Oscillating two-stream instability (OTSI) of a high amplitude laser or a plasma wave is investigated in plasmas with strongly coupled ions. It is shown that in some parameter regime, the pressure of strongly coupled ions becomes negative, which leads to enhance the bunching of ion and concomitant destabilization of OTSI. Applications of these results to ion accelerator and inertial confinement fusion experiments are discussed.

The influence of finite Larmor radius correction, tensor viscosity and uniform rotation on self-gravitational and firehose instabilities is discussed in the framework of the quantum magnetohydrodynamic and Chew–Goldberger–Low (CGL) fluid models. The general dispersion relation is obtained for transverse and longitudinal modes of propagation. In both the modes of propagation the dispersion relation is further analysed with respect to the direction of the rotational axis. In the analytical discussion the axis of rotation is considered in parallel and in the perpendicular direction to the magnetic field. (i) In the transverse mode of propagation, when rotation is parallel to the direction of the magnetic field, the Jeans instability criterion is affected by the rotation, finite Larmor radius (FLR) and quantum parameter but remains unaffected due to the presence of tensor viscosity. The calculated critical Jeans masses for rotating and non-rotating dense degenerate plasma systems are $3.5M_{\odot }$ and $2.1M_{\odot }$ respectively. It is clear that the presence of rotation enhances the threshold mass of the considered system. (ii) In the case of longitudinal mode of propagation when rotation is parallel to the direction of the magnetic field, Alfvén and viscous self-gravitating modes are obtained. The Alfvén mode is modified by FLR corrections and rotation. The analytical as well as graphical results show that the presence of FLR and rotation play significant roles in stabilizing the growth rate of the firehose instability by suppressing the parallel anisotropic pressure. The viscous self-gravitating mode is significantly affected by tensor viscosity, anisotropic pressure and the quantum parameter while it remains free from rotation and FLR corrections. When the direction of rotation is perpendicular to the magnetic field, the rotation of the considered system coupled the Alfvén and viscous self-gravitating modes to each other. The finding of the present work is applicable to strongly magnetized dense degenerate plasma.

A generalized hydrodynamic model is used to analyse the growth rate of the Jeans instability of a partially ionized strongly coupled plasma incorporating the effects of rotation and Hall current. The general dispersion relation is determined for the propagation of magnetohydrodynamic waves using the normal mode analysis theory. The general dispersion relation is further discussed in four different combinations of rotation and propagation of the system to signify the importance of rotation and neutral particles on the growth rates and conditions of Jeans instability in hydrodynamic and kinetic regimes. The different types of waves are also described in these cases. The influence of rotation and neutral particles on growth rate of the Jeans instability is analysed numerically and shown graphically. The possible applications of the present work are found in ultracold neutral plasmas, white dwarfs, neutron stars etc.

The present work aims to study the influence of relativistic–ponderomotive effects on cross-focusing of two co-propagating high-power hollow Gaussian laser beams [high-power laser beams (HGLBs)] in collisionless plasma. The effective dielectric constant has been derived on account of relativistic–ponderomotive nonlinearity. The phenomenon of cross-focusing for higher-order modes of HGLB is compared for the case when only relativistic nonlinearity is operative in the system and it is seen that the relativistic–ponderomotive effects make the focusing much stronger and relatively faster. The critical curves for various order of HGLB is discussed and compared with the case when only ponderomotive nonlinearity is present and it reveals that in the case of relativistic–ponderomotive case the spot size reduces effectively. The higher-order modes of propagation of HGLB are also found to be governed by the parameter of another propagating HGLB. The present study is useful in determining the propagation dynamics of HGLB.

Effect of relativistic nonlinearity on stimulated Raman scattering (SRS) of laser beam propagating carrying null intensity in center [hollow Gaussian beam (HGB)] is studied in collisionless plasma. The construction of the equations is done employing the fluid theory which is developed with partial differential equation and Maxwell's equations. The phenomenon of SRS is shown along with the excitation of seed plasma wave considering relativistic nonlinearity. The power of plasma wave is observed for higher order of HGB. The Raman back reflectivity is studied numerically for various orders of hollow Gaussian laser beam (HGLB) and the numerical analysis shows that these parameters play vital role on reflectivity characteristics. It is observed that the Raman back reflectivity is less for the higher order of HGLB.

The combined effects of filamentation and magnetic field on the third-harmonic generation of electromagnetic beams have been investigated considering extended paraxial rays in magneto plasma. The analysis is done using eikonal method in which eikonal and other relevant quantities are extended up to fourth power of r. The time scale of laser beam is chosen such that the relativistic mass variation of electron becomes dominated source of nonlinearity in refractive index. The expression for coupling between ultra-intense laser beam and electron plasma wave due to relativistic nonlinearity has been deduced. Interaction of the seed plasma wave with the incident filamented laser beam excites the plasma wave and generates third harmonics. The expressions for plasma wave power and third-harmonic power have been derived. The effect of the magnetic field on the power of plasma wave and the third-harmonic power has been carried out. The role of magnetic field has been found to decrease the power of plasma wave and so as the power of third harmonic. Our results can be helpful for various laser plasma diagnostics experiments in which magnetic field present externally or generated spontaneously in the high-power laser–plasma interaction.

