The head-on collision between two cylindrical/spherical ion acoustic solitary waves (IASWs) in un-magnetized plasmas comprising inertial ions and q-non-extensive electrons and positrons is investigated using the extended version of the Poincaré–Lighthill–Kuo perturbation method. How the interactions are taking place in cylindrical and spherical geometry are studied, and the collision is shown at different times. The non-planar geometry can modify analytical phase shifts following the head-on collision are derived. The effects of q-non-extensive electrons and positrons on the phase shift are studied. It is shown that the properties of the interaction of IASWs in cylindrical and spherical geometry are very different.

The driven wave formalism, as it was later applied to the solar coronal plasma processes, was first developed in our earlier work (Kaghashvili, E. Kh. 2007 Alfvén wave-driven compressional fluctuations in shear flows. Phys. Plasmas14, 44502) that presented the analytical solutions for the plasma density fluctuations. In the driven-wave formalism, we look for the short-term changes in the initial waveform due to the linear interaction of the initial natural mode of the system and the flow inhomogeneity. This formalism allows us to obtain the analytical solutions for the driven waves that are excited in the system. While a full set of driven wave solutions for magnetohydrodynamic variables in the cold plasma case were presented earlier (Kaghashvili, E. 2012c Driven wave-generated electric field in the solar corona. J. Geophys. Res. 117, A10103, doi:10.1029/2012JA018120), the purpose of this paper is to remove the cold-plasma restriction and to present the formal solutions for the initial linearly polarized Alfvén wave-driven fluctuations.

We determine the general dispersion relation for the propagation of magnetohydrodynamic (MHD) waves in astrophysical plasma by considering the effect of gravitational instability and viscosity with anisotropic pressure tensor and heat-conducting plasma. Basic MHD equations have been derived and linearized by the method of perturbation to develop the general form of dispersion relation equation. Our result indicates that the transverse propagation of waves in such a plasma is affected by the inclusion of heat conduction. For wave propagation, parallel to the magnetic field direction, we find that the fairhose mode is unaffected, whereas the mode corresponding to the gravitational instability is modified in astrophysical plasma with anisotropic pressure tensor being stable in the presence of viscosity and strong magnetic field at considerable wavelength.

The dynamics and propagation of ion acoustic (IA) waves are considered in an unmagnetized collisionless plasma, whose constituents are the relativistically degenerate electrons and positrons as well as the inertial cold ions. At a first step, a linear dispersion relation for IA waves is derived and analysed numerically. For nonlinear analysis, the reductive perturbation technique is used to derive a Korteweg–deVries equation, which admits a localized wave solution in the presence of relativistic degenerate electrons and positrons. It is shown that only compressive IA solitary waves can propagate, whose amplitude, width and phase velocity are significantly modified due to the positron concentration. The latter also strongly influences all the relativistic plasma parameters. Our present analysis is aimed to understand collective interactions in dense astrophysical objects, e.g. white dwarfs, where the lighter species electrons and positrons are taken as relativistically degenerate.

Nonlinear properties of magnetoacoustic waves are investigated in magnetized pair-ion plasmas with dust impurity. Three-fluid collisionless magneto-hydrodynamic model is considered and reductive perturbation method is employed to derive Korteweg-de Vries equation for magnetoacoustic solitary waves (MASWs). The effects of the charge number of dust particles, magnetic field intensity, and plasma number density are studied on MASWs. It is found that the variation of parameters causes significant changes in solitary structures. The present investigation may be useful to understand formation and propagation of MASW structures in dust pair-ion plasmas.

The paper is concerned with the analytical study of nonlinear coupling of slow Alfvén wave (SW) with ion acoustic waves (IAWs) in high-β and low-β plasmas. Here the pump wave (SW) number density gets perturbed in the presence of IAW. The model equations of IAW and SW turn out to be the modified Zakharov system of equations when the ponderomotive nonlinearities are incorporated in the IAW and SW dynamics. Growth rate of modulational instability has been calculated. The relevance of these investigations for solar wind plasma and solar coronal plasma has also been discussed.

