Hermite–Gaussian (HG) laser beam with transverse electromagnetic (TEM) mode indices (m, n) of distinct values (0, 1), (0, 2), (0, 3), and (0, 4) has been analyzed theoretically for direct laser acceleration (DLA) of electron under the influence of an externally applied axial magnetic field. The propagation characteristics of a TEM HG beam in vacuum control the dynamics of electron during laser–electron interaction. The applied magnetic field strengthens the $\vec v \times \vec B$ force component of the fields acting on electron for the occurrence of strong betatron resonance. An axially confined enhanced acceleration is observed due to axial magnetic field. The electron energy gain is sensitive not only to mode indices of TEM HG laser beam but also to applied magnetic field. Higher energy gain in GeV range is seen with higher mode indices in the presence of applied magnetic field. The obtained results with distinct TEM modes would be helpful in the development of better table top accelerators of diverse needs.

In the present research paper, the characteristics of dust-acoustic solitary waves (DASWs) and double layers (DLs) are studied. Ions are treated as non-thermal and variable dust charge is considered. The Korteweg–de Vries equation is derived using a reductive perturbation method. It is noticed that compressive solitons are obtained up to a certain range of relative density δ (=ni0/ne0) beyond which rarefactive solitons are observed. The study is further extended to investigate the possibility of DLs. Only compressive DLs are permissible. Both DASWs and DLs are sensitive to variation of the non-thermal parameter.

The problem of nonlinear self-focusing of elliptic Gaussian laser beam in collisionless magnetized plasma is studied using variation approach. The dynamics of the combined effects of nonlinearity and spatial diffraction is presented. With a and b as the beam width parameters of the beam along x and y directions, respectively, the phenomenon of cross-focusing is observed where focusing of a results in defocusing of b and vice versa. Although no stationary self-trapping is observed, oscillatory self-trapping occurs far below the threshold. The regularized phase is always negative.

The effect on the propagation of ion-acoustic solitons and double layers has been studied in collisionless weakly relativistic plasma consisting of two-electron temperature with isothermal electrons and finite ion temperature. The Korteweg de-Vries (KdV) equation is derived for ion-acoustic solitons propagating in a collisionless plasma. This equation is solved in a stationary frame to obtain the expression for soliton phase velocity, soliton width and peak soliton amplitude. It is observed that these quantities are significantly influenced by the relativistic effect, ion temperature, low-temperature electron density and ratio of cold to hot electron temperatures. Many features expected from hot ion theory and two species electron plasmas automatically emerge. The analysis is further extended to higher order nonlinearity and modified Korteweg de-Vries (mKdV) equation is derived. Even though compressive and rarefactive ion-acoustic solitons are obtained, only rarefactive ion-acoustic double layers are obtained in the present investigation.

In this paper, the characteristics of dust-acoustic solitary waves in dusty plasma are studied. Dust charge and temperature are treated as variables. The authors have used the pseudopotential method to investigate the possibility of compressive as well as rarefactive solitons. An expression for the pseudopotential has been derived. The pseudopotential is a function of the Mach number, the relative temperature of low and high ion components, the relative ion concentration of dust charge and the temperature. Numerical computation shows that for the chosen set of parameters, only compressive solitons exist and their amplitudes increase with increasing Mach number. An increase in the dust temperature results in the disappearance of the compressive soliton. It is the only small parameter regime where compressive as well rarefactive solitons coexist. The effect of the relative ion temperature on solitons is also investigated. In the small amplitude limit, an increase in the dust temperature leads to a transition from compressive to rarefactive solitons.

In the laser–plasma interaction experiments, self-focusing and filamentation affect quite a large number of other parametric processes including stimulated scattering processes. Nonlinearity considered in the present problem is the collisional type. The coupling between the main beam, ripple, and excited electron plasma wave is strong. Authors have investigated the growing interaction of a rippled laser beam with an electron plasma wave leading to enhanced Raman scattering. An expression for scattered power is derived and the effect of the externally applied magnetic field on the enhancement of scattered power is observed. From computational results, it is observed that the effect of increased intensity of the main beam leads to suppression of power associated with the Raman scattered wave.

Self-focusing is one of the key issues in laser plasma physics applications. Problems involving a multidimensional beam within an inhomogeneous plasma are diffficult to handle. This paper presents the investigation of two-dimensional self-focusing of a laser beam in a plasma whose density n(r, z) is a function of radial as well as z coordinates. The nonlinear mechanism responsible for modification of the background density and the dielectric function is of ponderomotive type. A variational technique is used here for deriving the equations for the beam width and the longitudinal phase. It is observed numerically that an initially diffracting beam is accompanied by oscillatory self-focusing of the beam with distance of propagation. The effect of inhomogeneity scale lengths is also observed. The increase in Lr (= L∥/L⊥) results in oscillatory self-focusing and defocusing with distance of propagation. Furthermore, critical fields for self-trapping of a laser beam as a function of refraction, diffraction lengths and scale lengths of inhomogeneities are also evaluated. Lastly, whatever parameters are chosen, the phase is always negative.