The Jeans self-gravitational instability is studied for dense quantum viscous plasma with Hall term and intrinsic magnetization generated by collective electron spin. The quantum magnetohydrodynamic model is employed to formulate the basic equations of the problem. The dispersion relation is obtained using the normal mode analysis, and further reduced for both transverse and longitudinal modes of propagation. The transverse mode of propagation is found to be unaffected by the Hall term but affected by quantum effect, viscosity, and magnetization parameters. The Jeans criterion of instability in the transverse direction is modified by Alfven velocity, magnetization parameter, and quantum effect. The non-gravitating magnetized mode is obtained in the longitudinal direction, which is modified by Hall parameter and is not affected by quantum term, whereas the gravitational mode is unaffected by the magnetization parameter but affected by viscosity and quantum parameters. It is observed that the Jeans condition of instability is affected by the quantum term. The growth rate of Jeans instability is plotted for various values of magnetization, quantum, and viscosity parameters of the quantum plasma medium.

This communication presents a comparison of two cases to study the process of laser beam propagation and Stimulated Brillouin Scattering (SBS) in laser plasma interaction. These two cases are, with imposing the restriction of paraxial approximation on the laser beam and, relaxing this restriction up to a certain extent. In this work, the study done by Sharma et al. (2009) using paraxial approximation is extended by taking contribution of the off-axial rays in the laser beam profile. The spitted profile of the laser beam is obtained due to uneven focusing of the off-axial rays and its effect on localization of the ion acoustic wave (IAW) has been studied. Including the off-axial part of the laser beam semi-analytical solution of the nonlinear coupled IAW equation has been found and this is examined that off-axial part affects background densities. The nonlinear coupling between the laser beam and IAW is severely affected by modified profile of the laser beam. Further, it is investigated that the SBS is also influenced by this coupling process. Therefore, the reflectivity of SBS has been compared with and without contribution of off-axial rays. A notable change is found in the magnitude of SBS reflectivity in modified-paraxial case in comparison to the paraxial case.

This paper presents the effect of laser beam filamentation on the localization of electron plasma wave (EPW) and stimulated Raman scattering (SRS) in unmagnetized plasma when relativistic and ponderomotive nonlinearities are operative. The splitted profile of the laser beam is obtained due to uneven focusing of the off-axial rays. 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 these two waves, localization of EPW takes place. Stimulated Raman scattering of this EPW is studied and back reflectivity has been calculated. Further, the localization of EPW affects the eigenfrequency 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.

This article presents the cross-focusing of two high power dark hollow Gaussian beams in plasma when relativistic nonlinearity is operative. A paraxial like approach has been used in the present analysis. In this study, the non-linear dielectric function has been expanded in terms of radial distance from the maximum of the irradiance, rather than from the axis, as is the case of Gaussian beams. The nature of propagation of a hollow Gaussian beam propagating in plasmas has been studied under the influence of relativistic non-linearity. The effect on the order (n) of hollow Gaussian beam on the cross-focusing of two beams has been explored in relativistic non-linearity in this publication.

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%.

This paper investigates the filamentation process of two co-axially propagating laser beams in collisionless plasma. On account of the ponderomotive nonlinearity, two laser beams affect the dynamics of each other, and cross-focusing takes place. The initial Gaussian laser beams are found to have non-Gaussian structures in the plasma. Using the laser beam and the plasma parameters, appropriate for the beat wave process, the filaments of the laser beams have been studied. Using these results, the Langmuir wave excitation at the beat wave frequency (when the laser beams are having filamentary structures) has been studied. The excited LW is modeled with the help of a driven oscillator and it is found that the excited Langmuir wave is not a plane wave; rather it has a turbulent structure. We have obtained the power spectrum of the excited beat wave (Langmuir wave), and calculated the spectral index. The stochastic electron acceleration has been studied in the presence of this Langmuir turbulence and relevance of these results to the beat wave process has been pointed out.

In this article, filamentation of a high power laser beam in hot collisionless plasma is investigated considering the ponderomotive nonlinearity. We have studied the effect of self focusing (filamentation) of the laser beam on the localization of ion acoustic wave (IAW) and on stimulated Brillouin scattering (SBS) process. The nonlinear coupling between the laser beam and IAW results in the modification of the Eigen frequency of IAW; consequently, enhanced Landau damping of IAW and a modified mismatch factor in SBS process occur. Due to enhanced Landau damping, there is a reduction in the intensity of IAW wave, and the SBS process gets suppressed. For the typical laser plasma parameters: the laser power flux = 1016 W/cm2, laser beam radius (r0) = 12 µm, n/ncr = 0.11, and (Te/Ti) = 10, the SBS reflectivity is found to be suppressed approximately by 10%.