The conventional Jeans model is modified by the addition of electric charging. The standard procedure of kinetic treatment results in a dispersion relation which describes both the Jeans instability and Langmuir oscillations, with the analog of Landau damping. Coulomb interactions tend to stabilize the Jeans instability diminishing the growth rate whereas the gravitational field tends to destabilize Langmuir oscillations. Collisions between particles are taken into account.

In this communication the interaction between two Gaussian electromagnetic beams in an ionic collision dominated plasma has been investigated, when the axes of the two beams are initially (z = 0) parallel along the z-axis in the xz plane; the beams are initially propagating in the z-direction. Taking into account the loss of electron energy by collisions and by thermal conduction, the energy balance equation for electrons has been solved to obtain the space dependence of the electron temperature and the dielectric function has been expressed as a function of the electron temperature; this expression for the dielectric function has been substituted in the wave equation and a solution of the resulting nonlinear equation obtained in the paraxial approximation. Second-order coupled ordinary differential equations have been obtained for the distance between the centers of the beams and the beam widths in the x- and y-directions as a function of the distance of propagation along the z-axis. The equations have been solved numerically for a range of parameters and a discussion of the results is presented for the case when the two beams have the same axial irradiance, frequency and width. From simple considerations it is seen that the beams attract each other when 2xo < wro and in this situation beams are close enough for the paraxial approximation to be valid.

Assuming a non-relativistic three species electron–positron–ion plasma, the counterstreaming instability is investigated for waves propagating parallel and perpendicular to a homogeneous background magnetic field. To support previous analytical investigations (Tautz and Sakai 2007), the instability is investigated by means of self-consistent particle-in-cell simulations. It is shown that the presence of a third particle species is responsible for a variety of new features that cannot be seen either from an electron–ion plasma or for an electron–positron plasma.

Assuming a non-relativistic three species electron–positron–ion plasma, the counterstreaming instability is investigated for waves propagating parallel and perpendicular to a homogeneous background magnetic field. From the exact linear dispersion relations, it is shown analytically how the growth rates change with increasing baryon loading, revealing new characteristics that cannot be found either for an unmagnetized plasma involving three particle species or for a plasma with only two particle species.

The longitudinal heating of a z-pinch plasma with short laser pulses is simulated using COMSOL Multiphysics. The heating of an existing pinch plasma for different electron densities with a short laser pulse is shown. It is illustrated that the initial electron density of the plasma has a significant impact on penetration of the pulse and subsequent heating of the plasma. With a Nd:YAG laser pulse the most effective heating occurs when the initial electron density is about 1/15 of the critical electron density of the plasma. It is shown that by increasing the initial electron density by even a factor of two above this level causes the absorption to increase dramatically, preventing penetration of the laser pulse and greatly limiting the heating of the plasma.

In this paper we study the propagation of nonlinear ion-acoustic waves in plasmas with negative ions. The Gardner equation governing these waves in plasmas with the negative ion concentration close to critical is derived. The weakly nonlinear theory of modulational instability based on the use of the nonlinear Schrödinger equation is discussed. The investigation of the nonlinear dynamics of modulationally unstable quasi-harmonic wavepackets is carried out by the numerical solution of the Gardner equation. The results are compared with the predictions of the weakly nonlinear theory.

Reconnection physics at micro-scales is investigated in an electron magnetohydrodynamics frame. A new process of collapse of the neutral current sheet is demonstrated by means of analytical and numerical solutions. It shows how at scales smaller than ion inertia length a compression of the sheet triggers an explosive evolution of current perturbation. Collapse results in the formation of a intense sub-sheet and then an X-point structure embedded into the equilibrium sheet. Hall currents associated with this structure support high reconnection rates. Nonlinear static solution at scales of the electron skin reveals that electron inertia and small viscosity provide an efficient mechanism of field lines breaking. The reconnection rate does not depend on the actual value of viscosity, while the maximum current is found to be restricted even for space plasmas with extremely rare collisions. The results obtained are verified by a two-fluid large-scale numerical simulation.

