Plural interactions of space charge wave harmonics during the development of two-stream instability

We construct a cubically nonlinear theory of plural interactions between harmonics of the growing space charge wave(SCW) during the development of the two-stream instability. It is shown that the SCW with a wide frequency spectrum is formed when the frequency of the first SCW harmonic is much lower than the critical frequency of the two-stream instability.Such SCW has part of the spectrum in which higher harmonics have higher amplitudes. We analyze the dynamics of the plural harmonic interactions of the growing SCW and define the saturation harmonic levels. We find the mechanisms of forming the multiharmonic SCW for the waves with frequencies lower than the critical frequency and for the waves with frequencies that exceed the critical frequency.     

Forming of Space Charge Wave with Broad Frequency Spectrum in Helical Relativistic Two-Stream Electron Beams

We elaborate a quadratic nonlinear theory of plural interactions of growing space charge wave(SCW) harmonics during the development of the two-stream instability in helical relativistic electron beams. It is found that in helical two-stream electron beams the growth rate of the two-stream instability increases with the beam entrance angle. An SCW with the broad frequency spectrum, in which higher harmonics have higher amplitudes, forms when the frequency of the first SCW harmonic is much less than the critical frequency of the two-stream instability.For helical electron beams the spectrum expands with the increase of the beam entrance angle. Moreover,we obtain that utilizing helical electron beams in multiharmonic two-stream superheterodyne free-electron lasers leads to the improvement of their amplification characteristics, the frequency spectrum broadening in multiharmonic signal generation mode, and the reduction of the overall system dimensions.     

Nonlinear harmonic generation in free-electron lasers with helical wigglers

It is widely believed that harmonics are suppressed in helical wigglers. However, linear harmonic generation (LHG) occurs by an azimuthal resonance that excites circularly polarized, off-axis waves, where the hth harmonic varies as exp((ihtheta). Nonlinear harmonic generation (NHG) is driven by bunching at the fundamental and has different properites from LHG. While NHG has been studied in planar wigglers, there has been no analysis of NHG in helical wigglers. The 3D simulation code medusa has been modified for this purpose, and it is shown that NHG is substantial in helical wigglers and that the even and odd harmonics have comparable intensities.     

Superheterodyne electron-wave free-electron lasers

A new class of free electron lasers (electron wave superheterodyne FEL) has been described. They differed from traditional ones by construction based on utilization of one of electron wave (plasma-beam, two-stream and others) instability mechanisms. In this case a parametrical interaction mechanism was used only for transformation of the longitudinal beam waves into the transverse electromagnetic ones. Nonlinear superposition the electron wave and parametric instabilities was interpreted as an effect of superheterodyne amplification.     

Production of nonisothermal electrons and Langmuir waves because of colliding ion holes and trapping of plasmons in an ion hole

We present new simulation studies exhibiting production of nonisothermal electron distributions and Langmuir waves by colliding ion holes and trapping of plasmons in an ion hole. We find that, during head-on ion hole collisions, streams of accelerated electrons are produced by the electrostatic potentials supporting the ion holes. Subsequently, Langmuir waves are excited by a two-stream instability involving energetic electron beams. The resulting Langmuir waves can be trapped in an ion hole. The present ion-hole-Langmuir wave interactions are unique kinetic phenomena which can be dealt with a Vlasov code, which we developed recently. The results can have relevance to the understanding of particle and field data that are forthcoming from different spacecraft missions in Earth's auroral ionosphere and the magnetosphere.     

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.     

S波段相对论Klystron双流放大器的粒子模拟

 相对论双流放大器是一种结构简单、高增益、高效率的高功率微波器件,它的主要作用机制是两个同心环形电子束之间的双流互作用。利用MAGIC粒子模拟程序,对S波段的相对论双流放大器进行了粒子模拟,研究了相对论双流放大器的双流互作用机制,进一步认识了作为相对论双流放大器的放大机制的双流不稳定性,为国内开展类似器件的研究打下了良好的基础。     

Two-stream instabilities in degenerate quantum plasmas

The quantum effects on the plasma two-stream instability are studied by the dielectric function approach. The analysis suggests that the instability condition in a degenerate dense plasma deviates from the classical theory when the electron drift velocity is comparable to the Fermi velocity. Specifically, for a high wave vector comparable to the Fermi wave vector, a degenerate quantum plasma has larger regime of instability than predicted by the classical theory. A regime is identified, where there are unstable plasma waves with frequency 1.5 times of a normal Langmuir wave.     

无碰撞等离子体中电子束流不稳定性的时空演化研究

应用二、三维相对论电磁粒子模拟程序研究双电子束流在无碰撞等离子体中传播引起的横向 电磁(Weibel类型)不稳定性和纵向静电不稳定性的发展演化过程.讨论了纯粹Weibel不稳定 性的发生和非线性饱和过程，观察到电流束合并、磁场重联等引起的电子横向加热现象.研 究了电流束传播方向激发的静电场对快电子束传播的影响，观察到其导致的束的横向调制、 磁场通道破坏现象.对这些过程的细致研究对更好的理解快点火物理中自生磁场的产生、快 电子输运等过程有重要意义.     

扭摆器中的微束团不稳定性

用理论和数值的方法, 首次研究了扭摆器中相干同步辐射效应诱发的微束团不稳定性. 这一不稳定性只存在于小能散的情况, 并当电子能量或峰值磁场取特定值时, 不稳定度达到最大值. 在BFEL的扭摆器中, 可能有轻微的不稳定性存在; 在CTF的扭摆器中, 则不会有不稳定性发生.     

