Kinetic theory of the plasma-dynamical modes and the transport coefficients of a relativistic plasma

The kinetic equation of an inhomogeneous relativistic plasma, consisting of an electron gas and a radiation field, is studied with particular regard to its eigenvalues in the hydrodynamical limit. The treatment is classical for the particles and quantum-mechanical for the field oscillators.After a suitable regularization, the eigenvalues are obtained by a perturbation theory through second order in the strength of the gradients. It is shown that these eigenvalues are in exact correspondence with the macroscopic relativistic plasma-dynamical modes. The important role played by the Vlassov operator in building up the peculiar structure of these modes is underlined. From a comparison of the macroscopic and microscopic eigenvalues we obtain general expressions for the thermal conductivity, the shear viscosity and the bulk viscosity of a relativistic plasma. The contribution of the radiation field to these quantities is a noteworthy feature of these expressions.     

������������Ӷ�˫�µ����������ݲ�����ɫɢ��ϵ

导出了无磁化无碰撞各向同性相对论正负电子对等离子体纵波的色散关系。使用逐次近似的标准技术,对两种极限情况下的纵波色散方程进行了解析研究。将完全色散方程进行变换,使它们完全适用于在需要完全相对论处理的温度范围内进行数值计算。用数值模拟方法得到了用解析方法不能得到的完全的色散曲线。     

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.     

Relativistic Boltzmann theory for a plasma: VII. Propagation of hydromagnetic waves

The kinetic theory of hydrodynamic modes is developed for a relativistic plasma. Using the Chapman-Enskog method in the case of plane wave disturbances a set of equations is derived describing, on a microscopic basis, the behaviour of small amplitude, low frequency waves. Diffusion and thermal modes, Alfvén and magneto-sound waves are discussed.     

等离子体填充盘荷波导高频特性分析

从麦克斯韦方程和流体理论出发，推导了填充磁化等离子体慢波结构的基本方程.在大磁场情况下，对等离子体填充盘荷波导的色散特性和耦合阻抗作了研究，结果表明填充等离子体使色散曲线上移，耦合阻抗提高.等离子体填充产生出模式谱非常丰富的周期性低频等离子体模式(TG模式).当等离子体密度增加到一定程度后，场模TM₀₁模的频率范围和TG₀₁模的频率范围相近，两个模式互相耦合产生出新的混合模G₁,G₂.如果相对论行波管工作在混合模上，将会产生新的工作机理. 关键词： 盘荷波导 等离子体填充 色散特性 相对论行波管     

Ion cyclotron instabilities in a mildly relativistic hydrogen-deuterium fusion plasma

A dispersion relation for the perpendicular propagation of the electromagnetic ion cyclotron wave around the second harmonic of the deuterium ion gyrofrequency in a mildly relativistic, anisotropic Maxwellian plasma with hydrogen as the majority species and deuterium as the minority component has been derived. The work has been carried out in the frame of reference of the majority hydrogen ions; to these ions the waves at 2Θ_D would be at its own gyrofrequency. Using a small quantityɛ to order all relevant parameters of the plasma, it was possible to derive the dispersion relations in a simple form. To the lowest order the relativistic factors do not enter the dispersion relation. The plasma can now support two modes—one above and the other below the hydrogen gyrofrequency in agreement with the assumptions. This was also verified numerically using a standard root solver thereby justifying the correctness of the ordering scheme. In the next higher order, the dispersion relation is a quartic equation and is sensitively dependent on the relativistic factors. The plasma can now support four modes, both above and below the hydrogen gyrofrequency and consistent with the ordering scheme used. However the modes can now coalesce resulting in complex conjugate roots to the dispersion relation thereby indicating an instability. The advantage of such a scheme is that two dispersion relations — one of which is independent of the relativistic factors and the other which is sensitively dependent on them can be separated out.     