Solitary waves are investigated in a magnetized electron–positron plasma consisting of equal hot and cool components of each species. The hot components have a Boltzmann distribution and the cool components are described by the fluid equations. A modified Korteweg–de Vries–Zakharov–Kuznetsov equation governing the oblique propagation of nonlinear electrostatic modes is derived using the reductive-perturbation technique. Soliton amplitudes are studied as a function of plasma parameters such as the particle number densities and the temperatures. Such results may be of relevance to the magnetosphere of pulsars.

The three-dimensional instability of two coupled electromagnetic waves in an unmagnetized plasma is investigated theoretically and numerically. In the regime of two-plasmon decay, where one pump wave frequency is approximately twice the electron plasma frequency, we find that the coupled pump waves give rise to enhanced instability with wavevectors between those of the two beams. In the case of ion parametric decay instability, where the pump wave decays into one Langmuir wave and one ion acoustic wave, the instability regions are added with no distinct amplification. Our investigation can be useful in interpreting laser-plasma as well as ionospheric heating experiments.

The random displacement of magnetic field lines in the presence of magnetic turbulence in plasmas is investigated from first principles. A two-component (slab/two-dimensional composite) model for the turbulence spectrum is employed. An analytical investigation of the asymptotic behavior of the field-line mean square displacement (FL-MSD) is carried out. It is shown that the magnetic field lines behave superdiffusively for very large values of the position variable z, since the FL-MSD σ varies as σ ~ z4/3. An intermediate diffusive regime may also possibly exist for finite values of z under conditions which are explicitly determined in terms of the intrinsic turbulent plasma parameters. The superdiffusive asymptotic result is confirmed numerically via an iterative algorithm. The relevance to previous results is discussed.

The dispersion relation for a quantum pair plasma is derived, by using a wave kinetic description. A general form of the kinetic dispersion relation for electrostatic waves in a two-component quantum plasma is established. The particular case of an electron–positron pair plasma is considered in detail. Exact expressions for Landau damping are derived, and the quasi-classical limit is discussed.

The Kelvin–Helmholtz instability on the interface of two magnetized compressible fluids with tangential discontinuity is studied in two situations. For a sharp interface, the stability conditions of the surface with tangential discontinuity is investigated. It is shown that in this case magnetohydrodynamic modes such as Alfvén and the magnetosonic waves can propagate. When a transition layer exists between two fluids and the density and magnetic field change across this layer, numerical solutions show that the increase of the Mach number and compressibility has a destabilizing effect while the magnetic field and density increase has a stabilizing effect.

We consider the possibility of self-similar solutions describing the implosion of hollow cylindrical annuli driven by an azimuthal magnetic field, in essence a self-similar imploding liner z-pinch. We construct such solutions for gasdynamics, for ideal ‘β=0’ plasma and for ideal magnetogasdynamics (MGD). In the latter two cases some quantities are singular at the annular boundaries. Numerical solutions of the full ideal MGD initial value problem indicate that the self-similar solutions are not attractive for arbitrary initial conditions, possibly as a result of flux-freezing.

A vircator with a coaxial cavity has the potential to increase the beam–microwave conversion efficiency. According to the E-field distribution pattern of the modes in the anode cavity of a coaxial vircator, the resonant frequency band of the injected electron beam and the lowest two operating modes are derived. The main frequency of the virtual cathode is also deduced. The optimal operating frequency and high-efficiency designing method of a coaxial cavity vircator is discussed. An experimental setup is designed and built to test the high-power microwave (HPM) generation mechanism described by theoretical analysis as well as increase the power efficiency. HPM frequency obtained in the experiment is in good agreement with the analysis. The power and energy efficiencies obtained in the experiment are, respectively, 8.7% and 6.8% with 50 ns pulse width. Frequency and phase stable HPM radiation is observed as well as pulse shortening is evidently depressed.

