The physical polarities of electromagnetic waves propagating in a magnetoplasma-filled cylindrical waveguide are studied by numerical calculations and simple analytical analyses. In the plane of the frequency–axial wave number, the obtained results show that dispersion curves of right-hand polarized (RHP) and left-hand polarized (LHP) electromagnetic waves propagating in an infinite magnetoplasma determine characteristic regions in which wave modes propagating in a magnetoplasma-filled cylindrical waveguide have different physical polarities. The frequency region slightly below and above $\omega_{{\rm r}_1}$ ($\omega_{{\rm r}_1}$ denotes the lower-branch frequency of the RHP electromagnetic wave propagating in an infinite magnetoplasma) is characterized by pure or physical dominant RHP modes. In the frequency region of $\omega_{\rm l}\,{<}\,\omega\,{<}\,\omega_{{\rm r}_2} (\omega_{\rm l}$ and $\omega_{{\rm r}_2}$ denote the frequency of the LHP wave and the upper-branch frequency of the RHP wave propagating in an infinite magnetoplasma), except for formal RHP waveguide ${\it EH}^{\rm u}$ modes with sufficient large axial wave numbers, all modes are pure or dominant physical LHP waves. The frequency region of $\omega\,{>}\,\omega_{{\rm r}_2}$ can be thought of as a RHP area. The physical polarity of wave modes clarified in this paper is helpful to understand the interaction between charged particles and waves propagating in a magnetoplasma-filled cylindrical waveguide.

The authors have identified three regimes of propagation of circularly polarized laser beams in plasmas, taking into account the relativistic laser plasma interaction. An appropriate expression for the nonlinear dielectric constant has been used in the analysis of laser-beam propagation in the paraxial approximation. Three regimes of propagation in a homogeneous plasma have been identified, viz.

I. In this regime the beam keeps on diverging.

II. In this regime the beam travels in a guided oscillatory and diverging mode, with the width lying between the original value and a maximum value.

III. In this regime the beam becomes self-focused, with the width lying between the original value and a minimum value.

For a given value of $\omega _{\rm p}/\omega $ the regimes are characterized by dimensionless power and dimensional beam width. The variation of beam width with distance of propagation has also been obtained for typical values of parameters in the three regimes.

The variation of beam-width parameter with distance of propagation has also been studied for inhomogeneous plasma and penetration in overdense plasmas is indicated.

The nonlinear coupling between short-wavelength electron-temperature-gradient (ETG) modes and zonal flows in plasmas is considered. The mode-coupling equations are derived by using a Boltzmann ion distribution and a fluid electron response described by the hydrodynamic and energy equations. A dispersion relation for the nonlinearly coupled ETG modes and the zonal flows is derived. The results show enhanced zonal flows, which can affect the electron energy transport in tokamaks and stellarators.

