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.     

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)     

Quantum regime of a plasma‐wave‐pumped free‐electron laser in the presence of an axial magnetic field

The quantum regime of a plasma‐whistler‐wave‐pumped free‐electron laser (FEL) in the presence of an axial‐guide magnetic field is presented. By quantizing both the plasma whistler field and axial magnetic field, an N‐particle three‐dimensional Hamiltonian of quantum‐FEL (QFEL) has been derived. Employing Heisenberg evolution equations and introducing a new collective operator which controls the vertical motion of electrons, a quantum dispersion relation of the plasma whistler wiggler has been obtained analytically. Numerical results indicate that, by increasing the intrinsic quantum momentum spread and/or increasing the axial magnetic field strength, the bunching and the radiation fields grow exponentially. In addition, a spiking behavior of the spectrum was observed with increasing cyclotron frequency which provides an enormous improvement in the coherence of QFEL radiation even in a limit close‐to‐classical regime, where an overlapping of these spikes is observed. Also, an upper limit of the intrinsic quantum momentum spread which depends on the value of the cyclotron frequency was found.     

Electron distribution function and recombination coefficient in ultracold plasma in a magnetic field

The electron distribution function and diffusion coefficient in energy space have been calculated for the first time for a weakly coupled ultracold plasma in a magnetic field in the range of magnetic fields B = 100?50000 G for various temperatures. The dependence of these characteristics on the magnetic field is analyzed and the distribution function is shown to depend on the electron energy shift in a magnetic field. The position of the “bottleneck” of the distribution function has been found to be shifted toward negative energies with increasing magnetic field. The electron velocity autocorrelators as a function of the magnetic field have been calculated; their behavior suggests that the frequency of collisions between charged particles decreases significantly with increasing magnetic field. The collisional recombination coefficient α _B has been calculated in the diffusion approximation for a weakly coupled ultracold plasma in a magnetic field. An increase in magnetic field is shown to lead to a decrease in α _B and this decrease can be several orders of magnitude.     

Nonlinear structure of Gaussian laser beam in an axial non-uniform collisional plasma

Nonlinear structure of Gaussian laser beam in axial non-uniform underdense collisional plasma is investigated. Due to the combination effect of nonlinear ohmic heating and non-uniform of plasma, and which it modifies electrons temperature and density distribution. On the one hand, due to the effect of the nonlinear ohmic heating, electron temperature and electron density oscillations become highly peaked. On the other hand, due to add the influence of non-uniform of plasma, lead to the departure from sinusoidal shape of electrons temperature, electron density and electromagnetic fields distributions. With the increase of laser intensity, these nonlinear variations become more and more obvious, and their oscillations wavelength decrease.     

Inverse Bremsstrahlung absorption coefficient in inhomogeneous plasma with nonextensive electron velocity distribution and Tsallis exponential electron density profile

Inverse bremsstrahlung (collisional) absorption of the laser beam is studied in plasma with a generalized (q-nonextensive) electron velocity distribution and some kind of generalized electron density profile. It is shown that for some values of parameters designating the q-nonextensive electron velocity distribution function and its generalized density profile, the calculated absorption coefficient reduces to the already known cases with Maxwellian velocity distribution with linear and exponential density profiles.     

Attenuation properties of EM wave by magnetized nonuniform plasma slab coated on perfect conductor plane

The total amplitude reflection coefficient of EM wave in a nonuniform plasma slab coated on perfect conductor plane is newly derived by using the scattering matrix method (SMM), and the attenuation is calculated. Three types of plasma electron density profile, that is the hyperbolic, sinusoidal, and linear profiles, are used. The external magnetic field and plasma parameters such as the maximum electron density and collision frequencies are discussed to calculate the attenuation of EM wave. The calculation results show that the plasma electron density profile and maximum electron density exert a large effect to the attenuation of EM wave and the attenuation under the uniform external magnetic field is taken place by the electron cyclotron resonance absorption, the up hybrid resonance absorption and geometric resonances absorption.     