Turbulent particle transport is investigated with a quasilinear theory that is motivated by the boron impurity transport experiments in the Alcator C-Mod. Eigenvalue problems for sets of reduced fluid equations for multi-component plasmas are solved for the self-consistent fluctuating field vectors composed of the electric potential φ, the main ion density δni, the impurity density δnz and the ion temperature fluctuation δTi. For Alcator C-Mod parameters, we investigate two drift wave models: (1) the density-gradient-driven impurity drift wave and (2) the ion-temperature-gradient-driven ion temperature gradient (ITG) mode. Analytic and numerical results for particle transport coefficients are derived and compared with the transport data and the neoclassical theory. We explore the ability of the model to explain impurity density profiles in three confinement regimes: H-mode, I-mode and internal transport barrier (ITB) regime in C-Mod. Related experiments reported on the Large Helical Device are briefly discussed.

The properties of nonlinear electrostatic acoustic rogue waves in a three-component plasma composed of electron, positron, and relativistic electron beam are investigated. The reductive perturbation method is used to obtain a Korteweg–de Vries equation. The dynamics of the modulationally unstable wave packets described by the Korteweg–de Vries equation gives rise to the formation of rogue pulses that is described by a nonlinear Schrödinger equation for small wave number. The effects of physical parameters on the profile of rogue waves are investigated numerically. The electrostatic rogue waves, as predicted here, may be associated with the nonlinear structures caused by the interaction of relativistic jets with plasma medium, such as in the active galactic nuclei and in the magnetosphere of collapsing stars.

A kinetic theory is used to investigate the theory of a free-electron laser with a helical wiggler and an ion channel based on the Einstein coefficient method. The laser gain in the low-gain regime is obtained for the case of a cold tenuous relativistic electron beam, where the beam plasma frequency is much less than the radiation frequency, propagating in this configuration. The resulting gain equation is analyzed numerically over a wide range of system parameters.

The nonlinear propagation of small but finite-amplitude dust-acoustic solitary waves in an unmagnetized, collisionless dusty plasma has been investigated. The fluid model is a generalization to the model of Mamun and Shukla to a more realistic space dusty plasma in different regions of space, viz., cometary tails, mesosphere, and Jupiter's magnetosphere, by considering a four-component dusty plasma consisting of the charged dusty plasma of opposite polarity, isothermal electrons and vortex-like ion distributions in the ambient plasma. A reductive perturbation method was employed to obtain a modified Korteweg–de Vries equation for the first-order potential. The effect of the presence of a positively charged dust fluid, the specific charge ratio μ, the temperature of the positively charged dust fluid, the ratio of constant temperature of free hot ions and the constant temperature of trapped ions, and ion temperature on the soliton properties and dusty grains energy are discussed.

Using the tridimensional magnetic probe, the current sheath velocity at 0.25 Torr is studied in Sahand, a Filippov-type plasma focus facility. The current sheath velocity in argon-filled plasma focus with different percentages of helium impurity at different operating voltages was studied. The highest average current sheath velocity of 12.26 ± 1.51 cm μs−1 at the top of the anode in the axial phase was achieved at 17 kV. Minimum average current sheath velocity is 5.24 ± 1.18 cm μs−1 at 12 kV with 80% argon + 20% helium as a working gas. The full width at half-maximum of peaks of the magnetic probe was found to be inversely related to the current sheath velocity, i.e. smaller at higher voltages for different impurity and decreased with increasing of impurity.

The equilibrium and stability properties of ideal magnetohydrodynamics (MHD) of compressible flow in a gravitational field with a translational symmetry are investigated. Variational principles for the steady-state equations are formulated. The MHD equilibrium equations are obtained as critical points of a conserved Lyapunov functional. This functional consists of the sum of the total energy, the mass, the circulation along field lines (cross helicity), the momentum, and the magnetic helicity. In the unperturbed case, the equilibrium states satisfy a nonlinear second-order partial differential equation (PDE) associated with hydrodynamic Bernoulli law. The PDE can be an elliptic or a parabolic equation depending on increasing the poloidal flow speed. Linear and nonlinear Lyapunov stability conditions under translational symmetric perturbations are established for the equilibrium states.

Characterization of self-similarity properties of turbulence in magnetized plasma is being carried out in DC glow discharge plasma. The time series floating potential fluctuation experimental data are acquired from the plasma by Langmuir probe. Continuous wavelet transform (CWT) analysis considering db4 mother wavelet has been applied to the experimental data and self-similarity properties are detected by evaluating the Hurst exponent from the wavelet variance plotting. From the CWT spectrum, effort is made to extract a highly correlated frequency by locating the brightest spot. Accordingly, those signals are treated for finding out correlation dimension and the Liapunov exponent so that the exact frequency responsible for the chaotic behavior could be found out.