Perturbation reductive procedures, as used to analyse various weakly nonlinear plasma waves (solitons and periodic waves), normally lead to the dynamical system being described by KdV, Burgers' or a nonlinear Schrödinger-type equation, with properties that can be deduced from an array of mathematical techniques. Here we develop a fully nonlinear theory of one-dimensional stationary plasma waves, which elucidates the common nature of various diverse wave phenomena. This is accomplished by adopting an essentially fluid dynamic viewpoint. In this unified treatment the constants of the motion (for mass, momentum and energy) lead naturally to the construction of the wave structure equations. It is shown, for example, that electrostatic, Hall–magnetohydrodynamic and ion–cyclotron–acoustic nonlinear waves all obey first-order differential equations of the same generic type for the longitudinal flow field of the wave. The equilibrium points, which define the soliton amplitude, are given by the compressive and/or rarefactive roots of a total plasma ‘energy’ or ‘momentum’ function characterizing the wave type. This energy function, which is an algebraic combination of the Bernoulli momentum and energy functions for the longitudinal flow field, is the fluid dynamic counterpart of the pseudo-potentials, which are characteristic of system structure equations formulated in other than fluid variables. Another general feature of the structure equation is the phenomenon of choked flow, which occurs when the flow speed becomes sonic. It is this trans-sonic property that limits the soliton amplitudes and defines the critical collective Mach numbers of the waves. These features are also obtained in multi-component plasmas where, for example, in a bi-ion plasma, momentum exchanges between protons and heavier ions are mediated by the Maxwell magnetic stresses. With a suitable generalization of the concept of a sonic point in a bi-ion system and the corresponding choked flow feature, the wave structures, although now more complicated, can also be understood within this overall fluid framework. Particularly useful tools in this context are the momentum hodograph (an algebraic relation between the bi-ion speeds and the electron speed, or magnetic field, which follows from the conservation of mass, momentum and charge-neutrality) and a generalized Bernoulli energy density for each species. Analysis shows that the bi-ion solitons are essentially compressive, but contain the remarkable feature of the presence of a proton rarefactive core. A new type of soliton, called an ‘oscilliton’ because embedded spatial oscillations are superimposed on the classical soliton, is also described and discussed. A necessary condition for the existence of this type of wave is that the linear phase velocity must exhibit an extremum where the phase speed matches the group speed. The remarkable properties of this wave are illustrated for the case of both whistler waves and bi-ion waves where, for the latter, the requisite condition is met near the cross-over frequencies. In the case of the whistler oscilliton, which propagates at speeds in excess of one half of the Alfvén speed (based on the electrons), an analytic solution has been constructed through a phase-portrait integral of the system in which the proton and electron dynamics must be placed on the same footing. The relevance of the different wave structures to diverse space environments is briefly discussed in relation to recently available high-time and spatial resolution data from satellite observations.

The phase shift of long-wavelength modes due to drift-wave turbulence is studied in the Hasegawa–Mima model. Although the growth rate has been the main focus, it is equally crucial to understand the frequency shift from the linear characteristics. The test-field model is applied in order to properly treat the sweeping effect of the large scales on a small scale. The frequency shift is found to be small compared with the growth rate and the non-local triad mode-interaction time turns out to be determined by the energy of the long-wavelength modes.

The destabilization of fast magnetoacoustic waves (FMWs) and Alfvén waves (AWs) in plasmas with energetic ions having strongly anisotropic velocity distribution is considered. It is shown that when the ratio of the energetic ion velocity to the Alfvén velocity is large enough, the growth rate of the low-frequency FMW instability has sharp maxima at certain angles of the wave propagation. On the other hand, low-frequency FMWs are always stable, whereas the AWs and high-frequency FMWs can be unstable when the waves propagate along the magnetic field. The developed theory is applied to a plasma of the flashing loops of the Solar Corona. It is found that the presence of a very small amount of the energetic ions can lead to instabilities with the growth rate, which considerably exceeds the inverse characteristic collisional times. It is concluded that the frequency spectrum of the destabilized waves can be rather wide, which may lead to the heating of the bulk plasma ions on the sub-harmonics of the ion gyrofrequency due to the mechanism suggested by Chen et al.

The fluid quintic dispersion equation and the full kinetic Boltzmann–Vlasov equation have been programmed for a one-species magnetoplasma in a form permitting direct comparison between them. The quintic equation yields five wave-modes, two electromagnetic, a Langmuir or Bernstein mode and two transversely polarized acoustic modes driven by the trace-free part of the anisotropic pressure tensor. The slower acoustic mode is found in the kinetic analysis to be evanescent, the other suffers appreciable Landau damping except in the first gyroharmonic band when its phase velocity approaches and even exceeds that of the Langmuir mode, with a resultant mixing of modal properties. The Langmuir or Bernstein mode refractive index surfaces found in the fluid and kinetic analyses are generally in good agreement, but gyroharmonic wave–particle interactions seen in the Bernstein modes are missed in the fluid analysis, such as resonant effects very close to the gyroharmonic frequencies and strong damping at all propagation angles when the wave frequency lies in a forbidden Bernstein region. In all cases the fluid analysis provides additional information on wave polarization and generalized energy fluxes–electromagnetic and acoustic–permitting easy identification of modes.

