Relativistic effects on the modulational instability of electron plasma waves in quantum plasma

Relativistic effects on the linear and nonlinear properties of electron plasma waves are investigated using the one-dimensional quantum hydrodynamic (QHD) model for a two-component electron?Cion dense quantum plasma. Using standard perturbation technique, a nonlinear Schr?dinger equation (NLSE) containing both relativistic and quantum effects has been derived. This equation has been used to discuss the modulational instability of the wave. Through numerical calculations it is shown that relativistic effects significantly change the linear dispersion character of the wave. Unlike quantum effects, relativistic effects are shown to reduce the instability growth rate of electron plasma waves.     

Propagation dynamics of relativistic electromagnetic solitary wave as well as modulational instability in plasmas

By one-dimensional particle-in-cell(PIC) simulations, the propagation and stability of relativistic electromagnetic(EM) solitary waves as well as modulational instability of plane EM waves are studied in uniform cold electron-ion plasmas.The investigation not only confirms the solitary wave motion characteristics and modulational instability theory, but more importantly, gives the following findings. For a simulation with the plasma density 10²³ m^-3 and the dimensionless vector potential amplitude 0.18, it is found that the EM solitary wave can stably propagate when the carrier wave frequency is smaller than 3.83 times of the plasma frequency. While for the carrier wave frequency larger than that, it can excite a very weak Langmuir oscillation, which is an order of magnitude smaller than the transverse electron momentum and may in turn modulate the EM solitary wave and cause the modulational instability, so that the solitary wave begins to deform after a long enough distance propagation. The stable propagation distance before an obvious observation of instability increases(decreases) with the increase of the carrier wave frequency(vector potential amplitude). The study on the plane EM wave shows that a modulational instability may occur and its wavenumber is approximately equal to the modulational wavenumber by Langmuir oscillation and is independent of the carrier wave frequency and the vector potential amplitude.This reveals the role of the Langmuir oscillation excitation in the inducement of modulational instability and also proves the modulational instability of EM solitary wave.     

Beam breakup and modulational instability in a bulk type I quadratic medium

The effect of a small modulation superimposed on a strip (1D) solitary wave propagating in a bulk quadratic medium was investigated both analytically and numerically near Type I phase matching. General, exact results were obtained. By using first order perturbation theory, we obtained the gain coefficient for the modulational instability and the modulation cut-off frequency and we investigated their dependence on various beam and material parameters. The wave evolves into a clean periodic sequence of solitary waves and does not reproduce the incident beam. We showed that the beam breakup observed experimentally is due entirely to noise induced modulational instability.     

Dissipative instability of a highly relativistic electron beam through the excitation of surface waves on a conducting medium

The possibility of the dissipative instability of a relativistic electron beam streaming near a conducting medium is investigated. The development of this dissipative beam instability through the surface wave excitation slightly disturbs the beam leading to the slightly heating of the conducting medium.     

Modulational instability of a strip beam in a bulk type I quadratic medium

The evolution of a strip (one-dimensional) fundamental beam with propagation distance owing to spatial modulational instabilities was analyzed in a quadratic medium near type I phase matching. We obtained the gain coefficient for the modulational instability and showed that the wave evolves into a clean periodic sequence of solitary waves and does not reproduce the incident beam.     

Modulational instability of a weakly relativistic ion acoustic wave in a warm plasma with nonthermal electrons

An investigation has been made of modulational instability of a nonlinear ion acoustic wave in a weakly relativistic warm unmagnetized nonthermal plasma whose constituents are an inertial ion fluid and nonthermally distributed electrons. Up to the second order of the perturbation theory, a nonlinear Schr?dinger type (NST) equation for the complex amplitude of the perturbed ion density is obtained. The coefficients of this equation show that the relativistic effect, the finite ion temperature and the nonthermal electrons modify the condition of the modulational stability. The association between the small-wavenumber limit of the NST equation and the oscillatory solution of the Korteweg－de Varies equation, obtained by a reductive perturbation theory, is satisfied.     

