Equation For Beam Width Parameter Research Articles

Study of propagation of skew cosh Gaussian laser beam in attenuated magneto plasma

Self-focusing of a laser beam is one of the major consequences of nonlinear interaction of laser with plasma. In this paper, self-focusing of skew cosh Gaussian (skew-ChG) laser beam is studied in anisotropic, collisional plasma where in externally exponentially decreasing magnetic field is applied. Skewness parameters in the field profile of skew-ChG laser beam eventually determine intensity profile of the beam. The symmetry in skewness parameter in two transverse directions simplifies the calculations considerably. Second order, nonlinear, ordinary, coupled differential equations for Beam Width Parameters (BWP) are obtained using Akhmanovs approach under Wentzel–Kramers–Brillouin (WKB) and paraxial approximations which are solved numerically. For given amplitude of applied magnetic field, attenuated oscillatory self-focusing is observed with respect to change in attenuation coefficient.

Third harmonic generation of a relativistic self-focusing laser in plasma under exponential density ramp

Abstract Present study focuses on self-focusing and its effect on third harmonic generation (THG) of a Gaussian laser beam in plasma under the influence of exponential density ramp. Relativistic nonlinearity has been taken into account which is aroused due the modification of electron’s mass in the presence of high intensity laser. Under strong ponderomotive force, electrons acquire very high quiver velocity and mass variation takes place. Equations for beam width parameter of incident laser and the amplitude of THG have been derived under WKB and paraxial ray approximation, and solved them numerically. It is found that the presence of exponential plasma density ramp results strong self-focusing of laser which further leads to enhance the efficiency of THG. Wiggler magnetic field adds an additional momentum to the photons of third harmonic due to which appreciable gain is observed in the normalized amplitude of THG. Significant enhancement in the THG amplitude has been reported in the presence of exponential density ramp for optimum values of intensity of incident laser, wiggler magnetic field and plasma frequency.

Influence of linear absorption and density ramp on self-focusing of the Hermite-Gaussian chirped pulse laser in plasma

An analysis of the self-focusing of Hermite Gaussian chirped pulse laser in the relativistic and ponderomotive regime under the influence of exponential plasma density ramp and linear absorption has been done. Differential equation for beam width parameter is derived by using paraxial ray approximation and then solved numerically. It is observed that self-focusing of the chirped pulse laser is strongly influenced by linear absorption. Also it is seen that with the increase in intensity of laser beam, plasma density ramp and chirped parameter value, self-focusing becomes more effective. Current work may be useful in understanding laser induced fusion, quantum dots etc.

Influence of light absorption in the interaction of asymmetric elegant Hermite-cosh-Gaussian laser beams with collisionless magnetized plasma

In the present paper, an analysis of self-focusing of asymmetric elegant Hermite-cosh-Gaussian laser beams having transverse electromagnetic (TEMmn) modes with mode indices m = 0 and n = 0, 2, and 4 in magnetized plasma has been presented. The nonlinearity in the effective dielectric function of plasma considered herein is mainly due to the ponderomotive mechanism. The nonlinear coupled differential equations for beam width parameters in both x and y dimensions of the beams are established by using Wentzel–Kramers–Brillouin and paraxial approximations through a parabolic equation approach. The behavior of beam width parameters with the dimensionless distance of propagation is presented graphically at different parameters of plasma and those of general beam's family considered. Specifically, complexity in beam width parameters is highlighted through the influence of light absorption, mode index, and decentered parameter. The results show that two unlike decentered parameters in transverse dimensions of the beam change beam-widths considerably at higher order mode indices. Absorption gives an important role in complexity of beam width parameters in transverse dimensions of the beam.

Effect of linear absorption on self focusing of Hermite Gaussian laser beam in plasma in relativistic and ponderomotive regime

Effect of linear absorption, intensity of fundamental laser pulse and plasma frequency on beam width parameter is investigated to study the self-focusing of Hermite-Gaussian(HG) laser beam in plasma under relativistic and ponderomotive regime. Intense short pulse laser propagates through plasma imparts oscillatory velocity to electrons and non linearity arises. Using the paraxial approach we have derived the second order differential equation for beam width parameter and the equation for normalized radius of incident beam is also obtained using the critical condition. The outcome of our study reveals that light absorption and intensity of radiation enhance the self focusing of Hermite-Gaussiam laser beam. It is observed that the beam width parameter shows significant decrease for higher values of linear absorption coefficient and plasma frequency. We also observe that radius of the incident beam decreases sharply with increasing intensity of incident pulse for higher values of plasma frequency.