磁场预增强的锥型波荡器

研究了波荡器磁场增强对提高自由电子激光器效率的影响。模拟计算发现采用磁场增强波荡器能使自由电子激光器的效率提高到１７．６％，采用磁场预先增强而后又增弱的锥型波荡器则能获得高达４３．３￥的输出效率，自由电子激光器的功率得到进一步的提高。     

电磁铁摇摆器磁场的二维数值计算

本文根据泊松方程用数值计算给出了电磁铁摇摆器的二维磁场分布,定量地讨论了磁极形状、磁隙大小、周期长短和电流大小等因素对峰值磁场强度的影响,重点讨论了如何根据二维磁场分布选择磁极形状才能提高峰值磁场强度和抑制磁饱和的问题。将计算的二维磁场分布和摇摆器磁场的理想波形相比较,可以帮助我们确定进入摇摆器的束流半径应该控制的范围。在对电磁铁摇摆器磁场二维数值计算的基础上,还探讨了适用ATA电子束的PALADIN摇摆器用于ETA电子束带来的结构设计和材料选择等问题。     

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.     

Temperature Effects on the Beat Heating of a Collisional Magnetoplasma

The beat heating of a magneto-plasma by two antiparallel electromagnetic waves at different temperatures is examined. The effects of plasma temperature, plasma electron collisions, plasma ion collisions and magnitude and direction of the magnetic field on the excitation of plasma electron waves and plasma ion waves are studied. A formula for the power absorption density of the plasma by using Maxwell's equations in conjuction with continuity and momentum equation. including collisions and pressure tensor terms, is derived. The contribution of the plasma temperature to the power absorption density, both at low and high beat frequencies, of the collisional and the non-collisional magnetised plasmas is found very significant and is illustrated numerically. The inclusion of pressure tensor term in the momentum equation is also found to cause characteristic changes in the power absorption density of the plasma with the orientation of magnetic field.     

Microwave ponderomotive action on the inhomogeneous collisionless and collisional plasmas

The nonlinear interaction of a high-power microwave (MW) with an unmagnetized inhomogeneous plasma is investigated in collisionless and collisional regimes. The electron density distribution and the nonlinear wave equation in an inhomogeneous plasma are obtained by taking into account the ponderomotive force due to the high-power MW. It is shown that the electron density distribution becomes very steepened in the presence of the ponderomotive force. In the collisional regime, the expression for electron temperature is also found by considering ohmic heating. It is indicated that the amplitude of oscillations of the electron temperature and dielectric permittivity increases and the wavelength of these oscillations decreases with increasing energy flux, hence modulation occurs.     

磁场逐渐增强的摇摆器

研究了用磁场增强摇摆器来提高自由电子激光器效率的机制．采用KMR方程，考虑空间电荷效应，模拟计算发现自由电子激光器的效率有了很大的提高，而且电子束能散度越大，对提高自由电子激光器效率越有帮助．因此采用磁场增强摇摆器能充分利用加速器的能量来莸得更高的自由电子激光器能量 关键词：     

脉冲CO2激光烧蚀锡靶等离子体的数值研究

使用一维辐射流体力学程序MULTI模拟了脉冲CO2激光烧蚀平面锡靶的过程,研究了脉冲宽度、峰值功率密度、靶材初始密度对锡等离子体电子密度、电子温度的时空分布的影响,并结合统计分析得到最有利于产生13.5 nm 极紫外光的激光脉冲宽度。模拟结果表明,脉冲宽度为100~200 ns的长脉冲激光产生的等离子体有利于实现极紫外输出的最佳条件,通过分析等离子体的电子密度、电子温度的分布对这一结论进行了解释。临界电子密度区域有效吸收了脉冲能量,而低密度的羽辉对激光与极紫外辐射的吸收很少。采用长脉冲激光,使得辐射极紫外等离子体持续时间更长,是提高极紫外辐射效率的有效手段。同时模拟还发现,靶材初始密度对等离子体参数的影响不大。     

