Nonlinear theory of resonant beam-plasma interaction: Nonrelativistic case

Analytic and numerical methods are used to study the nonlinear dynamics of the resonant interaction between a dense nonrelativistic electron beam and a plasma in a spatially bounded system. Regimes such as collective (Raman) and single-particle (Thomson) Cherenkov effects are considered. It is shown that in the first case, the motion of both the beam and plasma electrons exhibits significant nonlinearities. However, because of the weak coupling between the beam and the plasma, the nonlinear dynamics of the instability can be studied analytically and it can be strictly shown that saturation of instability is caused by a nonlinear shift of the radiation frequency and loss of resonance. In the second case, the nonlinear instability dynamics can only be studied numerically. In this regime, at low beam densities significant nonlinearity is only observed in the motion of the beam electrons while the plasma remains linear and saturation of the instability is caused by trapping of beam electrons in the field of the beam-excited plasma wave.     

Conditions for the Stable Acceleration of Ion Rings by Collapsed Liners

The conditions of suppressing the collective slowing-down of an ionic beam on electrons, which is caused by the excitation of electron plasma oscillations (beam instability) by ions, are found. In contrast to available explicit and implicit indications, a large spread of the energies only in an ionic beam is insufficient for this suppression. The acceleration of ions is shown to become stable when a sufficiently large spread of the electron velocities is simultaneously present. The beam instability of ions is suppressed by the Landau damping of the ion-excited plasma waves at electrons. The results obtained are used to analyze the possibility of ion acceleration by collapsed cylindrical plasma liners.     

Thermal effects in the dissipative instability of the electron beam-plasma systems

The effects of the thermal motion of the charged particles in the dissipative instability of the under and over-limiting currents of a relativistic electron beam in a fully magnetized beam-plasma waveguide is investigated. It is shown that by increasing the temperature of the plasma electrons, the resonant frequency of the waveguide slightly increases and the growth rates of the instability development decreases. In addition, an increase of the temperature of the plasma electron can change the dissipative hydrodynamic instability to the collisionless kinetic instability. Furthermore, the dissipative instability of the overlimiting electron beam is shown to be more sensitive with respect to the electron plasma temperature compared to the underlimiting electron beam case.     

On the influence of the electron-velocity spread in a beam on the mechanism of Cherenkov beam–plasma interaction

The instability of an electron beam in cold plasma is considered in the linear potential approximation with different velocity-distribution functions of beam electrons. It is demonstrated that the mechanism of beam instability in plasma changes as the electron-velocity spread is increased: the hydrodynamic single-particle instability mode evolves into the hydrodynamic collective mode or the single-particle kinetic one. Instability growth rates in different modes are determined analytically and numerically.     

Particle simulation of an ultrarelativistic two-stream instability

A two-stream instability in an unmagnetized plasma is examined by a particle-in-cell simulation. Each beam initially consists of cold electrons and protons that stream at a relative Lorentz factor 100. This is representative for plasma close to the external shocks of gamma-ray bursts. An electrostatic wave develops which saturates by trapping electrons. This wave collapses and the resulting electrostatic turbulence gives an electron momentum distribution that resembles a power law with a spectral break. Some electrons reach Lorentz factors over 1000.     

Influence of the beam-forming conditions on the development of space-charge oscillations in a long-pulse relativistic electron beam

The characteristics of the space-charge oscillations of a long-pulse relativistic electron beam in magnetically insulated diodes are determined for different geometries of the electron acceleration section and for explosive-emission cathodes of different materials. The important role of the stream of electrons having high transverse velocities in the evolution of the oscillations is demonstrated, and the laws governing the generation of this stream are determined. Possible mechanisms of the space-charge oscillations are described, taking into account the interaction of the electron stream in the beam halo with the main electron stream, the development of diocotron instability in the stream of electrons emitted by the outer lateral surface of the plasma emitter, and the instability of the space charge of “long-lived” electrons in the beam transport channel. Zh. Tekh. Fiz. 68, 102–106 (April 1998)     

