This article presents a preliminary study of the longitudinal self-compression of ultra-intense Gaussian laser pulse in a magnetized plasma, when relativistic nonlinearity is active. This study has been carried out in 1D geometry under a nonlinear Schrodinger equation and higher-order paraxial (nonparaxial) approximation. The nonlinear differential equations for self-compression and self-focusing have been derived and solved by the analytical and numerical methods. The dielectric function and the eikonal have been expanded up to the fourth power of r (radial distance). The effect of initial parameters, namely incident laser intensity, magnetic field, and initial pulse duration on the compression of a relativistic Gaussian laser pulse have been explored. The results are compared with paraxial-ray approximation. It is found that the compression of pulse and pulse intensity of the compressed pulse is significantly enhanced in the nonparaxial region. It is observed that the compression of the high-intensity laser pulse depends on the intensity of laser beam (a0), magnetic field (ωc), and initial pulse width (τ0). The preliminary results show that the pulse is more compressed by increasing the values of a0, ωc, and τ0.

We examine the electron acceleration induced by an ultra-relativistic intensity laser–plasma interaction in a two-dimensional plasma channel in the presence of a self-generated transverse magnetic field. We find that the electron dynamics is strongly affected by the laser pulse polarization angle, plasma density, and magnetic field strength. We investigate in detail, the dependencies of the electron acceleration in terms of different parameters and find excellent agreement with non-magnetized plasma in the absence of the magnetic field. The numerical results show that the self-generated magnetic field plays a constructive role in the electron acceleration process. It is shown that electron acceleration is more affected by self-generated magnetic field for the laser radiations with large polarization angles. The numerical results show the maximum enhancement for electron acceleration for a laser radiation with polarization angle θ = π/2.

An analytical and numerical study has been carried out for the generation of terahertz (THz) radiation by beating of two intense cosh-Gaussian laser beams (decentered Gaussian beams) in the rippled density magnetized plasma under the relativistic–ponderomotive regime. In this process, both laser beams exert a relativistic–ponderomotive force on plasma electrons at the beat frequency and impart them an oscillatory velocity in the presence of a static magnetic field. Due to coupling between this nonlinear oscillatory velocity with density ripple, nonlinear current is generated that excites the THz radiation at the different frequency. Higher-order paraxial-ray approximation (non-paraxial theory) has been used in this study. The effects of the decentered parameter, magnetic field, and density ripple on the THz radiation generation in ripple density magnetized plasma have been investigated. Further, the effect of beating of laser beams on the THz field amplitude and the efficiency of THz radiation have been studied. The amplitude and efficiency of the emitted radiation are found to be highly sensitive to the decentered parameter, magnetic field, and density ripple. It has been found that the amplitude and efficiency of the generated THz radiation increase significantly with increasing the values of decentered parameter, magnetic field, and density ripple.

A scheme of phase-matched terahertz generation by beating two co-propagating lasers in magnetized plasma, in the presence of a magnetosonic wave (MSW), is developed. The beat frequency ponderomotive force of the lasers imparts an oscillatory drift to electrons. The electron drift velocity couples with the electron density perturbation associated with the MSW to produce an irrotational nonlinear current $\left(\nabla \times {\vec J}\;{}^{\rm NL}\ne 0\right)$. The beat current density resonantly excites a THz (Terahertz) radiation when the phase-matching conditions are satisfied. The MSW mediates the phase matching. At 9.6 and 10.6 µm wavelengths, and background magnetic field of 285 kG, one may achieve normalized THz wave amplitude of the order of 10−3 and one obtains the ratio of THz power to pump power of the order of 10−6.

Laser beat wave heating of magnetized plasma via electron cyclotron damping is proposed and analyzed. A plasma density ripple is presumed to exist across the magnetic field. Two collinear lasers propagating along the magnetic field exert a beat frequency ponderomotive force on electrons, driving a large amplitude Bernstein quasi-mode which suffers cyclotron damping on electrons. Finite Larmor radius effects play an important role in the heating. Electron temperature initially rises linearly with time. As the temperature rises cyclotron damping becomes stronger and temperature rises rapidly. The process, however, requires ripple wavelength shorter than the wavelength of the beat wave.

