Energy transfer from particles to low-frequency turbulent fields in the non-uniform magnetized plasma is studied. Sufficient conditions for plasma stability are derived taking account of magnetic field shear.

The positive column of a gas discharge is investigated in the subcritical regime when no self-excited nonlinear ionization wave exists. We derive a model equation for the so-called wave of stratification, which is an externally excited envelope wave. The main point of this work is that, in contrast to previous papers, we take into account the radial structure of the homogeneous column. The mathematical description of the wave of stratification in the form of a complex Ginzburg–Landau equation follows by a systematic reductive perturbation method. The coefficients in the Ginzburg–Landau equation are first calculated in general and are then evaluated explicitly for a low-pressure argon discharge. The results are compared with those obtained from a frequently used simpler model that neglects any radial structure. Finally, the dynamics of the nonlinear wave of stratification is demonstrated via numerical simulations.

The Kelvin–Helmholtz (K–H) instability of two fluids of plasma streaming in opposite directions with the same velocity and in the presence of an external magnetic field is investigated. The usual magnetohydrodynamic equations with anisotropic pressure are considered. In the present problem, the two pressures parallel and perpendicular to the direction of the magnetic field are defined by polytropic pressure laws. The generalized pressure relations are used, and two equations of state for two pressures are assumed. The equations are linearized, and initially two different flow velocities are taken for the system. The flow is assumed to be in the direction perpendicular to the magnetic field. The problem is solved and a dispersion relation is obtained. From the dispersion relation, the K–H instability condition is obtained. It is found that the instability condition depends upon the polytropic indices of the pressure relations. The condition of instability is further obtained for MHD and Chew–Goldberger–Low systems. It is also found that the growth rate of the instability depends upon various polytropic indices.

We derive the dielectric tensor for multicomponent magnetized dusty plasmas, including the effect of capture of plasma electrons and ions by the dust particles. For propagation perpendicular to the external magnetic field and Maxwellian distributions of electrons and ions, we obtain compact expressions for the components of the dielectric tensor, which can be used to analyse wave propagation. An application to the magnetosonic wave is presented.

Propagation characteristics of dust acoustic solitons are studied in a magnetized dusty plasma consisting of ions, electrons and negatively charged dust grains. It is found that rarefactive solitons (solitons associated with negative potentials) are possible in such a plasma. The effects on the soliton characteristics of magnetic field strength, wave propagation angle, and densities and temperatures of the plasma particles are analysed.

The interaction among non-resonant ion acoustic plasma waves with different group velocities that are not close to each other is studied by an asymptotic perturbation method, based on Fourier expansion and spatio-temporal rescaling. It is shown that the nonlinear Schrödinger equation is not adequate, and instead a model system of nonlinear evolution equations is necessary to describe oscillation amplitudes of Fourier modes. This system is C-integrable, i.e. it can be linearized through an appropriate transformation of the dependent and independent variables. We demonstrate that the subclass of localized solutions gives rise to a solitonic phenomenology. These solutions propagate with the relative group velocity and maintain their shape during a collision, the only change being a phase shift. Numerical calculations confirm the validity of these predictions.

The general approach to Alfvén-wave current drive and induced plasma rotation in tokamaks with strongly elongated transverse cross-sections is considered. Model approximations are used to describe the circulating- and trapped-particle dynamics in all particle-trapping regions. This approach gives an accuracy of some percent. New terms, connected with the wave dissipation on trapped particles in the second and third trapped-particle regions for elongated tokamaks, are taken into account. The plasma rotation and longitudinal current, depending on the absorbed power of kinetic Alfvén waves, are discussed.

In the statistical quasilinear theory of weak plasma turbulence, charged particles moving in electrostatic fluctuations diffuse in velocity, i.e. the velocity variance 〈Δv2(t)〉 increases linearly with time t, for times long compared with the auto-correlation time τac of the field, which may be estimated as the reciprocal of the spectral width of the fluctuations. Recent test-particle simulations have revealed a new regime at very long timescales t[Gt ]τac where quasilinear theory breaks down, for intermediate field amplitudes. As this behaviour is not consistent with a diffusion on quasilinear timescales, the problem of the motion of particles in a broadband wave field, for the case of a slowly growing field, is considered here from a purely dynamical point of view, introducing no statistics on the field and no restriction on the amplitude of this field. By determining, on a given timescale, and in the frame of wave–particle interaction, the spectral width over which waves interact efficiently with a particle, a new timescale is found: the nonlinear time of wave–particle interaction τNL∝ (spectral density of energy)−1/3[Gt ]τac. This is the correlation time of the dynamics. For times shorter than τNL, the particles trajectories remain globally regular, and do not separate: they follow a quasifractal set of dimension 2. For times long compared with τNL, there appears a ‘true’ diffusive regime with mixing and decorrelation, due to nonlinear mixing in phase space and the localization of the wave–particle interaction. These theoretical results are confirmed by a numerical study of the velocity variance as a function of time. In particular, the particle dynamics really do become diffusive on timescales several orders of magnitude longer than that predicted by quasilinear theory (namely [Gt ]τNL[Gt ]τac). Finally, deviations from the quasilinear value of the diffusion coefficient and wave growth rate, discussed in the literature, are explained.