Modulational Instability of Ion-Acoustic Waves in a Warm Plasma with a Relativistic Electron Beam

The modulational instability of ion-acoustic wave in a collisionless, unmagnetized plasma consisting ofwarm ions, hot isothermal electrons, and relativistic electron beam is studied. A modified nonlinear Schrodinger equationincluding one additional term that comes from the effect of relativistic electron beam is derived. It is found that theinclusion of a relativistic electron beam would modify the modulational instability of the wave packet and could notadmit any stationary soliton waves.     

Merging of super-Alfvénic current filaments during collisionless Weibel instability of relativistic electron beams

The theoretical framework predicting the long-term evolution, structure, and coalescence energetics of current filaments during the Weibel instability of an electron beam in a collisionless plasma is developed. We emphasize the nonlinear stage of the instability, during which the beam density of filaments increases to the background ion density, and the ambient plasma electrons are fully expelled from the filaments. Our analytic and numerical results demonstrate that the beam filaments can carry super-Alfvénic currents and develop hollow-current density profiles. This explains why the initially increasing magnetic field energy eventually decreases during the late stage of the instability.     

THE PROCESS OF SPACE CURRENT NEUTRALIZATION OF INTENSE RELATIVISTIC ELECTRON BEAM UNDER AN EXTERNALLY APPLIED MAGNETIC GUIDE FIELD

The process of space current neutralization of intense relativistic electron beam under an externally applied magnetic guide field is discussed in this paper. Ionization by electron avalanching and by beam electrons impact and recombination is included in the calculation of plasma density buildup, with plasma heating by return current and two- stream instability taken into account. A code to evaluate the process of space current neutralization was set up. The calculations demonstrate that the optimum gas pressure increases as peak beam current increases and it decreases as the risetime of beam pulse increases.     

Model of the stabilized distribution function for oscillating electrons in a hollow cathode

The form of the velocity distribution function of oscillating electrons in a low-pressure discharge with a hollow cathode is determined using the simple model of mathematical billiards. The distribution function is nonequilibrium and permits the development of instability of the plasma beam type.     

Cherenkov instability of a magnetized beam-plasma system with allowance for a momentum spread of beam electrons

Cherenkov instability is considered in a completely magnetized homogeneous beam-plasma system featuring a thermal momentum spread of beam electrons. The thermal spread in the beam is described in the scope of both the hydrodynamic approach and the kinetic equation method by giving the electron momentum distribution function in the form of theMaxwellian and semi-Maxwellian distributions. It is shown that two beam-plasma instability regimes, the single-particle and collective Cherenkov effects (Compton and Raman regimes) differing by the physical mechanism and the increments, are possible in a system (waveguide) with homogeneous transverse beam and plasma density profiles. Solutions to dispersion equations for these and a more general regime are obtained and analyzed.     

逃逸电子和不稳定性波反常多普勒共振实验研究

利用电子回旋辐射诊断系统并结合其他相关诊断研究了HL-2A托卡马克中逃逸电子与波间的反常多普勒共振作用.结果显示:欧姆放电下提高等离子密度能抑制逃逸电子束的不稳定性,但等离子密度的再次降低导致逃逸电子又会激发不稳定性波,并耦合不稳定性波发生二次反常多普勒共振作用.利用统计方法分析了HL-2A上不同放电阶段逃逸电子反常多普勒共振阈值(ωpe/ωce)区间大致都在0.17-0.54范围内.此共振机制导致逃逸电子在速度空间被波散射,平行能量转化到垂直能量,pitch角增加,同步辐射功率增强,逃逸电子能量限制在反常多普勒效应的阈值能量附近.基于反常多普勒共振的逃逸抑制能有效减轻逃逸电子对装置第一壁的损坏.     