Obliquely propagating quantum solitary waves in quantum‐magnetized plasma with ultra‐relativistic degenerate electrons and positrons

The oblique propagation of the quantum electrostatic solitary waves in magnetized relativistic quantum plasma is investigated using the quantum hydrodynamic equations. The plasma consists of dynamic relativistic degenerate electrons and positrons and a weakly relativistic ion beam. The Zakharov‐Kuznetsov equation is derived using the standard reductive perturbation technique that admits an obliquely propagating soliton solution. It is found that two types of quantum acoustic modes, that is, a slow acoustic mode and fast acoustic mode, could be propagated in our plasma model. The parameter that determines the nature of soliton, that is, compressive or rarefactive soliton, for slow mode is investigated. Our numerical results show that for the slow mode, the determining parameter is ion beam velocity in the case of relativistic degenerate electrons. We also have examined the effects of plasma parameters (like the beam velocity, the density ratio of positron to electron, the relativistic factor, and the propagation angle) on the characteristics of solitary waves.     

Routh Order Reduction Method of Relativistic Birkhoffian Systems

Routh order reduction method of the relativistic Birkhoffian equations is studied.For a relativistic Birkhoffian system,the cyclic integrals can be found by using the perfect differential method.Through these cyclic integrals,the order of the system can be reduced.If the relativistic Birkhoffian system has a cyclic integral,then the Birkhoffian equations can be reduced at least by two degrees and the Birkhoffian form can be kept.The relations among the relativistic Birkhoffian mechanics,the relativistic Hamiltonian mechanics,and the relativistic Lagrangian mechanics are discussed,and the Routh order reduction method of the relativistic Lagrangian system is obtained.And an example is given to illustrate the application of the result.     

Whittaker Order Reduction Method of Relativistic Birkhoffian Systems

The order reduction method of the relativistic Birkhoffian equations is studied. For a relativistic autonomous Birkhoffian system, if the conservative law of the Birkhoffian holds, the conservative quantity can be called the generalized energy integral. Through the generalized energy integral, the order of the system can be reduced. If the relativistic Birkhoffian system has a generalized energy integral, then the Birkhoffian equations can be reduced by at least two degrees and the Birkhoffian form can be kept. The relations among the relativistic Birkhoffian mechanics, the relativistic Hamiltonian mechanics and the relativistic Lagrangian mechanics are discussed, and the Whittaker order reduction method of the relativistic Lagrangian system is obtained. And an example is given to illustrate the application of the result.     

Whittaker Order Reduction Method of Relativistic Birkhoffian Systems

The order reduction method of the relativistic Birkhollian equations is studied. For a relativistic autonomous Birkhotffian system, if the conservative law of the Birkhotffian holds, the conservative quantity can be called the generalized energy integral. Through the generalized energy integral, the order of the system can be reduced. If the relativisticBirkhoffian system has a generalized energy integral, then the Birkhoffian equations can be reduced by at least twodegrees and the Birkhoffian form can be kept. The relations among the relativistic Birkhoffian mechanics, the relativistic Hamiltonian mechanics and the relativistic Lagrangian mechanics are discussed, and the Whittaker order reduction method of the relativistic Lagrangian system is obtained. And an example is given to illustrate the application of theresult.     

Wave growth rate in a cylindrical metal waveguide with ion-channel guiding of a relativistic electron beam

This paper addresses the formulae and numerical issues related to the possibility that fast wave may be grown when a relativistic electron beam through an ion channel in a cylindrical metal waveguide.To derive the dispersion equations of the beam-wave interaction,it solves relativistic Lorentz equation and Maxwell’s equations for appropriate boundary conditions.It has been found in this waveguide structure that the TM 0m modes are the rational operating modes of coupling between the electromagnetic modes and the betatron modes.The interaction of the dispersion curves of the electromagnetic TM 0m modes and the upper betatron modes is studied.The growth rates of the wave are obtained,and the effects of the beam radius,the beam energy,the plasma frequency,and the beam plasma frequency on the wave growth rate are numerically calculated and discussed.     

Kinetic theory of a relativistic plasma

The BBGKY hierarchy of equations for a system of relativistic charged particles is derived. The electromagnetic field is included in the dynamical system by decomposing the transverse part of the field of each particle into oscillators. Self-consistent field equations are obtained for the relativistic plasma, and an expression is also obtained for the correlation function which leads to the Belyaev-Budker collision integral.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 78–82, March, 1981.     

