The reaction rate probability integral is extended from Maxwell–Boltzmann approach to a more general approach by using the pathway model introduced by Mathai in 2005 (A pathway to matrix-variate gamma and normal densities. Linear Algebr. Appl.396, 317–328). The extended thermonuclear reaction rate is obtained in the closed form via a Meijer's G-function and the so-obtained G-function is represented as a solution of a homogeneous linear differential equation. A physical model for the hydrodynamical process in a fusion plasma-compressed and laser-driven spherical shock wave is used for evaluating the fusion energy integral by integrating the extended thermonuclear reaction rate integral over the temperature. The result obtained is compared with the standard fusion yield obtained by Haubold and John in 1981 (Analytical representation of the thermonuclear reaction rate and fusion energy production in a spherical plasma shock wave. Plasma Phys.23, 399–411). An interpretation for the pathway parameter is also given.

The nonlinear decay of a circularly polarized wave is reconsidered. We deduce an explicit expression for the growth rate, and present it in a form which is significantly simpler than those of previous papers.

It is shown that a pre-existing electron density ripple in a dense plasma can excite electron neutrino oscillations. For our purposes, we use the dispersion relation for neutrino oscillations and derive the Mathieu equation for the propagation of neutrino oscillations in the presence of a spatially oscillating electron density ripple. The Mathieu equation predicts instability of neutrino oscillations. The criterion under which instability occurs is presented. Analytical expressions for the neutrino oscillation frequency and the growth rate are obtained. The possible relevance of our investigation to non-thermal neutrino oscillations in dense plasma environments (e.g. the supernovae, the core of white dwarf stars etc.) is briefly mentioned.

We discuss the dispersive properties of low-frequency electromagnetic (EM) perturbations in the magnetized core of self-gravitating white dwarf stars with ultra-relativistic degenerate electrons. For our purposes, we derive a dispersion relation by using the hydrodynamic equations for the ions under the action of EM and self-gravitating forces, and the inertialess electrons under the action of EM forces and the gradient of the ultra-relativistic pressure. The dispersion relation admits stability of a white dwarf star against a class of EM perturbations whose wavelengths are shorter than 15000 km.

A set of nonlinear governing equations for interactions of transverse plasmons with pair plasmas is derived from Vlasov–Maxwell equations. It is shown the ponderomotive force induced by high-frequency transverse plasmons will expel the pair particles away, resulting in the formation of density cavity in which transverse plasmons are trapped. Numerical results show the envelope of wave fields will collapse and break into a filamentary structure due to the spatially inhomogeneous growth rate. The results obtained would be useful for understanding the nonlinear propagation behavior of intense electromagnetic waves in pair plasmas.

This work presents the model equations governing the excitation of weak whistler by a stronger Kinetic Alfvén wave (KAW) in the plasma having β value (β ≫ me/mi, where beta is the ratio of the ion sound speed to the Alfvén speed), applicable to magnetotail in Earth's magnetosphere, when the ponderomotive nonlinearity is incorporated in the KAW dynamics. Numerical solution of the model equations has been obtained when the incident pump KAW is having a small perturbation. Energy exchange between main KAW and perturbation and the resulting localized structures of the KAW have been studied. A weak whistler signal propagating in these localized structures is amplified and leads to the development of envelope solitons. Our result reveals that the amplified (excited) whistler has an electric field power spectrum that is steeper than k−8/3. This result is consistent with recent observations by the Cluster spacecraft Eastwood et al. (Phys. Rev. Lett., vol. 102, 2009, 035001) in the magnetotail region of the Earth's magnetosphere.

It is shown that nonlinear interaction between large amplitude circularly polarized EM wave and dusty plasma leads to a non-stationary ponderomotive force, which in turn produces a vortex ring and magnetic field. Then the ensuing vortex ring in the direction of propagation of the pump wave can accelerate the micron-size dust particles, which are initially at rest and eventually form a non-relativistic dust jet. This effect is purely non-stationary and unlike linear vortices, dust particles do not rotate here. Specifically, it is pointed out that the vortex ring or closed filament can become potential candidate for the acceleration of dust in tokamak plasmas.