The paper gives graphical and analytical investigation of the effect of critical beam power on self-focusing of cosh-Gaussian laser beams in collisionless magnetized plasma under ponderomotive non-linearity. The standard Akhmanov's parabolic equation approach under Wentzel–Kramers–Brillouin (WKB) and paraxial approximations is employed to investigate the propagation of cosh-Gaussian laser beams in collisionless magnetized plasma. Especially, the concept of numerical intervals and turning points of critical beam power has evolved through graphical analysis of beam-width parameter differential equation of cosh-Gaussian laser beams. The results are discussed in the light of numerical intervals and turning points.

The Fokker–Planck transport equation describing the motion of energetic particles through a plasma is explored analytically. The latter equation provides a pitch-angle and position-dependent distribution function of the charged particles. In the current paper the first 14 moments of this equation are computed exactly for an arbitrary initial pitch angle. Such analytical forms are required in nonlinear treatments of perpendicular transport and other scenarios in plasma physics and astrophysics.

In this paper, self-focusing of asymmetric cosh-Gaussian laser beams in collisionless magnetized plasma has been studied. The non-linearity in dielectric constant considered herein is mainly due to the ponderomotive force. The non-linear coupled differential equations for the beam width parameters in transverse dimensions of the beam have been obtained by using WKB and paraxial approximations under parabolic equation approach. The numerical computation is completed by using fourth-order Runge–Kutta method. The effect of unlike decentered parameters in both transverse dimensions of the beam on self-focusing of cosh-Gaussian beams has been presented. Further, the effect of the static magnetic field and polarization modes of the laser has been explored.

The transmitted and reflected second harmonics (SH) generation by an oblique p-polarized laser pulse irradiated on vacuum-magnetized plasma interface is investigated. The laser pulse propagates through a homogenous, underdense, and transversely magnetized plasma. The transverse magnetic field plays the role of a self-generated magnetic field produced in laser plasma interaction. It is shown that if the transmitted and reflected SH components investigated as a simultaneous process, the maximum SH power deviates from previous reports specially near the critical angle. The deviation increases with laser field intensity and plasma density. The results reveal that the conversion efficiency increases slightly by increasing incident angle and drastically enhances near the critical angle. We show that the transmitted SH power decreases by increasing the magnetic field strength, in contrast to the normal incidence, which the SH power is increased. The comparison revealed that the SH efficiency is greater for transmitted component, while the reflected component is more proper for technical and experimental applications. This paper not only conforms the previous reports for angle far from the critical but also modifies them for the SH generation near the critical angle. Moreover, this paper gives a new insight for SH generation by a magnetized plasma.

A one-dimensional (1D) numerical model for studying enhanced terahertz (THz) radiation generation by mixing of ordinary and extraordinary modes of two-color laser pulses propagating in magnetized plasma has been presented. The direction of the static external magnetic field is such that one of the two laser pulses propagates in the extraordinary mode, while the other pulse propagates in the ordinary mode, through homogeneous plasma. A transverse electromagnetic wave with frequency in the THz range is generated due to the presence of the external magnetic field. It is observed that larger amplitude THz radiation can be generated by mixing of the ordinary and extraordinary modes of the two-color laser pulses as compared with the single laser pulse propagating in the extraordinary mode. Further, 2D simulations using the XOOPIC code show that the fields obtained via simulation study are compatible with those obtained from the numerical model.

Stimulated Raman backward scattering of an X-mode laser beam propagating in a homogenous plasma is studied in the presence of a transverse magnetic field. As the laser propagates in its X-mode in plasma, it decays into an upper hybrid wave and a down-shifted sideband wave. Beating the incident laser with the sideband exerts a nonlinear ponderomotive force acting on plasma electrons driving the excited upper hybrid wave. The incident wave then parametrically couples with the upper hybrid wave to drive the sideband. Using the fluid model and nonlinear current density, the nonlinear ponderomotive force is obtained to find the dispersion relation of the scattered sideband wave and the growth rate of the instability in the weakly relativistic regime. It is shown that the growth rate decreases and the cut-off points in the normalized wave number of the upper-hybrid wave become smaller by increasing the static magnetic field.