Ion-acoustic solitons in magnetized low-β plasma consisting of warm adiabatic positive and negative ions and non-thermal electrons have been studied. The reductive perturbation method is used to derive the Korteweg–de Vries (KdV) equation for the system, which admits an obliquely propagating soliton solution. It is found that due to the presence of finite ion temperature there exist two modes of propagation, namely fast and slow ion-acoustic modes. In the case of slow-mode if the ratio of temperature to mass of positive ion species is lower (higher) than the negative ion species, then there exist compressive (rarefactive) ion-acoustic solitons. It is also found that in the case of slow mode, on increasing the non-thermal parameter (γ) the amplitude of the compressive (rarefactive) soliton decreases (increases). In fast ion-acoustic mode the nature and characteristics of solitons depend on negative ion concentration. Numerical investigation in case of fast mode reveals that on increasing γ, the amplitude of compressive (rarefactive) soliton increases (decreases). The width of solitons increases with an increase in non-thermal parameters in both the modes for compressive as well as rarefactive solitons. There exists a value of critical negative ion concentration (αc), at which both compressive and rarefactive ion-acoustic solitons appear as described by modified KdV soliton. The value of αc decreases with increase in γ.

We show that comparatively simple expressions for the Alfven wave coupling coefficients can be deduced from the well-known Hall-magnetohydrodynamics (MHD) model equations.

The effect of discharge voltage on bi-Maxwellian electrons in the diffusion region of a double plasma device has been studied. The increase in discharge voltage enhances the flux of ionizing electrons to the diffusion region separated by a mesh grid. This energetic electron flux in turn affects other important parameters such as density, electron temperature, plasma potential and floating potential in the diffusion region. Furthermore, the dependence of density and temperature of both ionizing and plasma electrons on discharge voltage is investigated. The electron energy probability function obtained from probe data also indicates the bi-Maxwellian nature of electrons.

The interaction of a short pulse laser beam with an inhomogeneous plasma has been studied in the presence of an obliquely applied external magnetic field. The dispersion relation and the analytical growth rate have been obtained solving the nonlinear wave equation. It is found that the growth rate and the cut-off wavenumber are strongly influenced by the direction and magnitude of the applied magnetic field. Moreover, the growth rate has been modified by plasma inhomogeneity.

The nonlinear interaction of kinetic Alfvén waves (KAWs) with other possible plasma modes is considered to be responsible for the observed solar wind turbulent spectrum. In the present paper, a new channel of interaction between a KAW and an obliquely propagating Alfvén wave (AW) has been proposed. The governing dynamical equations are derived and the nonlinear interaction between the two wave modes KAW and AW is studied. The growth rate of modulational instability has been calculated. The nonlinear evolution of KAW filamentation and turbulent spectra has also been discussed. In the inertial range, energy cascade follows nearly Kolmogorov scaling, and after inertial range it follows −2.5 scaling in dispersive range. The obtained results indicate that the proposed mechanism may be responsible for transferring the energy from smaller wavenumbers to larger wavenumbers in the solar wind plasmas. The relevance of the present study with recent Cluster spacecraft observations has also been pointed out.

An analytical theory is developed for studying the phenomenon of generation of efficient odd and even high harmonics by the propagation of two-colour linearly polarized laser beams in a homogeneous underdense plasma. The wave equation governing the evolution of the amplitude of various harmonics driven by the current density at corresponding frequencies is set up. The ratio of the fundamental frequencies of the two laser beams is considered to be an arbitrary integer. A numerical evaluation of amplitudes of the third, fourth and fifth harmonics has been presented. It is seen that the third harmonic amplitude generated by the two-colour system is enhanced in comparison to that obtained by a single laser beam. The detuning distance for the former is also increased in comparison to the latter case.

The theoretical investigations on the effect of different plasmas on the growth and field emission properties of a spherical carbon nanotube (CNT) tip placed over cylindrical CNT surfaces have been carried out for the typical glow discharge plasma parameters. Different plasmas such as H2, Ar, CH4 and CF4 have been considered, and the growth of the CNT in the presence of various plasmas has been estimated in the present investigation. This study suggests that the field emission from the CNT grown in the presence of the H2 plasma is largest. It is also found that amongst the plasmas considered, the CF4 plasma is the most favourable for the growth of the large radius CNT, since the radius achieved in the CF4 plasma is the largest.