Beam Width Parameter Research Articles

Exponential plasma density progression based self-focusing of laser in cold quantum plasma

This manuscript presents the analysis on exponential plasma density progression based self-focusing of the Gaussian laser beam in cold quantum plasma. It is noticed that beam width parameter gets reduced significantly because of the nonlinear dielectric involvement of the relativistic plasma under exponential density ramp and hence, leads to stronger self-focusing. Also, the major contribution of cold quantum plasma in the embellishment of self-focusing of laser beam has been observed. A comparison has also been attempted by considering exponential versus tangential plasma density ramp and found the former one better than later one. The current analysis may have important uses in the area of laser driven particle accelerators, laser interaction with quantum plasma etc.

Relativistic ponderomotive self-focusing of quadruple Gaussian laser beam in cold quantum plasma

AbstractIn 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.

Contribution to the study of lowest order Bessel-Gaussian beams propagating in thermal quantum plasma

In this paper, the self-focusing of lowest order Bessel-Gaussian beams in relativistic thermal quantum plasma is investigated. To describe the behavior propagation beams in the considered medium plasma, nonlinear differential equation of beam-width parameter is derived by using Wentzel-Kramers-Brillouin and paraxial approximations. It is shown that the quantum effects enhance the relativistic self-focusing of laser beam in thermal quantum plasma by comparison to relativistic cold quantum and classical relativistic regimes.

Self-focusing and defocusing of cosh Gaussian laser beam in the presence of nonlinearity of ponderomotive force and temperature gradient

In this paper, the propagation of Cosh Gaussian laser beam and its interaction with isothermal plasma without temperature gradient as well as the effect of the exponential electron temperature gradient are investigated. Here the ponderomotive nonlinearity force is effective mechanism. This force can modify the electron density distribution. All the investigations are carried out for different initial plasma temperatures. Using Maxwell’s equations we obtained the nonlinear second-order differential equation of the dimensionless beam-width parameter (f) on the distance of propagation for several initial electron temperatures and exponential temperature variations. These equations are solved numerically by taking WKB and paraxial approximation. Under the effect of initial electron temperature, self-focusing and defocusing of hyperbolic cosine (cosh) Gaussian laser beam is distinguished. Furthermore, the exponential temperature gradient cause to stationary propagation mode breaks, and self-focusing or defocusing properties is observable.

Stronger self-focusing of a chirped pulse laser with exponential density ramp profile in cold quantum magnetoplasma

Stronger self-focusing of chirped pulse laser with exponential plasma density ramp profile in cold quantum magnetoplasma has been presented. Low value of the beam width parameter in the focal region due to nonlinear dielectric role of relativistic plasma with exponential density transition is observed. Further, the significant contribution of the cold quantum magnetoplasma with the optimized value of magnetic field lead to enhanced self-focusing. Here, in this present manuscript we have observed stronger self-focusing with increased value of the chirp parameter ‘b’. Also intensity of the laser beam imparts chief role in achieving the stronger self-focusing. The present work may have very valuable applications in the field of laser driven accelerators, laser driven fusion etc.

Generation of electron plasma wave and particle acceleration by beating of two intense cross focused elliptical laser beams in collisionless plasma

This paper presents the propagation of two intense cross-focused elliptical laser beams (ELBs) in a collisionless plasma and their effect on the excitation of electron plasma waves (EPWs) and particle acceleration, when relativistic and ponderomotive nonlinearities are operative. Due to the mutual interaction of the two ELBs, cross-focusing takes place in the plasma. An EPW is generated on account of the beating of the two cross-focused ELBs of frequencies ω1 and ω2. Nonlinear differential equations have been set up for the beamwidth parameters of the ELBs, the power of the EPW and the energy gained by the electrons using WKB and paraxial-ray approximations. Numerical simulations have been carried out to investigate the effect of various laser and plasma parameters such as incident laser intensity and plasma density on the focusing of ELBs in plasmas and its effect on the power of excited EPWs and particle acceleration. Numerical results show that the focusing and intensity of both beams in plasma increase with increasing values of incident laser intensity and plasma density. It is observed that the cross-focusing of two ELBs enhances the power of generated EPWs and the yield of energy gain. This study is useful for determining the propagation dynamics of ELBs in plasma and the results are helpful for various applications requiring multiple laser beams.

