In this paper, self-focusing of finite Airy–Gaussian (AiG) laser beams in collisionless plasma has been investigated. The source of nonlinearity considered herein is relativistic. Based on the Wentzel–Kramers–Brillouin (WKB) and paraxial-ray approximations, the nonlinear coupled differential equations for beam-width parameters in transverse dimensions of AiG beams have been established. The effect of beam's modulation parameter and linear absorption coefficient on the self-focusing/defocusing of the beams is specifically considered. It is found that self-focusing/defocusing of finite AiG beams depends on the range of modulation parameter. The extent of self-focusing is found to decrease with increase in absorption.

In the present paper, we have investigated self-focusing of the quadruple Gaussian laser beam in underdense cold quantum plasma. The non-linearity chosen is associated with the relativistic mass effect that arises due to quiver motion of electron and electron density perturbation caused by ponderomotive force. The non-linearity modifies the plasma frequency in the dielectric function and hence the refractive index of the medium. The focusing/defocusing of the quadruple laser depends on the refractive index of the medium. We have set up non-linear differential equation that controls the beam width parameter by using well-known paraxial ray approximation and Wentzel–Krammers–Brillouin approximation. The effect of intensity parameter and electron temperature is observed on laser beam self-focusing in the presence of cold quantum plasma. From the results, it is revealed that electron temperature and the initial intensity of the laser beam control the profile dynamics of the laser beam.

The paper presents an investigation on self-focusing of cosh-Gaussian (ChG) laser beam in a relativistic–ponderomotive non-uniform plasma. It is observed numerically that the selection of decentered parameter and initial beam radius determines the focusing/defocusing of ChG laser beam. For given value of these parameters, the plasma density ramp of suitable length can avoid defocusing and enhance focusing effect significantly. Focusing length and extent of focusing may also be controlled by varying slope of the ramp density. A comparison with Gaussian beam has also been attempted for optimized set of parameters. The results establish that ChG beam focuses earlier and sharper relative to Gaussian beam. We have setup the non-linear differential equation for the beam width parameter using Wentzel–Kramers–Brillouin and paraxial ray approximation and solved it numerically using Runge–Kutta method.

In the present paper, we have investigated self-focusing of Gaussian laser beam in relativistic ponderomotive (RP) cold quantum plasma. When de Broglie wavelength of charged particles is greater than or equal to the inter particle distance or equivalently the temperature is less than or equal to the Fermi temperature, quantum nature of the plasma constituents cannot be ignored. In this context, we have reported self-focusing on account of nonlinear dielectric contribution of RP plasma by taking into consideration the impact of quantum effects. We have setup the nonlinear differential equation for the beam-width parameter by paraxial ray and Wentzel Kramers Brillouin approximation and solved it numerically by the Runge Kutta Fourth order method. Our results show that additional self-focusing is achieved in case of RP cold quantum plasma than relativistic cold quantum plasma and classical relativistic case. The pinching effect offered by quantum plasma and the combined effect of relativistic and ponderomotive nonlinearity greatly enhances laser propagation up to 20 Rayleigh lengths.

The dispersion relation of electrostatic waves with phase velocities smaller than the electron thermal velocity is investigated in relativistic temperature plasmas. The model equations are the electron relativistic collisionless hydrodynamic equations and the ion non-relativistic Vlasov equation, coupled to the Poisson equation. The complex frequency of electrostatic modes are calculated numerically as a function of the relevant parameters kλDe and ZTe/Ti where k is the wavenumber, λDe, the electron Debye length, Te and Ti the electron and ion temperature, and Z, the ion charge number. Useful analytic expressions of the real and imaginary parts of frequency are also proposed. The non-relativistic results established in the literature from the kinetic theory are recovered and the role of the relativistic effects on the dispersion and the damping rate of electrostatic modes is discussed. In particular, it is shown that in highly relativistic regime the electrostatic waves are strongly damped.

The nonlinear dynamics of the outflow driven by magnetic explosion on the surface of compact object is investigated through special relativistic magnetohydrodynamic simulations. We adopt, as an initial equilibrium state, a spherical stellar object embedded in the hydrostatic plasma which has a density ρ(r) ∝ r−α and is threaded by a dipole magnetic field. The injection of magnetic energy at the surface of compact star breaks the dynamical equilibrium and triggers two-component outflow. At the early evolutionary stage, the magnetic pressure increases rapidly in time around the stellar surface, initiating a magnetically driven outflow. Then it excites a strong forward shock, shock driven outflow. The expansion velocity of the magnetically driven outflow is characterized by the Alfvén velocity on the stellar surface, and follows a simple scaling relation υmag ∝ υA1/2. When the initial density profile declines steeply with radius, the strong shock is accelerated self-similarly to relativistic velocity ahead of the magnetically driven component. We find that the evolution of the strong forward shock can be described by a self-similar relation Γsh ∝ rsh, where Γsh is the Lorentz factor of the plasma measured at the shock surface rsh. It should be stressed that the pure hydrodynamic process is responsible for the acceleration of the shock driven outflow. Our two-component outflow model, which is the natural outcome of the magnetic explosion, would deepen the understanding of the magnetic active phenomena on various magnetized stellar objects.

In the present paper, we have investigated the growth of a Gaussian perturbation superimposed on a Gaussian laser beam. The nonlinearity we have considered is of relativistic type. We have setup the nonlinear differential equations for beam width parameter of the main beam, growth and width of the laser spike by using the WKB and paraxial ray approximation. These are coupled ordinary differential equations and therefore these are simultaneously solved numerically using the Runge Kutta method. It has been observed from the analysis that self-focusing/defocusing of the main beam and the spike determine the growth dynamic of the spike.

This paper presents an effect of relativistic mutual interaction of two laser beams of different frequencies on the growth of a laser ripple in laser produced plasmas. The nonlinearity due to relativistic mass variation depends not only on the intensity of one laser but also on the second laser. Therefore, one laser beam affects the dynamics of the second beam and hence a mutual nonlinear interaction (cross-focusing) takes place. The dynamical equations governing the laser intensity of two laser beams and the perturbation present on one laser beam (ripple) have been set up and a numerical solution has been presented for typical laser plasma parameters. It is found that a change in the intensity of the second laser beam can affect the growth of the laser ripple significantly. This study is important in plasma beat wave excitation and collective laser particle accelerators.