Effect of axial electron temperature and plasma density ramp on self-focusing / defocusing of a laser beam in plasma

In the present study, we analyze the self-focusing / defocusing of an intense laser beam in the plasma under combined effect of density ramp and higher order axial electron temperature. The differential equation for beam width parameter is obtained and then solved numerically under paraxial ray approximation. The behavior of beam width parameter with propagation distance is extensively investigated for different values of optimized parameters and is strongly influenced by the higher order axial electron temperature, Tp4. The results indicate that the electron temperature component Tp4 is not of little significance than Tp0 and Tp2. Under the influence of plasma density ramp and higher order axial electron temperature Tp4 the defocusing is reduced and self-focusing becomes stronger, especially for large propagation distance. Furthermore, increase in the density ramp results more reduction in the laser beam spot size and hence, increase in the intensity of the laser which may be useful for various applications including laser-driven fusion.

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.

Self-focusing of Hermite-cosh-Gaussian laser beam in semiconductor quantum plasma

Self-focusing of Hermite-cosh-Gaussian (HchG) laser beam in semiconductor quantum plasma (ScQP) has been presented by considering the decentred parameter and quantum effect. We drive the equation of beam width parameter by using parabolic wave equation and solved it numerically by using WKB approximation. Our simulation results show that HchG beam gives freedom to source parameters that influence the self-focusing significantly. Additional self-focusing has been observed in ScQP than that of classical case of reference. The quantum plasma also adds pinching effect to laser propagation in semiconductor like germanium which further enhances the self-focusing more and more in ScQP.

Excitation of nonlinear ion acoustic wave and stimulated Brillouin scattering of hollow Gaussian beam in relativistic plasma

AbstractIn the present work, excitation of nonlinear ion acoustic wave (IAW) in collisionless plasma by laser beam having null intensity at the center is examined considering relativistic nonlinearity. The differential equation for beam-width parameter is determined considering relativistic nonlinearity using the paraxial and Wentzel–Kramers–Brillouin approximations by the parabolic equation method. The propagation features of the IAW are found to be modified due to the nonlinearity present in the system. The hollow Gaussian beam (HGB) gets nonlinearly coupled with the seed IAW, results in excitation of nonlinear IAW. The interaction of nonlinear IAW with pump beam demonstrated stimulated Brillouin scattering (SBS) of HGB. It is found that the power of IAW and power of SBS is affected with the order of HGB. The power of IAW and backscattered power of SBS is determined analytically and numerically for various orders of HGB. It is found that the power of IAW and the backscattering is diminished for higher order of HGB.

Evolution of a Gaussian laser beam in warm collisional magnetoplasma

In this paper, the spatial evolution of an intense circularly polarized Gaussian laser beam propagated through a warm plasma is investigated, taking into account the ponderomotive force, Ohmic heating, external magnetic field, and collisional effects. Using the momentum transfer and energy equations, both modified electron temperature and electron density in plasma are obtained. By introducing the complex dielectric permittivity of warm magnetized plasma and using the complex eikonal function, coupled differential equations for beam width parameter are established and solved numerically. The effects of polarization state of laser and magnetic field on the laser spot size evolution are studied. It is observed that in case of the right-handed polarization, an increase in the value of external magnetic field causes an increase in the strength of the self-focusing, especially in the higher values, and consequently, the self-focusing occurs in shorter distance of propagation. Moreover, the results demonstrate the existence of laser intensity and electron temperature ranges where self-focusing can occur, while the beam diverges outside of these regions; meanwhile, in these intervals, there exists a turning point for each of intensity and temperature in which the self-focusing process has its strongest strength. Finally, it is found that the self-focusing effect can be enhanced by increasing the plasma frequency (plasma density).

