Nonlinear propagation of ion plasma waves in dust-ion plasma including quantum-relativistic effect

In this paper we have theoretically investigated the quantum and relativistic effects on ion plasma wave in an unmagnetised dust-ion plasma. By using the method of normal mode analysis, we have obtained a linear dispersion relation. It has been analysed numerically for quantum and relativistic effects on the propagation of ion plasma wave. By using the standard reductive perturbation technique, we have derived a Korteweg–de Vries (KdV) equation which describes the nonlinear propagation of the wave. Numerically, it is shown that only compressive type of soliton can exist in the plasma under consideration. It is found that the solitary wave profile depends significantly on the quantum and relativistic parameters. The dust size, dust charge and the dust number density are also shown to have significant influences on these solitary waves. The results of this present investigation have some relevance to the nonlinear propagation of ion plasma wave in some astrophysical, space and laboratory plasma environments.     

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.     

Quantum ion-acoustic solitary waves in weak relativistic plasma

Small amplitude quantum ion-acoustic solitary waves are studied in an unmagnetized two- species relativistic quantum plasma system, comprised of electrons and ions. The one-dimensional quantum hydrodynamic model (QHD) is used to obtain a deformed Korteweg–de Vries (dKdV) equation by reductive perturbation method. A linear dispersion relation is also obtained taking into account the relativistic effect. The properties of quantum ion-acoustic solitary waves, obtained from the deformed KdV equation, are studied taking into account the quantum mechanical effects in the weak relativistic limit. It is found that relativistic effects significantly modify the properties of quantum ion-acoustic waves. Also the effect of the quantum parameter H on the nature of solitary wave solutions is studied in some detail.     

Quantum relativistic theory of Cherenkov beam instability in plasma

The quantum theory of Cherenkov instability of the relativistic electron beamin isotropic plasma is presented. Relativistic quantum nonlinear equations of Cherenkov beam-plasma instability are obtained. The relativistic quantum dispersion relation is derived in the linear approximation and instability development increments in extreme cases are determined.     

Modulation instability of lower hybrid waves leading to cusp solitons in electron–positron(hole)–ion Thomas Fermi plasma

Following the idea of three‐wave resonant interactions of lower hybrid waves, it is shown that quantum‐modified lower hybrid (QLH) wave in electron–positron–ion plasma with spatial dispersion can decay into another QLH wave (where electron and positrons are activated, whereas ions remain in the background) and another ultra‐low frequency quantum‐modified ultra‐low frequency Lower Hybrid (QULH) (where ions are mobile). Quantum effects like Bohm potential and Fermi pressure on the lower hybrid wave significantly reshaped the dispersion properties of these waves. Later, a set of non‐linear Zakharov equations were derived to consider the formation of QLH wave solitons, with the non‐linear contribution from the QLH waves. Furthermore, modulational instability of the lower hybrid wave solitons is investigated, and consequently, its growth rates are examined for different limiting cases. As the growth rate associated with the three‐wave resonant interaction is generally smaller than the growth associated with the modulational instability, only the latter have been investigated. Soliton solutions from the set of coupled Zakharov and NLS equations in the quasi‐stationary regime have been studied. Ordinary solitons are an attribute of non‐linearity, whereas a cusp soliton solution featured by nonlocal nonlinearity has also been studied. Such an approach to lower hybrid waves and cusp solitons study in Fermi gas comprising electron positron and ions is new and important. The general results obtained in this quantum plasma theory will have widespread applicability, particularly for processes in high‐energy plasma–laser interactions set for laboratory astrophysics and solid‐state plasmas.     

