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.     

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.     

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.     

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.     

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.     

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.     

Focusing effect and modulation mechanism of the beam self-fields on the electronʼs Larmor rotation in a free-electron laser with an axial guide magnetic field

It is revealed that at anti-resonance in a free-electron laser with a reversed guide magnetic field, the beam self-fields can act to focus the beam transport and prevent the electrons from striking on the waveguide wall before the wiggler exit. It is found that the focusing function results from the modulation of the periodically-varying self-field tangential and normal components on the electron?s Larmor rotation. As a potential application, substantial improvement of the wave gain and output power at anti-resonance could be expected, since the beam current loss can be obviated by using this modulation mechanism.     

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.     

反向导引磁场自由电子激光中平衡态电子相轨道

考虑电子束自身场情况下，给出了反向导引磁场自由电子激光中平衡态电子运动的一种正则描述。证明了在可积极限下，不动点附近相轨道的稳定性；并采用美国麻省理工学院的反向导引场自由电子激光实验参数，计算了不同束流强度下的Ｐｏｉｎｃａｒé截面。结果表明，即使自身场相当强（束流强度达到６０００Ａ），平衡态电子的相轨道仍保持其规则性，相空间没有出现混沌，这说明在自由电子激光器中，利用反向导引磁场可以获得比传统的采用正向导引磁场更好的电子束质量，从而改善器件的输出性能。 关键词：     

Gain calculation of a free-electron laser operating with a non-uniform ion-channel guide

Amplification of an electromagnetic wave by a free electron laser (FEL) with a helical wiggler and an ion channel with a periodically varying ion density is examined. The relativistic equation of motion for a single electron in the combined wiggler and the periodic ion-channel fields is solved and the classes of possible trajectories in this configuration are discussed. The gain equation for the FEL in the low-gain-per-pass limit is obtained by adding the effect of the periodic ion channel. Numerical calculation is employed to analyse the gain induced by the effects of the non-uniform ion density. The variation of gain with ion-channel density is demonstrated. It is shown that there is a gain enhancement for group I orbits in the presence of a non-uniform ion-channel but not in a uniform one. It is also shown that periodic ion-channel guiding is used to reach the maximum peak gain in a low ion-channel frequency (low ion density).     

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.     

Stochastic Resonance in a Single-Mode Laser Driven by Pump Noise and Quantum Noise with Cross-Correlated Real and Imaginary Parts

We present an analytic investigation of the signal-to-noise ratio (SNR) by studying a signal modulated model of a single-mode laser system driven by pump noise and quantum noise with correlated real and imaginary parts,and find there is a maximum in the curve of the dependence of SNR upon the cross-correlation coefficient λq between the real part and the imaginary part, i.e., stochastic resonance appears in the SNR vs. λq curve. Moreover, when the SNR is at the maximum, the cross-correlation coefficient λq = O, which is coincidentally at the minimum of the mean normalized intensity fluctuation. The influences on stochastic resonance by the intensities of the pump and the quantum noise, the amplitude of the modulation signal, and the net gain of the laser are also studied. Furthermore, in order to ensure that the results obtained in this paper is reliable, the valid range for the linear approximation method is discussed.     

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     

Deposition and characterization of YBCO/CeO2/YSZ/CeO2 multilayers on biaxially textured Ni substrates

CeO2/YSZ/CeO2 buffer layers were deposited on biaxially textured Ni substrates by pulsed laser deposition. The influence of the processing parameters on the texture development of the seed layer CeO2 was investigated. Epitaxial films of YBCO were then grown in situ on the CeO2/YSZ （yttria-stabilized ZrO2）/CeO2-buffered Ni substrates. The resulting YBCO conductors exhibited self-fleld critical current density Jc of more than 1 MA/cm^2 at 77K and superconducting transition temperature Tc of about 91K.     

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)     

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.     

非线性共振及束晕-混沌的场强参数特性

通过计算和分析周期聚焦磁场强度和表征束自生场强度的束导流系数的变化对强流粒子束运动特征的影响,系统研究了强流粒子束的非线性共振和束晕现象。采用庞加莱截面技术对束核包络振荡及其单粒子运动轨迹进行了数值模拟,清楚地展示了不同情况下束核包络非线性振荡以及对应的试验粒子空间分布。结果表明:束核自生场使得束核包络发生非线性振荡,随着束核自生场和聚焦磁场的增加,伴随着束核共振岛的出现,单粒子空间分布出现越来越多的束晕粒子。     

Tracking individual electron trajectories in a high harmonic spectrum

The harmonic spectrum generated by a few-cycle laser pulse propagating through a gas jet is calculated. Two complementary atomic response models are used, one based on the time-dependent Schrödinger equation and the other on quantum orbits in which only a single pair of electron trajectories are taken into account. The role played by individual electron trajectories in determining particular features of the spectrum are considered and phase-matching maps are used to help understand their structure. A method based on this connection is proposed for diagnosing the carrier-envelope phase and the pulse duration of the incident laser field.