Self-focusing of an elliptic-Gaussian laser beam in relativistic ponderomotive plasma using a ramp density profile

The propagation characteristics of an elliptic-Gaussian beam in non-uniform plasma have been investigated by taking into account the combined effects of relativistic and ponderomotive types of nonlinearity. Self-trapping, self-phase modulation, and beam width variation with propagation distance are given particular attention in the study. It is observed that the plasma density function significantly affects the propagation behavior of the beam. The beam radius along the x axis and y axis is separately influenced due to the density function, which, as a result of the cross-focusing phenomenon, results in the reduction of the effective beam radius during propagation of the beam. The longitudinal phase shift increases in the present case in comparison to uniform plasma. Self-trapping is also observed, which is, however, not comparable with that of a cylindrically symmetrical Gaussian beam. We have used the variational approach to set up the coupled nonlinear differential equations for the beam width parameters along the x and y axes and the longitudinal phase of the beam.

Relativistic effects on propagation of q-Gaussian laser beam in a rippled density plasma: Application of higher order corrections

AbstractA nonparaxial investigation for propagation characteristics of q-Gaussian laser beam in rippled density plasma is studied by considering the relativistic nonlinearity. The field distribution in the medium is expressed in terms of q parameter and beam width parameter f. Nonlinear parabolic partial differential equation governing the evolution of complex envelope in slowly varying approximation is solved in a modulated density profile. Analytical theory of self-focusing including higher order terms in the expansion of dielectric function up to fourth order is developed and the variation of beam width parameter f with the distance of propagation for different parameters is studied. One may note that increased value of density ripple, laser intensity and depth of modulation, increases self-focusing whereas a lower value of q shows strong self-focusing. A comparative study between paraxial and nonparaxial study has also conducted. This study is useful for research in high energy density physics.

Significant enhancement in the propagation of cosh-Gaussian laser beam in a relativistic–ponderomotive plasma using ramp density profile

AbstractThe 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.

On the exploration of graphical and analytical investigation of effect of critical beam power on self-focusing of cosh-Gaussian laser beams in collisionless magnetized plasma

AbstractThe 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.

Effect of light absorption and temperature on self-focusing of finite Airy–Gaussian beams in a plasma with relativistic and ponderomotive regime

In the present paper, we have studied the influence of light absorption and temperature on self-focusing of finite Airy–Gaussian beams in plasma by considering the combined effects of relativistic and the ponderomotive regime. The nonlinear differential equations of dimensionless beam-width parameter are derived using the paraxial ray and Wentzel–Kramers–Brillouin approximation, and they are solved numerically. The effect of absorption coefficient, plasma electron temperature, relative plasma density, intensity parameter and modulation parameter beam on the self-focusing of finite Airy–Gaussian beams in plasma is presented numerically and discussed.

Analytical investigation on domain of decentered parameter for self-focusing of Hermite-cosh-Gaussian laser beam in collisional plasma

In the present paper, an analytically investigated domain of decentered parameter and its effect on the self-focusing of Hermit-cosh-Gaussian (HChG) laser beams in a collisional plasma have been studied theoretically. The nonlinearity in the dielectric constant of plasma arising due to the nonuniform heating of carriers along the wavefront of the laser beam has been employed in the present investigation. The nonlinear differential equation of beam width parameter for various laser modes of HChG beam is obtained by following the standard Akhamanov's parabolic equation approach under Wentzel-Kramers-Brillouin and paraxial approximations. The analytical treatment has enabled us to define three distinct regions: self-focusing, self-trapping and defocusing, which are presented graphically.

Turning point temperature of self-focusing at laser–plasma interaction with weak relativistic-ponderomotive nonlinearity: effect of light absorption

In this communication, we have examined the influence of light absorption on turning point temperature of self-focusing in the interaction of Gaussian laser beam in plasma. The dielectric function of plasma introduced herein is under weak relativistic and ponderomotive regime. Differential equation for beam-width parameter has been established by using parabolic equation approach under WKB and paraxial approximations. Numerical analysis shows that light absorption plays an important role on turning point temperature of self-focusing under relativistic and ponderomotive regime. It is also found that variation of normalized plasma density, normalized laser intensity parameter and plasma dielectric function with dimensionless distance of propagation gives reasonably interesting results.

Effect of inertial ponderomotive force and self-focusing of the fundamental pulse on generation of second harmonic in magnetic plasma

In this paper, nonlinear propagation of the intense ultra short pulses through under dense plasmas are investigated analytically. Using paraxial theory, the beam width parameter is evaluated as a function of the propagation distance. The effect of the inertial ponderomotive force, ρm(u→⋅∇→) u→, on intensity of the second harmonic pulse and self focusing of laser pulse are considered. It is shown that the second harmonic amplitude depends on the propagation distance periodically. It is shown that the inertial ponderomotive force affects efficiency of the second harmonic generation, but it does not affect beam width parameter of the second harmonic wave.