This paper introduces the average-ion concept into the Debet–Huckle model, and obtains the average-ion Debet model to calculate the Debet length and energy level shift of the average ion. The place of the ion-sphere model in screened hydrogens theory is taken by the average-ion Debet model, and the electron densities of shock-generated, non-ideal argon plasmas for high-density and low-temperature at a few EA electron-volts are calculated. The results of the calculation are compared with the results of the ion-sphere model.

The nonlinear mechanism of the transformation of magnetohydrodynamic (MHD) Alfvén waves to kinetic Alfvén waves (KAWs) in the homogeneous magnetized plasma with small plasma parameter $\beta\,{\ll}\,1$ is investigated. As the generation mechanism, the parametric instability where the MHD Alfvén wave is the pumping wave is considered. On the basis of the two-fluid MHD and Vlasov equation, the nonlinear dispersion relation describing three-waves interaction, the instability growth rate and the threshold of the instability are found. The theoretical results are used for the interpretation of plasma heating in the solar corona.

The Boltzmann collision integral for binary encounters is restricted to rarefied gases and plasmas by the constraint that the mean free path be much larger than the range of interaction. For dense media the two lengths become comparable and a proper account of the mutual influence exerted by one particle on the other during a collision must be taken. There are also other situations involving charged–charged long-range interactions for which this condition is met even in rarefied plasmas. The matter is considered in this work with the solution of the BBGKY (Born, Bogoliubov, Kirkwood, (H. S.) Green, Yvon) equation to determine the joint distribution function for the encountering particles. It is shown, in particular, that for dense gases the results replace the traditional Enskog $\chi $ factor, whereas for plasmas oscillatory phenomena can be driven. The proposed theory constitutes an improvement over the revised Enskog theory (RET) to the extent that it is not restricted to the soft sphere encounters, but valid for any sort of field interaction between colliding particles. Moreover the correlation term replaces the unsuitable restitution coefficient of the RET approach, which is restricted to impact theory. The present material is important for studies in solar and terrestrial physics, which require the sole knowledge of the one particle distribution function, namely gas dynamics and Coulomb plasma research.

High-energy or relativistic electron beam acceleration along and across a magnetic field, and the generation of an electric field transverse to the magnetic field, both induced by the Compton scattering of almost perpendicularly propagating extraordinary waves, are investigated theoretically based on kinetic wave equations and transport equations. Compton scattering occurs via nonlinear Landau damping of two extraordinary waves interacting nonlinearly with the electron beam, satisfying the resonance condition of $\omega _{{\bf k}} -\omega _{{\bf k}'} - (k_{ \bot } - k'_{\bot})\nu_{\rm d} - (k_{\|} - k'_{\|})\nu_{\rm b}\,{=}\,m\omega _{\rm ce}$$(m\,{=}\,0, \pm 1)$, where $\nu_{\rm b}$ and $\nu_{\rm d}$ are the parallel and perpendicular velocities of the electron beam, respectively. The transport equations can be derived from the single-particle theory and also from Vlasov–Maxwell equations. The transport equations show that two extraordinary waves accelerate the electron beam in the ${\bf k}''$ direction (${\bf k}''\,{=}\,{\bf k} \,{-}\,{\bf k}'$). Simultaneously, an intense cross-field electric field ${\bf E}_{0}\,{=}\,{\bf B}_{0}\,{\times}\,{ \bf v}_{\rm d}/c$ is generated via the dynamo effect owing to the perpendicular drift of the electron beam to satisfy the generalized Ohm's law, which means that this cross-field electron drift is identical to the ${\bf E}\,{\times}\, {\bf B}$ drift. The single-particle theory is very useful for an easy and straightforward understanding of the physical mechanism of the electron beam acceleration and the generation of cross-field electric field, although the rigorously exact transport equations are derived from Vlasov–Maxwell equations.

Dust charging in the sheath is investigated with the single dust model. The sheath profile and variation of dust charge are revealed under the effect of ion temperature. It is shown that the dust particles are rapidly positively charged in the pure ion sheath near the wall and that the ion motion effectively shifts the zero-point of the dust charge to the wall.