Neutrino beam plasma instability

We derive relativistic fluid set of equations for neutrinos and electrons from relativistic Vlasov equations with Fermi weak interaction force. Using these fluid equations, we obtain a dispersion relation describing neutrino beam plasma instability, which is little different from normal dispersion relation of streaming instability. It contains new, nonelectromagnetic, neutrino-plasma (or electroweak) stable and unstable modes also. The growth of the instability is weak for the highly relativistic neutrino flux, but becomes stronger for weakly relativistic neutrino flux in the case of parameters appropriate to the early universe and supernova explosions. However, this mode is dominant only for the beam velocity greater than 0.25c and in the other limit electroweak unstable mode takes over.     

飞秒激光等离子体中电子热传导现象的数值模拟

采用相对论电磁粒子模拟程序研究了飞秒激光等离子体相互作用中产生的电流密度、电场和自生磁场的发展演化过程。介绍了电子的非局域热输运的基本特性以及激光加热过程中温度烧蚀前沿稠密等离子体子区的预热效应、临界面附近的限流效应,以及冕区的反扩散与限流效应,得到了经典Spitzer-Harm理论描述的电子热传导随自生磁场的演化情形。数值模拟表明:在线性强激光作用下,由于电子初始时刻的无规则热运动,在等离子体上激发电磁不稳定性,而不稳定性激发的强电磁场使电子束在非常短的距离内沉积能量,同时对在激光有质动力推开电子时形成的超热电子能量输运产生抑制作用。     

Observation of a hot high-current electron beam from a self-modulated laser wakefield accelerator

A highly relativistic electron beam produced by a 50 TW laser-plasma accelerator has been characterized by photonuclear techniques. The beam has large divergence that increases with plasma density. The electron yield also increases with plasma density and reaches up to 4x10(11) electrons ( >10 MeV), with beam current approaching the Alfvén limit. Effective electron temperatures exceeding 8 MeV are found, leading to an order of magnitude higher photonuclear activation yield than in solid target experiments with the same laser system.     

Field theory of dielectric Cherenkov maser

The effect of three-dimensional perturbed velocity and three-dimensional perturbed current density on the beam-wave interaction of dielectric Cherenkov maser is analysed by use of the self-consistent linear field theory. Three distinct cases are considered. First, the propagation of the electron beam in an annular dielectric liner enclosed by a loss-free conducting wall is investigated. The dispersion equation and the simultaneous condition of the beam-wave interaction are derived. It's clearly shown that the instability of the interaction results from the coupling of the TM mode in the dielectric lined slow-wave waveguide to the beam mode via the electron beam. And the coupling is proportional to the density of the beam. The growth rate of the wave produced by the electron beam are obtained. Then, the case of a relativistic electron beam guided by a longitudinal magnetic field in the same slow-wave structure is examined. The motion of electrons could be approximated to be one-dimensional when the simultaneous condition of the beam-wave interaction of dielectric Cherenkov maser is satisfied. Finally, the effect of the background plasma on the instability of the beam-wave interaction is studied.This work is supported by National Natural Science Foundation of China.     

The effect of the plasma density gradient on current filamentation instability

The filamentation instability is one of the basic beam-plasma instabilities that play a significant role in the energy deposition mechanism of the relativistic electrons generated by the laser-plasma interaction in the fast ignition scenario. In this paper, the effect of the density gradient into plasma on the filamentation instability was investigated in the Weibel unstable plasma, where the plasma temperature anisotropy can play an important role. Results indicated that the density gradient enhances the instability growth rate so that decreasing the density gradient from the critical surface to the core of fuel leads to instability for longer regions in k space. Also, investigations in the region close to the critical surface showed that for decreasing the beam number density n_b ≤ 0.01n₀, the instability occurs for while this can be different for higher values. Increasing the beam relativistic factor causes a decreasing peak of instability growth rate because of a reduction in beam current, whereas the initial thermal spread of plasma amplifies the filamentation instability.     

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).