Exponential density transition based self-focusing of Gaussian laser beam in collisional plasma

In this work, nonlinear aspects of a high intensity Gaussian laser beam propagating in plasma having upward density ramp of tangent and exponential profiles are studied. We have employed the nonlinearity in dielectric function of plasma due to nonuniform heating of carriers along the wavefront of the laser beam which is important in collisional plasmas. The differential equation governing the dimensionless beam width parameter is achieved by using Wentzel–Kramers–Brillouin (WKB) and paraxial approximations and solved it numerically by using Runge-Kutta fourth order method. Effect of exponential density ramp profile on self-focusing is systematically carried out and compared with tangent density ramp profile. It is found that exponential plasma density ramp causes the laser beam to become more focused than tangent density ramp over several Rayleigh length and gives reasonably interesting results.

Effect of q-parameter on relativistic self-focusing of q-Gaussian laser beam in plasma

The exponential function in an expression of intensity profile of Gaussian laser beam has been replaced by algebraic function having q exponent in it. In preliminary theoretical investigations, it has been observed that q-Gaussian intensity distribution function plays vital role in the dynamics of laser beam propagating in relativistic plasma. In present theoretical investigation, the usual parabolic equation approach under paraxial and WKB approximations has been adopted, taking into account relativistic nonlinearity. We have established the nonlinear differential equation for the beam-width parameter f and solved it numerically by using fourth order Runge-Kutta method. The effect of q parameter on the variation of beam width parameter f with normalized distance of propagation ξ has been presented graphically and discussed.

Weakly relativistic self-focusing of Gaussian laser beam in magnetized cold quantum plasma

AbstractIn the present paper, we have studied self-focusing of Gaussian laser beam in weakly relativistic magnetized cold quantum plasma. When interparticle distance is comparable to the de Broglie wavelength of charged particles, we cannot neglect the quantum contribution of plasma constituents. Therefore, propagation characteristics are studied by taking in to account quantum contribution in the presence of static magnetic field applied along the beam propagation. Our results show that the magnetic field plays a key role in achieving additional focusing, it modifies the quiver motion of electrons by adding cyclotron frequency to the natural frequency of oscillating electrons during laser beam propagation. The results are compared with those of weakly relativistic quantum plasma and weakly relativistic magnetized plasma. The self-focusing is found to be more pronounced when axial magnetic field is increased in the present model. We have setup the non-linear differential equation for the evolution of beam-width parameter by well-known paraxial ray approximation and solved it with the help of computational technique.

Mitigation of stimulated Raman backscattering by elliptical laser beam in collisionless plasma

This paper presents theoretical and numerical study of the propagation of an elliptical laser beam in collisionless plasma with relativistic-ponderomotive nonlinearities and its effect on the excitation of electron plasma wave (EPW) and resulting stimulated Raman backscattering (SRBS) process. Nonlinear interaction between an intense elliptical laser beams with the electron plasma wave leads stimulated Raman backscattering. Following Wentzel Kramers Brillouin (WKB) and paraxial-ray approximations, non-linear differential equations for the beam width parameters of elliptical laser beam, electron plasma wave and back-scattered beam are set up and solved numerically. Numerical simulations have been carried out to investigate the effect of laser and plasma parameters on the focusing of elliptical laser beam in plasma and further its effect on the excitation of electron plasma wave and backreflectivity of stimulated Raman scattering (SRS). The focusing of an elliptical laser beam, EPW and scattered wave are reduced at higher values of laser intensity in plasma. The amplitude of excited electron plasma wave, which depends on the focusing of main laser beam and electron plasma wave reduce for higher values of incident laser intensity. The results indicate that the focusing of waves mitigates the backreflectivity of SRS. The results are also compared with only relativistic nonlinearity and the Gaussian profile of laser beam. It is observed that an elliptical laser beam mitigates the backreflectivity of SRS at higher values of laser intensity. This study is relevant to inertial confinement fusion scheme, where SRS plays very important role.

Early and strong relativistic self-Focusing of cosh-Gaussian laser beam in cold quantum plasma

Relativistic self-focusing of cosh-Gaussian laser beam in the cold quantum plasma has been investigated theoretically. For a decentered parameter b=0.9, we present a comparative analysis for self-focusing of cosh-Gaussian laser beam in relativistic cold quantum (RCQ) and classical relativistic (CR) case. It is observed that as the beam penetrates deeper inside the RCQ plasma, the self-focusing ability of the laser beam enhances and shifted towards lower value of normalized propagation distance due to quantum contribution. The beam width parameter as a function of normalized propagation distance for various values of relative density parameter of the medium and intensity parameter has also been studied. The self-focusing is observed to be stronger with the increase in relative density parameter. Observation of early and strong self-focusing for higher values of relative density parameter and intensity parameter are reported. The present study might be very useful in the applications like the generation of inertial fusion energy driven by lasers, laser driven accelerators, scribing type of applications in electronics etc.

Self-focusing of asymmetric cosh-Gaussian laser beams propagating through collisionless magnetized plasma

AbstractIn 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.