate θ. Contour plots for the stream and magnetic force functions are obtained and the trapping phenomena for the flow field is discussed.     

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.     

Linear Theory of Free Electron Laser with a Plasma-Loaded Cylindrical Waveguide

The dispersion characteristics of plasma–loaded free-electron laser has been analyzed using linear fluid model. The device under consideration consists of the cylindrical metallic waveguide, completely filled with background plasma and a relativistic electron beam which passes through a helical wiggler magnetic field. The result predicts that reasonable plasma density tends to improve the growth rate of the low-frequency optical wave of FEL and causes an shiftup in the operating frequency, However it has little effect on the growth rate of the high-frequency wave. In the plasma–loaded FEL, for the FEL oscillator, it may be tuned by varying the plasma density; and for the FEL amplifier, the wider frequency bandwidth is gained. A critical density n ^c _p for the background plasma density is found.     

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)