Solitary Waves in Relativistic Electromagnetic Plasma

Solitary waves in relativistic electromagnetic plasmas are obtained numerically. The longitudinal momentum of electrons has been taken into account in the problem. It is found that in the moving frame with electromagnetic field propagating the solitary waves can exist in both cases, where the vector potential frequency is larger or smaller than the plasma characteristic frequency.     

Relativistic Spherical Plasma Waves in a Collisional and Warm Plasma

Under Lagrange coordinates, the relativistic spherical plasma wave in a collisional and warm plasma is discussed theoretically. Within the Lagrange coordinates and using the Maxwell and hydrodynamics equations, a wave equation describing the relativistic spherical wave is derived. The damped oscillating spherical wave solution is obtained analytically using the perturbation theory. Because of the coupled effects of spherical geometry,thermal pressure, and collision effect, the electron damps the periodic oscillation. The oscillation frequency and the damping rate of the wave are related to not only the collision and thermal pressure effect but also the space coordinate. Near the center of the sphere, the thermal pressure significantly reduces the oscillation period and the damping rate of the wave, while the collision effect can strongly influence the damping rate. Far away from the spherical center, only the collision effect can reduce the oscillation period of the wave, while the collision effect and thermal pressure have weak influence on the damping rate.     

Stable Propagating Waves and Wake Fields in Relativistic Electromagnetic Plasma

Stable propagating waves and wake fields in relativistic electromagnetic plasma are investigated. The incident electromagnetic field has a finite initial constant amplitude meanwhile the longitudinal momentum of electrons is taken into account in the problem. It is found that in the moving frame with transverse wave group velocity the stable propagating transverse electromagnetic waves and longitudinal plasma wake fields can exist in the appropriate regime of plasma.     

Nonplanar Electrostatic Solitary Waves in a Relativistic Degenerate Dense Plasma

By employing the reductive perturbation technique, the propagation of cylindrical and spherical ion acoustic solitary waves is studied in an unmagnetized dense relativistic plasma, consisting of relativistically degenerate electrons and cold fluid ions. A modified Korteweg-de-Vries equation is derived and its numerical solutions have been analyzed to identify the basic features of electrostatic solitary structures that may form in such a degenerate Fermi plasma. Different degrees of relativistic electron degeneracy are discussed and compared. It is found that increasing number density leads to decrease the amplitude the width of the ion acoustic solitary wave in both the cylindrical and spherical geometries. The relevance of the work to the compact astrophysical objects, particularly white dwarfs is pointed out.     

Collective Scattering of Electromagnetic Waves from a Relativistic Magnetized Plasma

Recently, laser and microwave scatterings have become one of the important diagnostic means for plasma. Laser and microwave correlative scattering spectrum is determined by particle-density fluctuations in a weak turbulent plasma. In a relativistic plasma, on the basis of complete electromagnetic interaction between particles, a general expression for particle density fluctuations and spectra of laser and microwave scattering from a magnetized plasma are derived. The laser and microwave scattering spectra provide information on electron density and temperature, ion temperature, resonance and nonresonance effects.     

Stability of the Relativistic Maxwellian in a Collisional Plasma

The relativistic Landau-Maxwell system is the most fundamental and complete model for describing the dynamics of a dilute collisional plasma in which particles interact through Coulombic collisions and through their self-consistent electromagnetic field. We construct the first global in time classical solutions. Our solutions are constructed in a periodic box and near the relativistic Maxwellian, the Jüttner solution.Acknowledgements The research is supported in part by NSF grants.     

The Stability of the Relativistic Alfvén Waves

Within the framework of the special relativity, the system of reference comoving with Alfvén wave is defined and the form of the perturbations with respect to this system are deduced. The system of equations corresponding to the interaction of the waves, in the case when the relativistic Alfvén wave can generate new Alfvén waves and magnetosonic waves, is obtained in the most general form. In the one-dimensional case the time dependent perturbation method is used for obtain the dispersion equation for the relativistic coupled waves (decay processes). Finally, by solving numerically the dimensionless dispersion equation, the instability domains of the Alfvén waves are obtained. It is shown that there are possible decay processes and modulational instabilities.     

Cylindrical and Spherical Ion-Acoustic Shock Waves in a Relativistic Degenerate Multi-Ion Plasma

A rigorous theoretical investigation has been made to study the existence and basic features of the ion-acoustic (IA) shock structures in an unmagnetized, collisionless multi-ion plasma system (containing degenerate electron fluids, inertial positively as well as negatively charged ions, and arbitrarily charged static heavy ions). This investigation is valid for both non-relativistic and ultra-relativistic limits. The reductive perturbation technique has been employed to derive the modified Burgers equation. The solution of this equation has been numerically examined to study the basic properties of shock structures. The basic features (speed, amplitude, width, etc.) of these electrostatic shock structures have been briefly discussed. The basic properties of the IA shock waves are found to be significantly modified by the effects of arbitrarily charged static heavy ions and the plasma particle number densities. The implications of our results in space and interstellar compact objects like white dwarfs, neutron stars, black holes, and so on have been briefly discussed.     

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.     