An off-axis 50-period electromagnet wiggler for millimeter-wavefree-electron laser experiment

An off-axis 50-period planar, short-wavelength (~10 mm) electromagnet wiggler is developed and characterized for millimeter-wave generation using a sheet electron beam in a free-electron laser experiment. Three-dimensional (3-D) magnetic field measurements of the electromagnet wiggler have been carried out. The measured wiggler magnetic field is 0.16 G/A ±3% while the mean value of wiggler wavelength is 0.998±3% cm. Due to off-axis arrangement of poles, there is a magnetic mirror field in the X direction, to confine the sheet beam     

Effects of relativistic and ponderomotive nonlinearities on the interaction of high-power laser beam with an inhomogeneous warm plasma

The influence of relativistic-ponderomotive nonlinearities and the plasma inhomogeneity on the nonlinear interaction between a high-power laser beam and a warm underdense plasma are studied. It is clear that the relativistic ponderomotive force and the electron temperature modify the electron density distribution and consequently change the dielectric permittivity of the plasma. Therefore, by presenting the modified electron density and the nonlinear dielectric permittivity of the warm plasma, the electromagnetic wave equation for the propagation of intense laser beam through the plasma is derived. This nonlinear equation is numerically solved and the distributions of electromagnetic fields in the plasma, the variations of electron density, and plasma refractive index are investigated for two different background electron density profiles. The results show that the amplitude of the electric field and electron density oscillations gradually increase and decrease, during propagation in the inhomogeneous warm plasma with linear and exponential density profiles, respectively, and the distribution of electron density becomes extremely sharp in the presence of intense laser beam. It is also indicated that the electron temperature and initial electron density have an impact on the propagation of the laser beam in the plasma and change the plasma refractive index and the oscillations' amplitude and frequency. The obtained results indicate the importance of a proper choice of laser and plasma parameters on the electromagnetic field distributions, density steepening, and plasma refractive index variations in the interaction of an intense laser beam with an inhomogeneous warm plasma.     

Experimental and numerical studies of sheet electron beampropagation through a planar wiggler magnet

Detailed experimental studies on sheet relativistic electron beam propagation through a long planar wiggler are reported and compared with numerical simulations. The planar wiggler has 56 periods with a period of 9.6 mm. Typically, the wiggler field peak amplitude is 5 kG. The experimental efforts are focused on controlling the deviation of the beam toward the side edge of the planar wiggler along the wide transverse direction. It is found that a suitably tapered magnetic field configuration at the wiggler entrance can considerably reduce the rate of deviation. The effects of the following techniques on beam transport efficiency are discussed: side focusing, beam transverse velocity tuning at the wiggler entrance, and beam spread limiting. High beam transport efficiency (almost 100%) of a 15-A beam is obtained in some cases     

Pulse Slippage of Resonant Third Harmonic Generation in Electron-Hole Plasma

Effect of pulse slippage on resonant third harmonic generation of a short pulse laser in electron-hole plasma in the presence of wiggler magnetic field has been investigated. The group velocity mismatch of the third harmonic pulse and the fundamental pulse is significant in electron hole plasma. As the third harmonic pulse has higher group velocity than that of fundamental pulse, therefore, it moves faster than the fundamental pulse. It gets slipped out of the domain of fundamental pulse and its amplitude saturates. Phase matching condition is satisfied by applying wiggler magnetic field,which provides additional angular momentum to the third harmonic photon to make the process resonant. Enhancement in the efficiency of third harmonic generation of an intense short pulse laser in electron-hole plasma embedded with a magnetic wiggler is seen.     

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     

Nonlinear interaction of electron beam with magnetized warm plasma

The nonlinear interaction of electron beam with inhomogeneous semi-bounded collisional magnetized warm plasma under external static magnetic field has been studied. The second-harmonic generation at the beam entrance into the plasma is considered. This process leads to an increase in the amplitude of the electric field in the inhomogeneous region and, in turn, to higher absorption.