The basic features of dusty plasmas, particularly basic characteristics of dust in a plasma, and typical dusty plasma parameters for different space and laboratory plasma conditions, are presented. The complexity and the diversity of the field of dusty plasma physics are briefly discussed. Theoretical and experimental discoveries of linear and nonlinear features of waves, particularly dust-ion-acoustic and dust-acoustic waves, in dusty plasmas are reviewed.

In a cylindrical geometry, a low-pressure magnetized argon plasma is lit, using the rf upper hybrid resonance. As a radial dc electric field is formed, a perpendicular drift velocity is obtained on the charged particles and a collisional instability is raised. The description, study and identification of that wave were given in the last published work from NCSR ‘Demokritos’, both experimentally and theoretically. Since then, the research has been continued and significant results have been obtained concerning the fields of plasma parameters, wave further understanding, growth research and boundaries' strong influence. The aim of the present paper is to inform that the rising instability has many of the characteristics of drift instabilities that are caused by the density gradient, as well as the ability of it's frequency to overcome the ion gyro-frequency. In addition, it gives an answer to the well-known problem of the need to consider a small component of the wave vector in the parallel direction, in order the wave to rise through the electron-neutral collisions' proceedings; a strong influence of cavity length on wave amplitude has been observed and measured.

The heliosphere is predominantly a partially ionized plasma that consists of electrons, ions and significant neutral atoms. Nonlinear interactions among these species take place through direct collision or charge-exchange processes. These interactions modify linear and nonlinear properties of the plasma. In this work, we develop a one-dimensional linear theory to investigate linear instabilities in such a system. In our model, the electrons and ions are described by a single fluid compressible magnetohydrodynamic (MHD) model and are coupled self-consistently to the neutral fluid via compressible hydrodynamic equations. The coupling is mediated by the charge-exchange process. Based on our self-consistent analysis, we find that the charge-exchange coupling is more effective at larger length scales, and the Alfvén waves are not affected by the charge-exchange coupling. By contrast, the fast and slow waves are driven linearly unstable.

This paper presents the nonlinear dynamics of the dispersive Alfvén wave (DAW) in the low-β plasmas (β≪me/mi; known as inertial Alfvén waves) applicable to solar corona. The pump DAW is perturbed by a low-frequency slow Alfvén wave (SW). When the ponderomotive nonlinearities are incorporated in the DAW and SW dynamics, the model equations of DAW and SW turn out to be the modified Zakharov system of equations (MZSE) Growth rate and threshold field for modulational (filamentation) instability have been calculated. The dependence of the growth rate on the perturbation wave number and the pump wave parameters such as k0xλe (inertial) has also been presented. It is obvious from this investigation that DAW can become unstable when it nonlinearly interacts with the SW and modulational instabilities can be triggered. The relevance of these investigations for solar corona has been discussed.

The filamentation of the high-power laser beam is investigated by taking off axial contribution when relativistic nonlinearity is considered. The effect of filamentation of the laser beam is studied on the localization of the electron plasma wave (EPW) and on the stimulated Raman scattering (SRS). The semi-analytical solution of the nonlinearly coupled EPW equation in the presence of laser beam filaments has been found. It is observed that due to this nonlinear coupling between two waves, localization of EPW takes place. This localization of EPW affects the Eigen frequency and damping of plasma wave. The new enhanced damping of the plasma wave has been calculated and it is found that the SRS process gets suppressed due to the localization of plasma wave in laser beam filamentary structures. For typical laser beam and plasma parameters with wavelength λ (=1064 nm), power flux (=1018 W cm−2) and plasma density n/ncr (=0.2); the SRS back reflectivity is found to be suppressed by a factor of approximately 8%.

A new equation of motion that governs weakly nonlinear phenomena in ideal magnetohydrodynamics (MHDs) is derived as a natural extension of the well-known linearized equation of motion for the displacement field. This derivation is made possible by expanding the MHD Lagrangian explicitly up to third order with respect to the displacement of plasma, which necessitates an efficient use of the Lie series expansion. The resultant equation of motion (i.e. the Euler–Lagrange equation) includes a new quadratic force term which is responsible for various mode–mode coupling due to the MHD nonlinearity. The third-order potential energy serves to quantify the coupling coefficient among resonant three modes and its cubic symmetry proves the Manley–Rowe relations. In contrast to earlier works, the coupling coefficient is expressed only by the displacement vector field, which is already familiar in the linear MHD theory, and both the fixed and free boundary cases are treated systematically.