Planar and Nonplanar Shock Waves in a Degenerate Quantum Plasma

The nonlinear propagation of modified electron‐acoustic (mEA) shock waves in an unmagnetized, collisionless, relativistic, degenerate quantum plasma (containing non‐relativistic degenerate inertial cold electrons, both nonrelativistic and ultra‐relativistic degenerate hot electron and inertial positron fluids, and positively charged static ions) has been investigated theoretically. The well‐known Burgers type equation has been derived for both planar and nonplanar geometry by employing the reductive perturbation method. The shock wave solution has also been obtained and numerically analyzed. It has been observed that the mEA shock waves are significantly modified due to the effects of degenerate pressure and other plasma parameters arised in this investigation. The properties of planar Burgers shocks are quite different from those of nonplanar Burgers shocks. The basic features and the underlying physics of shock waves, which are relevant to some astrophysical compact objects (viz. non‐rotating white dwarfs, neutron stars, etc.), are briefly discussed. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonlinear Evolution of Driven Electron Plasma Oscillations in Inhomogeneous Plasmas

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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.     

Linear theory of plasma filled backward wave oscillator

An analytical and numerical study of backward wave oscillator (BWO) in linear regime is presented to get an insight into the excitation of electromagnetic waves as a result of the interaction of the relativistic electron beam with a slow wave structure. The effect of background plasma on the BWO instability is also presented.     

Modulational instability of ion—acoustic waves in a warm plasma

Using the standard reductive perturbation technique,a nonlinear Schroedinger equation is derived to study the modulational instability of finite-amplitude ion-acoustic waves in a non-magnetized warm plasma.It is found that the inclusion of ion temperature in the equation modifies the nature of the ion-acoustic wave stability and the soliton stuctures.The effects of ion plasma temperature on the modulational stability and ion-acoustic wave properties are inestigated in detail.     

On the quantum theory of beam instability in plasma

The quantum theory of induced Cherenkov radiation by an electron beam of longitudinal waves in isotropic plasma is presented. Nonrelativistic quantum nonlinear equations of Cherenkov beam-plasma instability are obtained. A quantum dispersion relation is derived in the linear approximation and instability development increments are determined.     

线性偏振激光在相对论等离子体中的调制不稳定性

 从相对论等离体中电磁波的非线性色散方程出发,利用Karpman方法获得了线性偏振波模所满足的非线性控制方程,在非线性色散方程和非线性控制方程的基础上对线性偏振激光在相对论等离体中传播的调制不稳定性进行分析,给出了调制不稳定的时间增长率与扰动态波数之间的函数关系。     

On the theory of Langmuir waves in a quantum plasma

Nonlinear quantum-mechanical equations are derived for Langmuir waves in an isotropic electron collisionless plasma. A general analysis of dispersion relations is carried out for complex spectra of Langmuir waves and van Kampen waves in a quantum plasma with an arbitrary electron momentum distribution. Quantum nonlinear collisionless Landau damping in Maxwellian and degenerate plasmas is studied. It is shown that collisionless damping of Langmuir waves (including zero sound) occurs in collisionless plasmas due to quantum correction in the Cherenkov absorption condition, which is a purely quantum effect. Solutions to the quantum dispersion equation are obtained for a degenerate plasma.     

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.     

Investigation of self-focusing a Gaussian laser pulse in a weakly relativistic and ponderomotive regime inside a collisionless warm quantum plasma

This article investigates nonlinear self-focusing of an intense right hand circularly polarized Gaussian profile laser pulse in a weakly relativistic and ponderomotive regime inside a collisionless and unmagnetized warm quantum plasma. The nonlinear propagation equation for laser pulse in plasma has been derived. Then, the evolution differential equation for laser spot-size was obtained with considering the parabolic equation approach under the Wentzel-Kramers-Brillouin and paraxial ray approximations. This differential equation was solved numerically by fourth-order Runge-Kutta method. It is shown that our solution confirms the results of the self-focusing of the laser pulse in a weakly relativistic ponderomotive regime in cold quantum plasma in extreme conditions. Numerical results indicate that self-focusing of the laser pulse in the presence of relativistic and ponderomotive nonlinearity inside warm quantum plasma is improved in comparison with relativistic and ponderomotive cold quantum plasma.     

