Self-focusing of Hermite–Gaussian laser beams in plasma under plasma density ramp

Self-focusing of Hermite–Gaussian laser beams in plasma under plasma density ramp has been investigated. It is known that a laser beam shows an oscillatory self-focusing and defocusing behavior with the propagation distance. To overcome the defocusing, localized upward plasma density ramp is introduced, so that the laser beam attains a minimum spot size and maintains it with only a mild ripple. The density ramp could be important for the self-focusing of a Hermite–Gaussian laser by choosing the laser and plasma parameters appropriately. Self-focusing becomes stronger as the propagation distance increases. The behavior of beam-width parameters with the distance of propagation is presented graphically.     

Nonlinear Interaction of Elliptical Laser Beam with Collisional Plasma:Effect of Linear Absorption

In the present work,nonlinear interaction of elliptical laser beam with collisional plasma is studied by using paraxial ray approximation.Nonlinear differential equations for the beam width parameters of semi-major axis and semi-minor axis of elliptical laser beam have been set up and solved numerically to study the variation of beam width parameters with normalized distance of propagation.Effects of variation in absorption coefficient and plasma density on the beam width parameters are also analyzed.It is observed from the analysis that extent of self-focusing of beam increases with increase/decrease in plasma density/absorption coefficient.     

Off-axial contribution of beam self-focusing in plasma with density ripple

Off-axial contribution of beam self-focusing in plasma with density ripple is investigated. Apply paraxial ray theory and Wentzel–Krammers–Brillouin approximation, the results shown that, in interaction of laser and plasma with density ripple, beam self-focusing presents some interesting diverse features when off-axial contribution is obvious. In the paper, we find, on the one hand, density ripple can minimize the defocusing and beam still retains a localized profile with an oscillatory self-focusing and defocusing, on the other hand, with the increase of off-axial contribution, laser beams presents four various self-focusing features, which laser beam intensity profile splits into three-splitted with central axial convex profile, three-splitted with equal amplitude profile, three-splitted with central axial concave profile and two-splitted intensity profile.     

Stimulated Brillouin scattering of elliptical laser beam in collisionless plasma

This paper presents an investigation of self-focusing of elliptical laser beam in collisionless plasma and its effect on stimulated Brillouin scattering. The pump beam interacts with a pre-excited ion-acoustic wave leading to Brillouin back-scattered process. The transverse intensity gradient of a pump beam generates a ponderomotive force, which modifies the background plasma density profile in a direction transverse to pump beam axis. This modification in density effects the incident laser beam, ion-acoustic wave and back-scattered beam. Non-linear differential equations for the beam width parameters of pump laser beam, ion-acoustic wave and back-scattered beam are set up and solved numerically. It is observed from the analysis that the focusing of waves enhances the SBS back-reflectivity.     

Self-focusing of Gaussian laser beam in collisionless plasma and its effect on stimulated Raman scattering process

This paper presents an investigation of self-focusing of Gaussian laser beam in collisionless plasma and its effect on stimulated Raman scattering process. The pump beam interacts with a pre-excited electron plasma wave thereby generating a back-scattered wave. On account of Gaussian intensity distribution of laser beam, the time independent component of the ponderomotive force along a direction perpendicular to the beam propagation becomes finite, which modifies the background plasma density profile in a direction transverse to pump beam axis. This modification in density affects the incident laser beam, electron plasma wave and back-scattered beam. We have set up the non-linear differential equations for the beam width parameters of the main beam, electron plasma wave, back-scattered wave and SRS-reflectivity by taking full non-linear part of the dielectric constant of collisionless plasma with the help of moment theory approach. It is observed from the analysis that focusing of waves greatly enhances the SRS reflectivity.     

Density Transition Based Self-Focusing of cosh-Gaussian Laser Beam in Plasma with Linear Absorption

Density transition based self-focusing of cosh-Gaussian laser beam in plasma with linear absorption has been studied. The field distribution in the plasma is expressed in terms of beam width parameter, decentered parameter, and linear absorption coefficient. The differential equation for the beam width parameter is solved by following Wentzel—Kramers—Brillouin (WKB) and paraxial approximation through parabolic wave equation approach. The behaviour of beam width parameter with dimensionless distance of propagation is studied at optimum values of plasma density, decentered parameter and with different absorption levels in the medium. The results reveal that these parameters can affect the self-focusing significantly.     

Self-Focusing and de-Focusing of Intense Left- and Right-Hand Polarized Laser Pulse in Hot Magnetized Plasma in the Presence of an External Non-Uniform Magnetized Field

In this paper, self-focusing of an intense circularly polarized laser beam in the presence of a non-uniform positive guide magnetic field with slope constant parameter δ in hot magnetized plasma, using Maxwell’s equations and relativistic fluid momentum equation is investigated. An envelope equation governing the spot-size of laser beam for both of left- and right-hand polarizations has been derived, and the effects of the plasma temperature and magnetic field on the electron density distribution of hot plasma with respect to variation of normalized laser spot-size has been studied. Numerical results show that self-focusing is better increased in the presence of an external non-uniform magnetic field. Moreover, in plasma density profile, self-focusing of the laser pulse improves in comparison with no non-uniform magnetic field. Also, with increasing slope of constant parameter of the non-uniform magnetic field, the self-focusing increases, and subsequently, the spot-size of laser pulse propagated through the hot magnetized plasma decreases.     