二维双流不稳定性静电粒子模拟

为研究双温电子等离子体中束流不稳定性的演化过程,用二维粒子模拟(PIC)代码对双温电子束流不稳定性进行了模拟,其中泊松方程用松弛迭代法求解,代码满足电荷守恒、动量守恒和能量守恒条件。在电子双流不稳定性的非线性演化过程中,得到相空间的空洞结构,实空间也相应出现了电子空洞。给出了不稳定性增长率以及相应色散关系。     

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.     

Stability of the Driving Bunch in the Plasma Wakefield Accelerator

We investigate the stability of the driving electron or positron beam in the plasma wakefield accelerator (PWFA). Although the beam is subject to self-focusing, filamentation, and two-stream instability, we find that all of these can be stabilized by introducing thermal energy and an axial magnetic field.     

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.     

Return current instability and its effects on beam-plasma system

The return current induced in a plasma by a relativisitc electron beam generates a new electron-ion two-stream instability (return current instability). Although the effect of these currents on the beam-plasma e-e instability is negligible, there exists a range of wave numbers which is unstable only to return current (RC) instability and not to e-e instability. The electromagnetic waves propagating along the direction of the external magnetic field, in which the plasma is immersed, are stabilized by these currents but the e.m. waves with frequencies,ω ²≪Ω _e ² ≪ω _pe ² (Ω _e andω _pe being cyclotron and plasma frequency for the electrons of the plasma respectively) propagating transverse to the magnetic field get destabilized. Heuristic estimates of plasma heating, due to RC instability and due to decay of ion-acoustic turbulence generated by the return current, are made. The fastest time scale on which the return current delivers energy to the plasma due to the scattering of ion-sound waves by the electrons can be ∼ω _pi ⁻¹ (ω _pi being the plasma frequency for the ions).     

Anisotropic fast electron emission from a microwave irradiated plasma slab

Experimental measurements of the anisotropic electron emission from a microwave irradiated plasma slab are presented. The indicate that electron emission is due to the occurence of the oscillating two-stream instability.     

Kinetic Nonlinear Buneman's Instability in Field-Free Isothermal Collisonal Plasma

A nonlinear dispersion relation is derived and solved for a 1-D electron-ion two-stream (Buneman) instability excited in an isothermal field-free plasma. The major nonlinear mechanism is the qualilinear modification of the background distribution function. We take into consideration the effect of Coulomb collisions which describes the broadening of the Cherenkov interaction of waves with particles. Nonlinear effects seem to lead, in field-free plasma, to the increase in the current velocity and consequently, to the growth of the instability and a rapid turbulent heating of plasma electrons. The methods used here to solve the Vlasov's kinetic equation may also be used to investigate other types of current micro-instabilities in plasmas.     

Splitting Scheme Integration of the Two-and-One-Half-Dimensional Vlasov Equation

A numerical splitting scheme technique is applied to the integration of the Vlasov equation in two-space and three velocity dimensions. Calculations are performed for a cold, stationary ion, mobile electron plasma in the presence of a constant external magnetic field. Results for Landau damping and the two-stream instability are presented in both one and two velocity dimensions. The Landau damping results show a plateau structure in the electron velocity distribution function in both the parallel and perpendicular directions formed as a result of the damping of a high initial electric field propagating at 45° to the parallel velocity axis. The two-stream velocity distribution function shows pitch angle scattering and velocity diffusion for an electron beam initially propagating at 45° to the magnetic field direction through a low-temperature equal density background. The two-stream distribution function evolves to a stable quasi-isotropic plateau structure similar to that found in auroral sounding rocket data.     

Oscillating two-stream instability of laser wakefield-driven plasma wave

The laser wakefield-driven plasma wave in a low-density plasma is seen to be susceptible to the oscillating two-stream instability (OTSI). The plasma wave couples to two short wavelength plasma wave sidebands. The pump plasma wave and sidebands exert a ponderomotive force on the electrons driving a low-frequency quasimode. The electron density perturbation associated with this mode couples with the pump-driven electron oscillatory velocity to produce nonlinear currents driving the sidebands. At large pump amplitude, the instability grows faster than the ion plasma frequency and ions do not play a significant role. The growth rate of the quasimode, at large pump amplitude scales faster than linear. The growth rate is maximum for an optimum wave number of the quasimode and also increases with pump amplitude. Nonlocal effects, however reduce the growth rate by about half.     

Permanent magnet wigglers for reducing the emittance of the Petra III synchrotron radiation source

The Petra III synchrotron radiation source was developed based on the Petra-II 6-GeV electron accelerator (DESY). After installing the system for radiation damping, the horizontal emittance of the electron beam of Petra III decreased from 5 nm rad to 1 nm rad, which is a record parameter for this class of installations. The system of radiation damping includes 20 permanent magnet wigglers installed in two straight sections, 50 m each. The total radiation power of the wigglers reaches 800 kW. The wigglers used in the radiation damping system of Petra III were developed in collaboration with DESY (Hamburg) and fabricated by the Budker Institute of Nuclear Physics. The wiggler length is 4.04 m, the gap between the poles is 24 mm, the maximum magnetic field is B = 1.52?1.56 T, and the period is λ = 20 cm. This paper describes the design features of the permanent magnet wigglers and the methods and results of adjustment of the wiggler operating parameters.