Ultrarelativistic excitation of beat waves in a hot magnetized plasma

Summary A theoretical investigation is made on the nonlinear relativistic excitation of an electrostatic electron plasma wave at the beat frequency of two high-power colinear laser beams in a hot, homogeneous and magnetized plasma. The relativistic Vlasov equation expressed in gyrokinetic variables has been employed to find the nonlinear response of the magnetized plasma electrons. It is noted that the power density associated with the excited beat wave is much higher for the relativistic consideration than that for the nonrelativistic consideration. The authors of this paper have agreed to not receive the proofs for correction.     

K-P-Burgers equation in negative ion-rich relativistic dusty plasma including the effect of kinematic viscosity

The stationary solution is obtained for the K–P–Burgers equation that describes the nonlinear propagations of dust ion acoustic waves in a multi-component, collisionless, un-magnetized relativistic dusty plasma consisting of electrons, positive and negative ions in the presence of charged massive dust grains. Here, the Kadomtsev–Petviashvili(K–P) equation, threedimensional(3D) Burgers equation, and K–P–Burgers equations are derived by using the reductive perturbation method including the effects of viscosity of plasma fluid, thermal energy, ion density, and ion temperature on the structure of a dust ion acoustic shock wave(DIASW). The K–P equation predictes the existences of stationary small amplitude solitary wave,whereas the K–P–Burgers equation in the weakly relativistic regime describes the evolution of shock-like structures in such a multi-ion dusty plasma.     

离子通道中相对论电子注的切连科夫辐射

对入射等离子体的相对论电子注(REB)在离子通道中可能产生切连科夫(Cherenkov)辐射的问题进行了论证与研究.利用线性理论分析了离子背景下的注-波互作用关系，导出了系统的色散方程与同步辐射条件.结果表明，系统的电磁不稳定性是由离子通道中TM模与电子注模通过电子注耦合所致，其微观机理是离子对电子注的聚焦.对处于运动等离子体状态下的离子-注系统进行了严格地理论分析，获得了通道内辐射波的频偏与波增长率公式，并通过数值模拟计算讨论了系统有关参数对它们的影响. 关键词： 离子通道 等离子体 切连科夫辐射     

Arbitrary magnetosonic solitary waves in spin 1/2 degenerate quantum plasma

Linear and nonlinear compressional magnetosonic waves are studied in magnetized degenerate spin-1/2 Fermi plasmas. Starting from the basic equations of a quantum magnetoplasma we develop the system of quantum magnetohydrodynamic (QMHD) equations. Spin effects are incorporated via spin force and macroscopic spin magnetization current. Sagdeev potential approach is employed to derive the nonlinear energy integral equation which admits the rarefactive solitary structure in the subAlfvenic region. The quantum diffraction due to Bohm potential does not affect the amplitude of soliton but has a direct effect on its width. The width of soliton is broadened with the increase in the quantization of the system due to quantum diffraction. However, the nonlinear wave amplitude is reduced with the increase in the value of magnetization energy due to electron spin-1/2 effects. The degeneracy effect due to quantum plasma beta enhances the amplitude of magnetosonic soliton. The importance of the work relevant to compact astrophysical bodies is pointed out.     

Localization of intense electromagnetic waves in a relativistically hot plasma

We consider nonlinear interactions between intense short electromagnetic waves (EMWs) and a relativistically hot electron plasma that supports relativistic electron holes (REHs). It is shown that such EMW-REH interactions are governed by a coupled nonlinear system of equations composed of a nonlinear Schro dinger equation describing the dynamics of the EMWs and the Poisson-relativistic Vlasov system describing the dynamics of driven REHs. The present nonlinear system of equations admits both a linearly trapped discrete number of eigenmodes of the EMWs in a quasistationary REH and a modification of the REH by large-amplitude trapped EMWs. Computer simulations of the relativistic Vlasov and Maxwell-Poisson system of equations show complex interactions between REHs loaded with localized EMWs.