We discuss the nonlinear evolution of the Weibel instability of two counter-streaming electron beams in the relativistic and non-relativistic regimes in the framework of a two-fluid description. We show the presence of two singularities per wavelength, responsible for the formation of very large density spikes. In the case of non-symmetric beams, we observe the compressive wave-break of the fast electron population, and the generation of a dipolar magnetic field associated with a central fast thin current and two larger slow return currents. This structure is very similar to those observed in PIC simulations of laser-plasma interactions.

Hamiltonian and Lagrangian perturbation theory is used to describe linear wave propagation in inhomogeneous media. In particular, the problems of wave propagation on an inhomogeneous string, and the propagation of sound waves and entropy waves in gas dynamics in one Cartesian space dimension are investigated. For the case of wave propagation on an inhomogeneous heavy string, coupled evolution equations are obtained describing the interaction of the backward and forward waves via wave reflection off gradients in the string density. Similarly, in the case of gas dynamics the backward and forward sound waves and the entropy wave interact with each other via gradients in the background flow. The wave coupling coefficients in the gas-dynamical case depend on the gradients of the Riemann invariants R± and entropy S of the background flow. Coupled evolution equations describing the interaction of the different wave modes are obtained by exploiting the Hamiltonian and Poisson-bracket structure of the governing equations. Both Lagrangian and Clebsch-variable formulations are used. The similarity of the equations to equations obtained by Heinemann and Olbert describing the propagation of bidirectional Alfvén waves in the solar wind is pointed out.

Nonlinear structures in the formof coherent tripolar vortices, associated with shear-Alfvén perturbations in the presence of both magnetic and velocity shears, are studied analytically.

A molecular plasma generated by a particle beam generally departs strongly from a Maxwellian distribution and exhibits a pronounced depletion of electrons as soon as cold electrons cross the first vibrational barrier. We show that this situation produces screened Coulomb interactions that enlarge the Coulomb cross-section in the neighbourhood of this first vibrational threshold. Including these screened interactions through the Balescu–Lenard operator with all excitation transitions leads to a modification of the distribution at the first vibrational barrier. An application is given to the case of low-pressure nitrogen lasers.

A theoretical investigation of extraordinary polarized surface waves at the second harmonics of ion and electron cyclotron frequencies propagating across an external steady magnetic field is carried out in the case of weak plasma spatial dispersion when the thermal velocities of plasma particles are much less than the phase velocities of the considered waves. These waves are eigenmodes of a planar plasma–vacuum waveguide structure that is situated in a steady magnetic field oriented parallel to the plasma surface. A cold charged-particle beam is assumed to propagate over the plasma interface. Excitation of surface X modes at the second harmonics of electron and ion cyclotron frequencies due to the beam–plasma interaction is studied analytically. The dependence of surface-type X-mode (STXM) growth rates on the considered waveguide structural parameters is also studied.

A recently proposed method to calculate the spectrum of linear, incompressible, unbounded plasma flows is applied to magnetohydrodynamic flows about X points. The method transforms the two-dimensional spectral problem in physical space into a one-dimensional problem in Fourier space. The latter problem is far easier to solve. Application of this method to X-point plasma flows results in two kinds of essential spectra. One kind corresponds to stable perturbations and the other one to perturbations that become overstable whenever the square of the poloidal Alfvén Mach number becomes larger than 1. Apart from these two spectra, no other spectral values were found.

We reply here to a criticism of our paper (Tsytovich et al. 1996) by Iglesias (1997).

In our paper we present a very general formulation of collective effects in bremsstrahlung that is valid for any non-equilibrium non-Maxwellian particle distribution. This result is given in (2.20) early in the paper. The standard treatments of bremsstrahlung found in books like Bekefi (1966) are only for thermal plasmas, where the fluctuation–dissipation theorem is valid. Note that the fluctuation–dissipation theorem cannot be used for non-thermal or non-dipole fields, and in this respect the method we use is more general. Our method is the more complex of the approaches used, but, as stated, it can handle situations that cannot be treated by the standard approach. Our main result is the formula (2.20), which is valid for any non-equilibrium non-Maxwellian particle distribution, and which cannot be found anywhere else in the literature. Furthermore, we find new qualitative effects indicating that the ion–ion bremsstrahlung (which is always neglected in the literature) is not small in the case where the collective effects are taken into account, and is in fact, for certain frequencies, of the order of the electron–electron bremsstrahlung. The other qualitatively new result is that, where collective effects are important, the electron–electron bremsstrahlung is not of the order v2Te/c2, as it is for the case in the absence of collective effects, but of the order ω2pe/ω2 times less – which, for example in the solar interior, where ω2pe/ω2 is of the order of v2Te/c2, is then of the order of v4Te/c4.