Nonlinear propagation of Gaussian laser beam in an inhomogeneous plasma under plasma density ramp

Nonlinear propagation of Gaussian laser beam in an inhomogeneous plasma under plasma density ramp is studied. The differential equation for beam width parameter is derived by parabolic wave equation approach under paraxial approximation. For different values of plasma density, laser intensity and initial beam width, the behavior of beam width parameter with the normalized propagation distance is examined. It is found that the beam width parameter decreases with a higher rate. The frequency of the oscillations increases while amplitude decreases and the laser beam focuses up to long distance. Further, increase in relative plasma density causes reduction in the amplitude of spot size of laser beam near the propagation axis.

Effect of light absorption on relativistic self-focusing of Gaussian laser beam in plasma

In the present paper, we have studied the effect of light absorption on relativistic self-focusing of Gaussian laser beam propagating through plasma. We have obtained the differential equation for beam width parameter by using parabolic equation approach under the usual WKB and paraxial approximations. The effect of light absorption on the behavior of beam-width parameter, normalized intensity and plasma dielectric function is presented graphically and discussed. It shows that absorption play an important role in weakening the relativistic self-focusing of laser beam during propagation in plasma and gives reasonably interesting results.

Role of Density Profiles for the Nonlinear Propagation of Intense Laser Beam through Plasma Channel

In this work role of density profiles for the nonlinear propagation of intense laser beam through plasma channel is analyzed. By employing the expression for the dielectric function of different density profile plasma, a differential equation for beamwidth parameter is derived under WKB and paraxial approximation. The laser induces modifications of the dielectric function through nonlinearities. It is found that density profiles play vital role in laser-plasma interaction studies. To have numerical appreciation of the results the propagation equation for plasma is solved using the fourth order Runge-Kutta method for the initial plane wave front of the beam, using boundary conditions. The spot size of the laser beam decreases as the beam penetrates into the plasma and significantly adds self-focusing in plasma. This causes the laser beam to become more focused by reduction of diffraction effect, which is an important phenomenon in inertial confinement fusion and also for the understanding of self-focusing of laser pulses. Numerical computations are presented and discussed in the form of graphs for typical parameters of laser-plasma interaction.

Self-focusing of Gaussian laser beam in weakly relativistic and ponderomotive regime using upward ramp of plasma density

We have studied the steady state self-focusing of Gaussian laser beam in weakly relativistic and ponderomotive regime for upward increasing plasma ramp density profile. We have obtained the differential equation for beam width parameter by using parabolic equation approach under the usual Wentzel–Kramers–Brillouin and paraxial approximations. The variation of beam width parameter with respect to dimensionless distance of propagation is presented graphically by varying the parameters of density profile, intensity parameter, and electronic temperature. It shows that the above stated parameters play an important role in propagation characteristics and give reasonably interesting results.

Combined effect of ponderomotive and relativistic self-focusing on laser beam propagation in a plasma

Propagation of a Gaussian laser beam in a plasma is analyzed by including the nonlinearity associated with the relativistic mass and the ponderomotive force. We set up the nonlinear differential equation for beam width parameter using parabolic equation approach and solve it numerically. Our results show that the ponderomotive self-focusing contributes in the relativistic self-focusing of the laser beam. An impact of plasma electron temperature, relative density parameter, and intensity parameter on the propagation of the laser beam has been explored.

Self-focusing of Gaussian Laser Beam Through Collisional Plasmas: Moment Theory Approach

In the present paper, self-focusing of Gaussian laser beam through collisional plasma is studied by moment theory approach. Nonlinear differential equation for beam width parameter of laser beam has been set up and solved numerically to study the variation of beam width parameter with normalized distance of propagation. Effect of absorption coefficient and plasma density on the beam width parameter has been studied. It is observed from the analysis that increasing the value of absorption coefficient brings about reduction in extent of self-focusing on account of decrease in energy of beam, which is equivalent to weakening of nonlinearity effect. On the other hand, increase in plasma density results in a sharp decrease in focusing length due to increase in nonlinear part of dielectric constant.

Dynamics of Gaussian spikes on Gaussian laser beam in relativistic plasma

AbstractIn 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.