The effects of limiter biasing on the equilibrium density and potential profiles of the scrape-off layer (SOL) in tokamak plasma are investigated by including ionization and cross-field mobility. It is shown that a broadening of SOL can take place by the inclusion of ionization for low negative biasing. Various microinstabilities relevant for SOL plasmas have been studied. Generalized low-frequency dispersion relation is derived. It is shown that limiter biasing significantly modifies the SOL fluctuations. It is also shown that growth rate of conductive wall instability is smaller for negative biasing than positive biasing case. New mode, the modified Simon–Hoh, and ion temperature gradient instabilities are found to contribute significantly to the growth of curvature- and electron temperature-gradient-driven conductive wall instabilities.

It is shown that nonlinear self-interaction of energetic particle-driven geodesic acoustic mode does not generate a second harmonic in radial electric field using the fluid model. However, kinetic effects of energetic particles can induce a second harmonic in the radial electric field. A formula for the second-order plasma density perturbation is derived. It is shown that a second harmonic of plasma density perturbation is generated by the convective nonlinearity of both thermal plasma and energetic particles. Near the midplane of a tokamak, the second-order plasma density perturbation (the sum of second harmonic and zero frequency sideband) is negative on the low field side with its size comparable to the main harmonic at low fluctuation level. These analytic predictions are consistent with the recent experimental observation in DIII-D.

Through a simple one-dimensional collisionless plasma sheath model, behavior of the floating potential in an electronegative plasma sheath is studied. Specially, the floating potential behavior as a function of the plasma electronegativity for various negative ion temperatures has been studied. It has been observed that negative ion temperature strongly affects the variation of floating potential.

Intense non-thermal radiation spikes were observed prior to energy quench in HT-7 tokamak. The dynamic properties of non-thermal electrons have been analyzed. Observation manifests that some non-thermal electrons are confined in the vicinity of q = 1 magnetic surface which results in hot spot phenomenon just before disruption.

In 1962 E. G. Harris published a solution to the problem of a current sheet separating regions of oppositely directed magnetic field in a fully ionized plasma. The resulting solution has become known as the ‘Harris sheet’ and has been of great utility to the plasma physics community. In this paper, the footsteps of Harris are retraced with the addition of a multiply charged massive dust component. A set of highly nonlinear differential equations for a current sheet in a dusty plasma are presented. An analytic solution, similar to that of Harris, is found for the depleted electron regime. This solution is of great relevance to many astrophysical and laboratory dusty plasmas. Current sheet thickness and asymptotic field strength are calculated for various dusty plasma environments.

The basic features and multi-dimensional instability of electrostatic solitary waves propagating in an ultra-relativistic degenerate dense magnetized plasma have been investigated by the reductive perturbation method and the small-k perturbation expansion technique. The Zakharov–Kuznetsov (ZK) equation has been derived, and its numerical solutions for some special cases have been analysed to identify the basic features (viz. amplitude, width, instability, etc.) of these electrostatic solitary structures. The implications of our results in some compact astrophysical objects, particularly white dwarfs and neutron stars, have been briefly discussed.

On a characteristic surface Ω of a hyperbolic system of first-order equations in multi-dimensions (x, t), there exits a compatibility condition which is in the form of a transport equation along a bicharacteristic on Ω. This result can be interpreted also as a transport equation along rays of the wavefront Ωt in x-space associated with Ω. For a system of quasi-linear equations, the ray equations (which has two distinct parts) and the transport equation form a coupled system of underdetermined equations. As an example of this bicharacteristic formulation, we consider two-dimensional unsteady flow of an ideal magnetohydrodynamics gas with a plane aligned magnetic field. For any mode of propagation in this two-dimensional flow, there are three ray equations: two for the spatial coordinates x and y and one for the ray diffraction. In spite of little longer calculations, the final four equations (three ray equations and one transport equation) for the fast magneto-acoustic wave are simple and elegant and cannot be derived in these simple forms by use of a computer program like REDUCE.