磁化尘埃等离子体中的冲击波及其横向扰动稳定性

利用双曲函数法得到ZKB方程的一组冲击波解,并对波在横向扰动下的动力学稳定性进行研究.对冲击波解进行线性稳定性分析,并构造高精度的有限差分格式求解所得本征值问题.结果表明：对于正耗散的情形,该冲击波在线性意义下稳定;对于负耗散情形,该冲击波在线性意义下不稳定.构造有限差分格式对受扰动的冲击波进行非线性动力学演化,结果表明：对于正耗散的情况,该冲击波是稳定的.     

Beam Loading in Plasma Waves

Certain key accelerator issues relevant to plasma-based accelerators are studied in this article. Analytic results for important quantities of interest, such as maximum beam current, efficiency, and energy spread will be given. These results will then be compared with one-and two-dimensional particle-in-cell (PIC) computer simulations. Special emphasis will be placed on those schemes that offer not only high accelerating gradients, but also high efficiency and small energy spread.     

Thermodynamic Potential of Relativistic Electron Plasma

Within the real time formalism of quantum field theory at finite temperatures based on the closed-time-path Green's function approach, a closed analytical expression of the thermodynamic potential of a relativistic electron plasma is derived under the random phase approximation by summing up all ring diagrams. The result is natural extension to the relativistic case sf our previous formula derived in the case of a Coulomb gas.     

The Initial Value Problem in Relativistic Plasma

The Landau problem in relativistic plasma is considered in detail. It is shown how all modes in the plasma arise through proper treatment of the inverse Laplace transforms without imposition of any external conditions. A correct derivation of the asymptotic behavior of the electric field is included and estimates of the contribution of more rapidly decaying Landau modes are made analytically and are compared with numerical computations.     

Stability of Covariant Relativistic Quantum Theory

In this paper we study the relativistic quantum-mechanical interpretation of the solution of the inhomogeneous Euclidean Bethe-Salpeter equation. Our goal is to determine conditions on the input to the Euclidean Bethe-Salpeter equation so the solution can be used to construct a model Hilbert space and a dynamical unitary representation of the Poincaré group. We prove three theorems that relate the stability of this construction to properties of the kernel and driving term of the Bethe-Salpeter equation. The most interesting result is that the positivity of the Hilbert space norm in the non-interacting theory is not stable with respect to Euclidean covariant perturbations defined by Bethe-Salpeter kernels. The long-term goal of this work is to understand which model Euclidean Green functions preserve the underlying relativistic quantum theory of the original field theory. Understanding the constraints imposed on the Green functions by the existence of an underlying relativistic quantum theory is an important consideration for formulating field-theory motivated relativistic quantum models.This work supported in part by the U.S. Department of Energy, under contract DE-FG02-86ER40286     

Linear Analyses of Langmuir and EM Waves in Relativistic Hot Plasmas

The linear Langmuir and electromagnetic (EM) waves in relativistic hot plasmas are discussed, and the dispersion relations are obtained based on the covariant Maxwell's and fluid equations. When kBT/mc²>1, the effective mass of electrons will be increased obviously. As the results, many other influences are induced, such as the decrease of the plasmas frequency and the critical frequency, the reduction of the electron sound velocity and the electrons' oscillation velocity, and so on. Numerical results show that these influences can affect the dispersion relations of Langmuir and EM waves seriously even in linear regime.     

激光激发水中产生超声波的实验研究

采用压电陶瓷水听器研究了Nd：YAG脉冲激光激发水中产生瞬态超声波的特性,给出了声压信号随距离的变化关系。研究结果表明：用激光产生水下声波是完全可行的。当观测点与光击穿区的距离r远大于柱体长度时,垂直于光传播方向的激光瞬态超声波幅值与r成反比;当观测点与光击穿区的距离r很小时,垂直于光传播方向的声压幅值与产成反比。此外,当激光入射角度发生变化,超声脉冲的幅值也随之发生变化,其幅值在激光束垂直入射的时候最大。     

Whistler-Mode Waves Growth by a Generalized Relativistic Kappa-Type Distribution

The instability of field-aligned Whistler-mode waves in space plasmas is studied by using a recently developed generalized relativistic kappa-type （KT） distribution. Numerical calculations are performed for a direct comparison between the new KT distribution and the current kappa distribution. We show that the wave growth for the KT distribution tends to occur in the lower wave frequency （e.g.,ω 〈~0.1Ω） due to a larger fractional number of the resonant electrons ηrel （which controls the wave growth）, while primarily locating in the higher wave frequency for the kappa distribution. Moreover, the relativistic anisotropy Are1 by the KT distribution is found to be smaller than that by the kappa distribution, leading to a smaller peak of wave growth. The results present a further understanding of plasma wave instability particularly in those plasmas where relativistic electrons are present.     

Relativistic Magnetosonic Solitary Wave in Magnetized Multi-Ion Plasma

In the presence of an applied uniform magnetic field Bo, the properties of 2-dimensional （2D） magnetosonic solitary waves of relativistic amplitude in the plasma containing electron, light ions He^＋, and heavy ions O＋ are presented. In the weakly relativistic limit, a Kadomtsev Petviashvili （KP） equation is derived by reductive perturbation method. We give the N-soliton solution of the KP equation and find dromion solutions of a potential of the physical field. The interaction law of the dromions is obtained, which shows there is no exchange of energy, momentum, and angular momentum before and after interaction of the dromions except for phase shifts.