In this paper we review some theoretical aspects of the dynamics of the mesoscale filaments extending along the magnetic field lines in the edge plasma, which are often called ‘blobs’. We start with a brief historical survey of experimental data and the main ideas on edge and SOL plasma transport, which finally evolved into the modern paradigm of convective very-intermittent cross-field edge plasma transport. We show that both extensive analytic treatments and numerical simulations demonstrate that plasma blobs with enhanced pressure can be convected coherently towards the wall. The mechanism of convection is related to an effective gravity force (e.g. owing to magnetic curvature effects), which causes plasma polarization and a corresponding E× B convection. The impacts of different effects (e.g. X-point magnetic geometry, plasma collisionality, plasma beta, etc.) on blob dynamics are considered. Theory and simulation predict, both for current tokamaks and for ITER, blob propagation speeds and cross-field sizes to be of the order of a few hundred meters per second and a centimeter, respectively, which are in reasonable agreement with available experimental data. Moreover, the concept of blobs as a fundamental entity of convective transport in the scrape-off layer provides explanations for observed outwards convective transport, intermittency and non-Gaussian statistics in edge plasmas, and enhanced wall recycling in both toroidal and linear machines.

The generation of large-scale zonal flows by small-scale electrostatic drift waves in electron temperature gradient driven turbulence model is considered. The generation mechanism is based on the modulational instability of a finite amplitude monochromatic drift wave. The threshold and growth rate of the instability as well as the optimal spatial scale of zonal flow are obtained.

The weakly nonlinear dynamics of dust ion-acoustic waves (DIAWs) are investigated in a dusty plasma consisting of hot ion fluid, variable charge stationary dust grains and non-thermally distributed electrons. The Korteweg–de Vries equation, as well as the Korteweg–de Vries–Burgers equation, are derived on the basis of the well-known reductive perturbation theory. It is shown that, due to electron non-thermality and finite ion temperature, the present dusty plasma model can support compressive as well as rarefactive DIA solitary waves. Furthermore, there may exist collisionless DIA shock-like waves which have either monotonic or oscillatory behavior, the properties of which depend sensitively on the number of fast non-thermal electrons. The results complement and provide new insights into previously published results on this problem (Mamun, A. A. and Shukla, P. K. 2002 IEEE Trans. Plasma Sci. 30, 720).

Small-amplitude electrostatic solitary waves are investigated in an unmagnetized dusty plasma with hot variable charge non-thermal dust grains. These nonlinear localized structures are small-amplitude self-consistent solutions of the Vlasov equation in which the dust response is non-Maxwellian. Localized solitary structures that may possibly occur are discussed and the dependence of their characteristics on physical parameters is traced. Our investigation may be taken as a prerequisite for the understanding of the electrostatic solitary waves that may occur in space dusty plasmas.

We present a new efficient wave decay channel involving nonlinear interactions between a compressional Alfvén wave, a kinetic Alfvén wave, and a modified ion sound wave in a magnetized plasma. It is found that the wave coupling strength of the ideal magnetohydrodynamic (MHD) theory is much increased when the effects due to the Hall current are included in a Hall–MHD description of wave–wave interactions. In particular, with a compressional Alfvén pump wave well described by the ideal MHD theory, we find that the growth rate is very high when the decay products have wavelengths of the order of the ion thermal gyroradius or shorter, in which case they must be described by the Hall–MHD equations. The significance of our results to the heating of space and laboratory plasmas as well as for the Solar corona and interstellar media are highlighted.

The pinch process of plasma columns generated by capillary discharge is studied theoretically with a snow-plow model. The multiple pinch evolution of plasma is obtained from the theoretical results. The effects of pressure and current amplitude on multiple pinches are calculated, and the results show that the pinch time decreases nonlinearly with decreasing pressure or increasing current. In the experiment, the laser spike of Ne-like Ar at 46.9 nm is obtained with an X-ray diode (XRD). The pressure filling in the capillary is changed to observe the variation of lasing onset time. According to real current waveforms, the pinch process is simulated. The results show that the laser spike occurs around the third pinching time. In addition, the experimental results indicate that there is an optimum pressure for the laser output.