Relativistic and nonrelativistic modulational instability of a laser radiation in an unmagnetized laser-produced plasma: Kinetic theory

Summary This paper presents a rigorous theoretical investigation of the relativistic and nonrelativistic modulational instability of a high-power laser radiation propagating in a collisionless and unmagnetized laser-produced plasma. The kinetic equationviz. the relativistic Vlasov equation has been employed to find the nonlinear response of electrons for this four-wave parametric process in the plasma. The actual motivation behind this theoretical investigation is to find the relativistic effect on this four-wave paremetric processviz. the modulational instability. Here, it can be noted that the modulational instability of the laser radiation under our situation has not a large but considerable relativistic effect and for the same set of plasma parameters the growth rate of the instability in ultrarelativistic consideration is approximately three times higher than that in the nonrelativistic consideration. The authors of this paper have agreed to not rective the proofs for correction.     

在弱相对论条件下哨声波的调制不稳定性

本文在研究哨声波调制不稳定性时,除考虑由有质动力引起的密度变化和流速改变两个非线性效应外,还计及由弱相对论效应引起电子质量变化的非线性效应,得到了在形成孤子的条件、产生不稳定性的条件、和不稳定性增长率等方面与非相对论情况不同的结果。     

Intense circularly polarized waves in plasmas

The nonlinear propagation of an intense circularly polarized electromagnetic wave in a cold plasma is investigated. A relativistic modulational instability and an exact localized solutions are found.     

Explosive instability in a backward wave oscillator

A plasma filled backward wave oscillator supports Trivelpiece-Gould (TG) and TM modes. The former can be driven unstable by a relativistic electron beam via Cerenkov interaction or by the plasma return current as two stream instability. This unstable TG mode can parametrically couple to a TM mode via a negative energy beam mode giving rise to an explosive instability     

Nonlinear interactions between electromagnetic waves and electron plasma oscillations in quantum plasmas

We consider nonlinear interactions between intense circularly polarized electromagnetic (CPEM) waves and electron plasma oscillations (EPOs) in a dense quantum plasma, taking into account the electron density response in the presence of the relativistic ponderomotive force and mass increase in the CPEM wave fields. The dynamics of the CPEM waves and EPOs is governed by the two coupled nonlinear Schr?dinger equations and Poisson's equation. The nonlinear equations admit the modulational instability of an intense CPEM pump wave against EPOs, leading to the formation and trapping of localized CPEM wave pipes in the electron density hole that is associated with a positive potential distribution in our dense plasma. The relevance of our investigation to the next generation intense laser-solid density plasma interaction experiments is discussed.     

Interplay of collisions and temperature on the filamentary structures of a relativistic electron beam in plasmas

A systematic study on the Weibel instability induced filamentation of a relativistic electron beam is made by including the effects of collisions and temperature. The stabilization and de-stabilization of the beam filamentation due to beam temperature and plasma collisions, respectively, is explored through an analytical model and PIC simulations. The de-stabilization of the beam filamentation is attributed to the collision driven negative energy wave generation in the beam plasma system.     

Coupling Instability of a Warm Relativistic Electron Beam with Ion-Channel Guiding

In this paper, the coupling instability of warm relativistic electron beam (WREB) propagating through the ion channel guiding is investigated in detail. Obtaining the equilibrium state of the system by considering the self-electric and azimuthal magnetic field, the fluid-Maxwell equations as well as linear perturbation theory are employed to derive the dispersion relation of the excited modes in the system. Numerical analysis of the obtained dispersion relation shows that the electromagnetic (EM) instability can be induced nearly the center of the beam through coupling between the fast electron plasma wave (FEPW), originated from the longitudinal oscillation of WREB, and fast forward electromagnetic wave (FFEW). In this sense, growing the perturbation amplitude occurs due to transport the kinetic energy of WREB to the EM wave at the specific frequency range, where the phase velocity of FEPW and FFEW is coincided. The results of the present investigation will greatly contribute to the understanding of the stability of the warm relativistic electron beam in laboratory experiments, such as in free electron laser experiments, where the ion-channel guiding is used to confine the electrons against the self-repulsive forces generated by the beam itself.     