In this paper, the characteristics of dust-acoustic solitary waves in dusty plasma are studied. Dust charge and temperature are treated as variables. The authors have used the pseudopotential method to investigate the possibility of compressive as well as rarefactive solitons. An expression for the pseudopotential has been derived. The pseudopotential is a function of the Mach number, the relative temperature of low and high ion components, the relative ion concentration of dust charge and the temperature. Numerical computation shows that for the chosen set of parameters, only compressive solitons exist and their amplitudes increase with increasing Mach number. An increase in the dust temperature results in the disappearance of the compressive soliton. It is the only small parameter regime where compressive as well rarefactive solitons coexist. The effect of the relative ion temperature on solitons is also investigated. In the small amplitude limit, an increase in the dust temperature leads to a transition from compressive to rarefactive solitons.

In this work we delineate the physical picture for the propagation of electromagnetic oscillations in a moving plasma. We present calculations devoted to describing the dispersion features of the radiation that propagates within a magnetoactive plasma. Both classical and relativistic treatments have been employed. We have concluded that if the outflow is moving with small velocities, the general motion of the plasma does not affect the propagation of transverse electromagnetic waves. The waves are refracted according to the ordinary refraction law deduced for non-moving magnetoactive plasmas. The global movement does not change the dispersion relations, and the shapes of the corresponding curves remain unaltered. In the relativistic formulation, we have derived the equations that determine the electromagnetic wave spectrum for a moving magnetoactive plasma. In this case, it is found that the flow velocity affects the plasma dispersion properties and is responsible for new dispersion branches: transverse and longitudinal perturbations. The ordinary and extraordinary electromagnetic modes are modified and described by dispersion relations whose points of resonance are also in explicit dependence on the plasma velocity. Furthermore, the relativistic motion causes the split of electromagnetic modes into two independent waves that propagate at different rates. This effect is remarkable for highly relativistic velocities. The results presented in this work may be applied in order to incorporate suitable corrections to the dispersion models, developed to explain the anomalous features of observed lines or continuum radiation, associated with astrophysical relativistic outflows which are present in gamma-ray bursts, blazars, relativistic jets in AGNs (active galactic nuclei), quasars and microquasars.

The emission coefficient due to classical electron–ion bremsstrahlung is calculated for a non-ideal plasma with an effective interaction. An approach due to Gould is used to obtain the emission coefficient for bremsstrahlung. It is shown that this result can also be derived from an approximation to the force–force correlation function assuming no correlations among particles. The trajectory for electrons in the effective potential is determined by the numerical solution of Newton's equation. Comparison is made with molecular dynamics results for the dynamical collision frequency.

Analytic approximations to relativistic plasma dispersion functions are derived in terms of the exponential integral function, ${\rm Ei}(x)$, for relativistic temperatures $T\gapprox m_{\rm e}c^2$ (where $m_{\rm e}c^2$ is the electron rest energy). It is shown that a simpler, useful approximation to these functions can be obtained based on known approximations to the exponential integral function.

The energy–momentum tensor is usually obtained by symmetrizing the canonical tensor, which is sometimes difficult. The fact that the energy–momentum tensor must always be gauge invariant, and insight gained by investigating the Maxwell kinetic equations, lead one to conclude that this tensor should be readily obtainable for a certain class of Lagrange densities. The appropriate method to achieve this consists in performing gauge-invariant variations within the framework of Noether's theory. These variations are equivalent to shifts in space and time, and are considered here instead of the usual shift variations, which are not gauge invariant. These features indicate the existence of a certain underlying structure which is made evident by the proposed method. The Lagrange densities of the class in question are characterized by having a gauge-invariant contribution additional to the Maxwell part. For vanishing potentials, such Lagrange densities lead directly to a symmetric canonical tensor; this implies that there are only scalar fields. Maxwell's equations, being the basic part of such theories, are treated first. Then, the coupled system of electromagnetic fields and the usual scalar fields describing charged matter is considered. Finally, a different kind of scalar field which occurs in a structural non-standard form in collisionless phase-space theories (Vlasov or collisionless Boltzmann-like equations) is treated.

