Relativistic Boltzmann theory for a plasma: IX. Attenuation of hydromagnetic waves

Expressions are given for the space attenuation coefficient of hydromagnetic waves in a relativistic plasma. By taking into account all transport processes known from the Chapman-Enskog procedure a hitherto unnoticed dissipative effect is found. A comparison is made with the attenuation of sound waves in relativistic neutral gases.     

Relativistic Boltzmann theory for a plasma: III. Viscous phenomena

The linear laws pertaining to viscous phenomena are derived for a relativistic plasma in an electromagnetic field. The results found in this microscopic context fit precisely into the general scheme obtained on a macroscopic level by Hooyman, de Groot and Mazur.     

Relativistic Boltzmann theory for a plasma: II. Reciprocal relations

The linear or phenomenological laws such as Ohm's law, Fourier's law and Fick's law are derived for a relativistic plasma in an electromagnetic field. It is shown that the choice of a reference frame as proposed by Landau and Lifshitz entails-in contrast to, for instance, the choice of Eckart-the validity of Onsager's reciprocity relations.     

Propagation of hydromagnetic waves in a semi-infinite plasma

The generation and propagation of hydromagnetic waves in a semi-infinite plasma bounded by an oscillating flat boundary of arbitrary electrical conductivity is analysed. The resistive and ion-cyclotron terms are retained in the governing equations. The two-dimensional plasma flow is permeated by four distinct modes of wave propagation, two of which are modified shear waves and the remaining modes penetrate through the inviscid region of the plasma. It is found that, a perfectly conducting bounding surface is able to generate all the four wave modes whereas the effect of an insulating boundary is confined within the modified viscous layer of the plasma.I thank Prof. S. S. Chawla for his guidance and advice. It is a pleasure to acknowledge the numerous valuable suggestions made by the referee.     

Relativistic Boltzmann theory for a plasma: I. The entropy production

An expression for the entropy production has been derived on the basis of which it is argued that the choice of reference frame as proposed by Landau and Lifshitz is to be preferred rather than any other possibility.     

Relativistic Boltzmann theory for a plasma: VI. The relativistic Landau equation

The relativistic Landau equation is obtained as the Fokker-Planck approximation to the relativistic Boltzmann equation. It is shown that, as far as the transport coefficients are concerned, both equations yield identical results in the dominant term approximation. Special attention is given to Møller-, Bhabha- and Mott-scattering processes. In the case of relativistic electron-electron collisions a detailed determination of the Coulomb logarithm is given.     

Relativistic Boltzmann theory for a plasma: X. Electrical conduction of the cosmological fluid

General expressions are derived for the transport coefficients related to the vectorial transport phenomena in a plasma. As an example, the electrical conductivity of the cosmological fluid is calculated.     

Relativistic nonlinear waves in a magnetised plasma

Relativistic propagation of a nonlinearly-coupled circularly-polarised electromagnetic wave and a Langmuir wave along the applied magnetic field is considered. Analytical solutions are given or are indicated for some special cases like purely transverse waves and purely longitudinal waves. In the presence of an applied magnetic field, the incident circularly polarised electromagnetic wave is found to propagate further into denser regions of the plasma — a result which is in accord with the so-called inverse Faraday effect. Finally, we shall consider general coupled transverse and longitudinal waves for which we give an approximate solution. We investigate whether this system of coupled waves exhibits any internal resonances and consequent energy exchange between them.     

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根据狭义相对性原理,应用Lorentz变换法则,从相对运动媒质静止参考系中的有关结论,获取了实验室参考系中所需结果。通过证明平面波相位是Lorentz不变量,指出实验室参考系中平面波解的存在性。由Lorentz变换导出了实验室参考系中平面波色散关系表示式,据此给出运动媒质的波动方程。由Lorentz变换导出运动媒质中平面波Maxwell方程。基于这些结果,应用Lorentz变换获得了平面波从自由空间垂直入射到各向同性运动等离子体半空间时反射波与透射波的有关特性。     

Toward a theory of plasma waves in bilayer graphene

An expression for the longitudinal dielectric permeability of a nondegenerated electron gas in bilayer graphene is derived. In the calculations, the single-band low-energy approximation is used for the electron spectrum. The dispersion relation and the damping rate of plasma waves in bilayer graphene are found.     

Propagation of electromagnetic waves in hot magnetoactive plasma

The paper derives the general form of the tensor of dielectric permittivity? _ij(ω,k), Eq. (15), of non-relativistic hot magnetoactive collisionless plasma taking into consideration the influence of spatial dispersion. The general form of the tensor? _ij(ω,k) is used to express the tensorε _ij(ω,k) in the region of weak and strong spatial dispersion and in some special cases. A general dispersion equation (30) is derived and an analysis is made of the waves propagating in hot magnetoactive plasma. The expressions derived are used to investigate the damping of a right-handed circularly polarized wave propagating in hot magnetoactive plasma in the direction of the magnetic field.     

Relativistic kinetic theory of quantum systems: VII. Transport coefficients for (eve) and (evμ) mixtures

For (ev_e) and (ev_μ) binary mixtures the transport coefficients are evaluated as functions of the temperature and composition of the system. The particles are assumed to interact according to the Weinberg-Salam model. Results for the two mixtures are compared, and are contrasted to corresponding results obtained on the basis of a mean free path model.     

Relativistic Boltzmann-theory for a plasma: V. Reduction of the collision integrals

The complicated twelve-fold collision-integrals occurring in relativistic kinetic theory are reduced to sums of two-fold integrals which can easily be evaluated once the interactions of the particles of the system in question are specified.     

Propagation of waves in a multicomponent plasma having charged dust particles

Propagation of both low and high frequency waves in a plasma consisting of electrons, ions, positrons and charged dust particles have been theoretically studied. The characteristics of dust acoustic wave propagating through the plasma has been analysed and the dispersion relation deduced is a generalization of that obtained by previous authors. It is found that nonlinear localization of high frequency electromagnetic field in such a plasma generates magnetic field. This magnetic field is seen to depend on the temperatures of electrons and positrons and also on their equilibrium density ratio. It is suggested that the present model would be applicable to find the magnetic field generation in space plasma.     

Propagation of ion-acoustic waves in a dusty plasma with non-isothermal electrons

For an unmagnetised collisionless plasma consisting of warm ions, nonisothermal electrons and cold, massive and charged dust grains, the Sagdeev potential equation, considering both ion dynamics and dust dynamics has been derived. It has been observed that the Sagdeev potential V(ϕ) exists only for ϕ > 0 up to an upper limit (ϕ ≃ 1.2). This implies the possibility of existence of compressive solitary wave in the plasma. Exhaustive numerics done for both the large-amplitude and small-amplitude ion-acoustic waves have revealed that various parameters, namely, ion temperature, non-isothermality of electrons, Mach numbers etc. have considerable impact on the amplitude as well as the width of the solitary waves. Dependence of soliton profiles on the ion temperature and the Mach number has also been graphically displayed. Moreover, incorporating dust-charge fluctuation and non-isothermality of electrons, a non-linear equation relating the grain surface potential to the electrostatic potential has been derived. It has been solved numerically and interdependence of the two potentials for various ion temperatures and orders of non-isothermality has been shown graphically.      

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.