Nonlinear Langmuir waves in a relativisitc plasma

Langmuir waves in a relativistic plasma are considered using kinetic equations without consideration of captured particles. The frequency shift found for such waves contains contributions from four-wave interaction, and a contribution produced by the relativistic dependence of electron momentum on velocity.     

Spectroscopy of Baryons as Relativistic Three-Quark Systems

We present results from a study of baryon spectral properties within a relativistic constituent-quark model. In particular, we demonstrate the performance of a universal quark model for all light-, strange-, and heavy-flavor baryons with regard to their spectroscopy. Thereby we produce insights into the effective interaction between constituent quarks of the various flavors up, down, strange, charm, and bottom. The relativistically invariant mass spectra are obtained by two different methods for calculating the microscopic three-quark systems: a stochastic variational method, solving the eigenvalue problem of the invariant mass operator expressed by differential equations, and a Faddeev integral-equation method, adapted to treating long-range interactions, such as the quark confinement. The corresponding results agree very well, generally within a few percents. Taking into account relativistic effects through Poincaré invariance of the mass operator, or equivalently of the Hamiltonian, turns out to be of utmost importance.     

Ion acoustic soliton propagation in a magnetized relativistic plasma

Summary The Korteweg-de Vries equation for ion acoustic waves in the presence of weakly relativistic ion streaming velocity is derived in a magnetic plasma. It is found that relativistic effects are important in the solitary wave propagation for both fast and slow modes. Earlier results are reconfirmed. To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.     

Nonlinear distribution function for a plasma obeying Vlasov-Maxwell system of equations

The nonlinear distribution function of Allis, generalised to include the transverse electromagnetic waves in a plasma, is used to set up the coupled wave equations for the longitudinal and the transverse modes. These are solved, keeping terms up to the cubic order of nonlinearity, by using the method of multiple scales. The equations of wave modulation are derived, which are solved to discuss the nature of the modulational instability and solitary wave propagation. It is found that the solutions so obtained satisfy conditions which are very similar to the well known Lighthill criterion for stability, appropriately modified due to the coupling of the two modes. The role of the average constant current due to any flow of the resonant and trapped electrons in determining the stability, is also discussed.     

Cyclic integrals and reduction of rotational relativistic Birkhoffian system

The order reduction method of the rotational relativistic Birkhoffian is studied.For a rotational relativistic Birkhoffian system.the cyclic integrals can be found by using the perfect differential method.Through these cyclic integrals,the order of the system can be reduced.If the rotational relativistic Birkhoffian system has a cyclic integral,then the Birkhoffian equations can be reduced at least two degrees and the Birkhoffian form can be kept.An example is given to illustrate the application of the results.     

Relativisitic longitudinal non-Abelian oscillations in quark-antiquark plasma

We study the relativistic version of the non-Abelian, longitudinal wave in quark-antiquark plasma reported earlier by Bhat et al [Phys. Rev. D39, 649 (1989)]. We have also relaxed various approximations they made in their analysis. Both the quark and antiquark dynamics are taken in our analysis. The non-linearity arising from non-Abelian field as well as from plasma are included. Hence it is an exact longitudinal mode in relativistic quark-antiquark plasma, relevant to the study of quark gluon plasma. We find that earlier results are reproduced for non-relativistic and low amplitude oscillations, but are modified for relativistic or large amplitude waves. Further more, the above results are based on just four first-order equations for gauge invariant quantities derived from gauge covariant twelve first-order equations.     

Quasi-Potential Equations for a Complex Two-Particle System in the Context of Scalar Theories with Self-Action

Within the framework of the covariant simultaneous approach of quantum field theory, a complex system of two identical scalar particles with third- and fourth-order self-action is examined. Explicit forms of the retarded component of the Green's two-time function and of the energy-dependent interaction operator of the system are obtained in the lowest orders of perturbation theory. Three-dimensional quasi-potential equations for the relativistic wave function of a bound state are derived. Based on the results obtained, a complex system of two Higgs bosons is examined.