In this paper we describe a relatively simple and transparent method of obtaining collisionless drift-kinetic, gyrokinetic and more general theories, including local charge, energy and momentum conservation laws. An important feature of the new formalism is, contrary to present-day theories, the exact gauge invariance, thus avoiding certain inconsistencies. The present paper starts with the introduction and proof of the correctness of a Lagrangian for combined Maxwell-kinetic theories in general coordinates as concerns the particle motion. The kinetic part of it is formulated in Eulerian form by means of the equations of motion in the form of Hamilton–Jacobi's equation, used only as a tool, and Dirac's constraint theory. Charge and current densities automatically distinguish between ‘particle-like’ (guiding-centre), polarization and magnetization contributions. This formalism is applied to averaging coordinates derived by a method similar to Kruskal's. Certain properties of the averaging coordinates, according to the basic requirements imposed on them, can be used to obtain a gyroangle independent Lagrangian, from which one can obtain a Lagrangian for the combined Maxwell-kinetic theories in a reduced phase space that is applicable to situations in which one is not interested in the dependence on some kind of gyroangle describing the gyromotion, whose treatment can, however, easily be added. The basic perturbation theory, which aims at obtaining averaging phase-space coordinates, is done solely within the Kruskal formalism in which only the electric and magnetic fields appear, but not the corresponding potentials. This formalism provides, in particular, information about the allowed amplitudes of fluctuations. The results are later used to obtain approximate expressions for the Lagrange functions in the drift-kinetic and the gyrokinetic ordering. For the definition of certain approximations to the exact Lagrangian the central principle is the exact gauge invariance. The terms of the zeroth and first orders needed for such an approximation are given. For the drift-kinetic ordering Littlejohn's Lagrangian is readily rederived and hence the drift-kinetic theory as obtained and investigated by the present authors in some previous work. Conservation laws and their mathematical structures corresponding to the gyroangle-independent Lagrangian are obtained in a following paper. There, in particular, a detailed description of how to obtain variations of gyroangle averaged quantities in the reduced phase space is given, and it is explained how these variations are used in a modified form of Noether's theory which observes exact gauge invariance.

Magnetohydrodynamic processes in thin accretion disks involving magnetic viscosity are investigated. The relevant MHD equations for the thin disk approximation and the anomalous magnetic viscosity dependent on temperature $T$ and radius $r$ are included. These stationary structures, including distributions of the surface mass density, temperature, in-flow velocity and magnetic fields of a disk around a young stellar object, are numerically examined. It is shown that the consideration of anomalous viscosity is necessary for the validity of the distributions. For example, the surface density is a decreasing function of radius because of it and there is a strange increasing part in the distribution of the density if it is ignored. In particular the distribution of effective temperature is a smoothly decreasing function of radius with power index $q\,{=}\,{-}\frac{1}{2}$, corresponding to the observed radiation flux density, provided that the magnetic fields are suitably chosen.

The effect of variable dust charge, dust temperature and trapped electrons on small-amplitude dust acoustic waves is investigated. It is found that both compressive and rarefractive solitons as well as double layers exist depending on the non-isothermality parameter. A modified Korteweg de Vries (MKdV) equation is derived. Critical cases, at which the nonlinear coefficient is approximately zero, are derived. In the vicinity of the critical values, KdV and further MKdV (FMKdV) equations are obtained. Employing quasipotential analysis, the Sagdeev potential equation has been derived. Because of the presence of free and trapped electrons, the plasma acoustic wave exhibits different features of various solitary waves. The Sagdeev potential equation, at a small amplitude, shows that the ordering of non-isothermality in the dusty plasma plays a unique role. In the case of a plasma with first-order non-isothermality, the Sagdeev potential equation shows the compressive solitary-wave propagation while, for a plasma with higher-order non-isothermality, the solution of this equation reveals the coexistence of compressive and rarefractive solitary waves. In addition, for certain plasma parameters, the solitary wave disappears and a double layer is expected. Again, with the better approximation in the Sagdeev potential equation, more features of solitary waves, known as spiky and explosive, along with the double layers, are also highlighted. The findings of this investigation may be useful in understanding laboratory plasma phenomena and astrophysical situations.