This paper presents a theoretical model for efficient terahertz (THz) radiation by self-focused amplitude-modulated laser beam in preformed ripple density plasma. The density of plasma is modified due to ponderomotive nonlinearity which arises because of the nonuniform spatial profile of the laser beam in magnetized plasma and leads to the self-focusing of the laser beam. The rate of self-focusing depends on the intensity of the amplitude-modulated beam as well as on the externally applied magnetic field strength. The electron also experiences time-dependent ponderomotive force by the laser beam at modulated frequency. A nonlinear current at THz frequency arises on account of the coupling between the ripple density plasma and nonlinear oscillatory velocity of the electrons. The yield of the generated THz radiation enhances with enhancement in self-focusing of the laser beam and applied magnetic field.

The modulational instability associated with propagation of an intense laser pulse through a transversely magnetized plasma is investigated in the presence of collisional effects. The source-dependent expansion method for analyzing the wave equation is employed. The dispersion relation is obtained and modulational instability and its growth rate are studied. It is shown that in the absence of collisional effects the modulational instability is restricted to the small wavenumber region and the constant magnetic field reduces the growth rate of the instability. In contrast, in the collisional plasma, there is no upper limit of wavenumber for the existence of modulational instability. In addition, in this case, the growth rate of instability increases as the collision frequency goes up.

The main purpose of this theory is to present a simple picture of magnetic field generation by a relativistic equilibrium counterstreaming electron–negative hydrogen ion (e–H−) plasmas propagating parallel to an ambient external magnetic field. The existence of such kind of plasma flows can be imagined during the negative hydrogen ion propagation through neutralizing plasma, in order to generate an energetic neutral hydrogen beam. The produced magnetic field deflects the electron and negative hydrogen ion flows and reduces the efficiency of hydrogen neutral beam generation. We focused our analysis on the influences of the negative hydrogen ion contribution, the particles thermal velocity and the external magnetic field on the growth rate of generated sheared magnetic field. The dispersion relation is obtained using a relativistic two-fluid model and Maxwell equations. The analytical and numerical solutions admit generation of a purely growing transverse electromagnetic field across the ambient external magnetic field. It is shown that H− current filaments are responsible for deep penetration of the sheared magnetic fields into plasma, however, applying a weak magnetic field ${\rm \omega} _{{\rm ce}}^2 {\rm \ll} {\rm \omega} _{{\rm pe}}^2 $ suppresses magnetic field generation for a counterstreaming e–H− plasma in the absence of H− ions dynamics. On the other hand, a magnetic field exists with a small growth rate for strongly magnetized (${\rm \omega} _{{\rm ce}}^2 \;{\rm \gg}\; {\rm \omega} _{{\rm pe}}^2 $) e–H− plasma when the influence of H− ions is included. Although the growth rate is small, we expect that magnetic field generation is further amplified and the penetration depth is increased owing to H− ions stream, on a time scale much longer than the plasma period $t\;{\rm \gg}\; {\rm \omega} _{{\rm pe}}^{ - 1} $.

The modulation instability of a circularly polarized laser pulse in a magnetized non-Maxwellian plasma is investigated. Based on a relativistic fluid model, the nonlinear interaction of an intense circularly polarized laser beam with a non-Maxwellian magnetized plasma is described. Nonlinear dispersion relation and growth rate of the instability for left- and right-hand polarizations are derived. The effect of temperature, external magnetic field, value of Kappa and state of polarization on the growth rate are analyzed. It is shown that the growth rate increases with increase in the magnetic field for the right-hand polarization and inversely it decreases for the left-hand one. Also it is observed that existence of super-thermal particles causes the decrease in the growth.

Resonant excitation of terahertz (THz) radiation by nonlinear coupling of two filamented spatial-Gaussian laser beams of different frequencies and wave numbers is studied in plasma having transverse static electric field. The static ponderomotive force due to filamented lasers is balanced by the pressure gradient force which gives rise to transverse density ripple, while, the nonlinear ponderomotive force at frequency difference of beating lasers couples with density ripple giving rise to stronger transverse nonlinear current which results into the excitation of THz radiation at resonance. The coupling is further enhanced by the presence of static electric field and spatial-Gaussian nature of laser beams. An increase of six-fold in the normalized amplitude of THz is observed by applying a direct current field of about 50 KV. Effects of frequency, laser beam width, and periodicity factor of modulated laser amplitude are studied for the efficient THz radiation generation. These results can be utilized for generating controlled tunable THz sources for medical applications using low filament intensities (~ 1014 W/cm2) of beating lasers.