Characterization of the initial filamentation of a relativistic electron beam passing through a plasma

The linear instability that induces a relativistic electron beam passing through a plasma with return current to filament transversely is often related to some filamentation mode with the wave vector normal to the beam or confused with Weibel modes. We show that these modes may not be relevant in this matter and identify the most unstable mode on the two-stream or filamentation branch as the main trigger for filamentation. This sets both the characteristic transverse and longitudinal filamentation scales in the nonresistive initial stage.     

Cubic dispersion relation for a relativistic backward-waveoscillator

The cubic approximation to the dispersion relation for a relativistic backward-wave oscillator is obtained, and the utility and limits of the approximation are presented. The approximation is obtained by Taylor series expansion of the wave admittance in the dispersion relation for the transverse-magnetic and free-streaming modes of a relativistic, thin, hollow, cylindrical electron beam moving along the axis of a disc-loaded waveguide in a strong axial magnetic field. The resulting cubic dispersion relation yields instability growth rates and frequencies which fall off beyond their maximum more sharply with increasing wavenumber than for the complete dispersion relation. The approximation is found to be quite good near the operating points of contemporary high-power relativistic backward-wave oscillators, namely, for relatively long wavelength and small ratio of Budker's parameter to the relativistic gamma factor of the beam     

Radiation guiding in a plasma wave wiggler free-electron laser

The radiation guiding of a plasma wave wiggler free-electron laser (FEL) in the Compton regime was examined. It was found that a Langmuir wave supported by a plasma cylinder acts as a wiggler for the generation of high-frequency coherent radiation when an annular relativistic electron beam passes through it. The radiation mode in the Compton regime tends to be localized close to the radius of the beam. A normal-mode analysis of this process revealed that the growth rate of the instability increases as the square root of the beam current. The treatment presented is restricted to the case where the radial width of the FEL radiation mode is larger than the beam radius, but smaller than the waveguide radius     

Ion sound wave excitation in a plasma under a Langmuir turbulence regime

Ion sound wave excitation in a warm non-relativistic (W_b ≤ 400 eV) electron beam unmagnetized plasma system is studied experimentally. The spectrum of these waves shows two peaks at frequencies of 70 and 230 kHz respectively. The origin of these waves is connected with modulational instability and cavity collapse. We show that the energy of bulk accelerated electrons can explain the measured value of kr_De for high-frequency sound waves. The energy of ion sound waves is not high enough to have an influence on the Langmuir turbulence dynamics.     

Modulational instability of ultra-intense linearly polarized laser pulse in electron–positron plasmas

Based on the wave equation of ultra-intense linearly polarized laser pulse propagating in electron–positron plasmas, the modulational instability is investigated. The nonlinear dispersion relation and the growth rate of instability are derived. The effects of plasmas number density, temperature, and laser intensity on the growth rate are analyzed. Results show that in an electron–positron plasma with certain background density, the intensity of the modulation instability is mainly determined by the competition between the nonlinearity in the interaction and the relativistic light ponderomotive driven density responses.     

A study of the effect of self-generated pressure gradient sources on the resistive filamentation instability

In the field of fast ignition scheme, self-generated magnetic fields via beam resistive filamentation have a significant role in the angular divergence of the relativistic electron beam, which can be affected by the intensity of other self-generated magnetic fields. In this context, the effects of pressure gradient sources arising from temperature and density gradient of the pellet along the beam flow direction are investigated. The results showed that the resistive filamentation instability can be strongly amplified compared to the fully homogeneous plasma. In this respect, for the distance away from the critical surface, the instability is protected for a longer wave number. Also, the beam and plasma properties such as the beam relativistic factor, the beam number density, and the degree of the plasma temperature anisotropy might be effective.     

线偏振激光在磁化等离子体中的调制不稳定性

 采用洛伦兹变换推导了线性偏振激光在磁化等离子体中的非线性色散关系,根据Karpman方法推导出横波的非线性控制方程,利用线性偏振激光在磁化等离子体中的非线性色散关系和非线性控制性方程,分析了在磁化等离子体中有限振幅的扰动引起的调制不稳定性,得到了线性偏振激光的调制不稳定的时间增长率与扰动波数之间的函数关系。分析结果表明：激光等离子体的临界面附近的磁调制不稳定性的时间增长率显著增大。