Self-focusing of an intense circularly-polarized laser beam in a hot electron-positron-ion magneto-plasma is studied. Using a relativistic fluid model, nonlinear equation describing laser-plasma interaction in the quasi-neutral approximation is derived. Expanding nonlinear current density in terms of normalized vector potential and saving only the parabolic terms, we investigated the self-focusing phenomenon for right- and left-hand circularly polarized laser beams. The evolution of laser beam spot size with Gaussian profile is considered. Effects of the external magnetic field, fraction of electron-positron pairs, and also the kind of polarization on the self-focusing property are studied. It is shown that a mixture of electron-positron pairs to the ion-electron plasma modifies the behavior of plasma with respect to the external magnetic field.

Brillouin backward scattering is investigated in the interaction of linearly polarized short laser pulse with a homogenous underdense transversely magnetized plasma by taking into account the relativistic and nonlinearity effects up to third order. The plasma is embedded in a uniform magnetic field perpendicular to both of propagation direction and electric vector of the radiation field. Temporal growth rate of instability is calculated by using of the nonlinear wave equation. Results are significantly different in comparison with lower order computations. The growth rate of Brillouin backward instability shows a decrease due to the presence of external magnetic field, while relativistic and higher order nonlinearities due to the external magnetic field, give rise the Brillouin backward scattering instability.

A scheme of terahertz radiation generation is proposed by beating of two extra-ordinary lasers having frequencies and wave numbers $\lpar {\rm \omega}_1\comma \; \vec k_1 \rpar $ and $\lpar {\rm \omega}_2\comma \; \vec k_2 \rpar $, respectively in a magnetized plasma. Terahertz wave is resonantly excited at frequency $\lpar {\rm \omega}_1 - {\rm \omega}_2 \rpar $ and wave number (k1 − k2 + q) with a wave number mismatch factor q which is introduced by the periodicity of plasma density ripples. In this process, the lasers exert a beat ponderomotive force on plasma electrons and impart them an oscillatory velocity with both transverse and longitudinal components in the presence of transverse static magnetic field. The oscillatory velocity couples with density ripples and produces a nonlinear current that resonantly excites the terahertz radiation. Effects of periodicity of density ripples and applied magnetic field are analyzed for strong THz radiation generation. The terahertz radiation generation efficiency is found to be directly proportional to the square of density ripple amplitude and rises with the magnetic field strength. With the optimization of these parameters, the efficiency ~10−3 is achieved in the present scheme. The frequency and power of generated THz radiation can be better tuned with the help of parameters like density ripple amplitude, periodicity and applied magnetic field strength in the present scheme.

The self-focusing of an intense right circularly polarized Gaussian laser pulse in magnetized plasma is studied. The ions are taken to be immobile and relativistic mass effect is incorporated in both the plasma frequency (ωp) and the electron cyclotron frequency (ωc) while determining the ponderomotive force on electrons. The ponderomotive force causes electron expulsion when the effective electron cyclotron frequency is below twice the laser frequency. The nonlinear plasma dielectric function due to ponderomotive and relativistic effects is derived, which is then employed in beam-width parameter equation to study the self-focusing of the laser beam. From this, we estimate the importance of relativistic self-focusing in comparison with ponderomotive self-focusing at moderate laser intensities. The beam width parameter decreases with magnetic field indicating better self-focusing. When the laser intensity is very high, the relativistic gamma factor can be modeled as ${\rm \gamma} = 0.8\left({{{{\rm \omega} _c } / {\rm \omega} }} \right)+ \sqrt {1 + a_0^2 }$$\text{γ}=0.8({\text{ω}}_c/\text{ω})+\sqrt{1+a_0^2}$ where ω and a0 are the laser frequency and the normalized laser field strength, respectively. The cyclotron effects on the self-focusing of laser pulse are reduced at high field strengths.