Comparison of two theories during self-focusing of Gaussian laser beam in thermal conduction-loss predominant plasmas

In the present paper, self-focusing phenomenon occurring as a result of non-linear interaction of intense laser beam with thermal conduction-loss predominant plasmas is studied by following both approaches viz. paraxial theory approach and moment theory approach. Non-linear differential equations for the beam width parameters of laser beam have been set up and solved numerically in both cases to study the variation of beam width parameters with normalized distance of propagation. Effects of laser intensity as well as plasma density on the beam width parameters have also been analyzed. It is observed from the analysis that in case of moment theory approach, strong self-focusing of laser beam is observed as compared to paraxial theory approach.     

Stimulated Raman scattering of gaussian laser beam in relativistic plasma

This paper presents an investigation of Stimulated Raman Scattering of gaussian laser beam in relativistic Plasma. The pump beam interacts with a pre-excited electron plasma wave and thereby generate a back-scattered wave. Due to intense laser beam, electron oscillatory velocity becomes comparable to the velocity of light, which modifies the background plasma density profile in a direction transverse to pump beam axis. The relativistic non-linearity due to increase in mass of the electrons effects the incident laser beam, electron plasma wave and back-scattered beam. We have set up the non-linear differential equations for the beam width parameters of the main beam, electron plasma wave, back-scattered wave and derived SRS back-reflectivity by taking full non-linear part of the dielectric constant of relativistic plasma with the help of moment theory approach. It is observed from the analysis that self-focusing of the pump beam greatly affects the SRS reflectivity, which plays a significant role in laser induced fusion.     

Self-Focusing/Defocusing of Chirped Gaussian Laser Beam in Collisional Plasma with Linear Absorption

This paper presents an investigation on the self-focusing/defocusing of chirped Gaussian laser beam in collisional plasma with linear absorption. We have derived the differential equation for the beam width parameter by using WKB and paraxial approximations and solved it numerically. The effect of chirp and other laser plasma parameters is seen on the behavior of beam width parameter with dimensionless distance of propagation. The results are discussed and presented graphically. Our simulation results show that the amplitude of oscillations decreases with the distance of propagation. Due to collisional frequency, the laser beam shows fast divergence which can be minimized by the introduction of chirp parameter. The chirp decreases the effect of defocusing and increases the ability of self-focusing of laser beam in collisional plasma.     

Propagation of cosh Gaussian laser beam in plasma with density ripple in relativistic – ponderomotive regime

Self-focusing of cosh Gaussian laser beam in plasma with periodic density ripple has been investigated. The pondermotive force on electron and the relativistic oscillation of the electron mass causes periodic self-focusing/defocusing of the cosh Gaussian laser beam. The beam converges in the region of high plasma density due to dominance of self-focusing effect over diffraction effect and diverges in the low density region. Non-linear partial differential equation governing the evolution of complex envelope in slowly varying approximation is solved using paraxial ray approximation. The variation of beam-width parameter is studied with distance of propagation for different values of ripple wave number d and decentred parameter b. In order to get strong self-focusing, wavelength and intensity parameters of cosh Gaussian laser beam are optimized.     

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.     

超强短脉冲激光在不同密度分布等离子体中的自聚焦

讨论高斯型强激光束在具有初始柱对称密度分布的低密度冷等离子体中传播时，等离子体密度分布的不同对激光自聚焦的影响.推导出可以判断更有利于自聚焦发生的评价函数，这样通过比较不同密度分布的评价函数值就可以判断哪种密度分布更有利于自聚焦的发生.为了说明这种方法的有效性，对评价函数进行分析得出：在相同的激光场中等离子体柱的轴心密度给定时(以激光的光轴为轴)，离轴越远的地方密度越大及密度变化越陡，自聚焦越容易发生；相对论效应与有质动力共同作用比相对论的单独作用，自聚焦更容易发生.数值模拟证实了评价函数能准确的预测在不 关键词： 自聚焦 相对论效应 有质动力 评价函数     

Effects of relativistic and ponderomotive nonlinearities on the interaction of high-power laser beam with an inhomogeneous warm plasma

The influence of relativistic-ponderomotive nonlinearities and the plasma inhomogeneity on the nonlinear interaction between a high-power laser beam and a warm underdense plasma are studied. It is clear that the relativistic ponderomotive force and the electron temperature modify the electron density distribution and consequently change the dielectric permittivity of the plasma. Therefore, by presenting the modified electron density and the nonlinear dielectric permittivity of the warm plasma, the electromagnetic wave equation for the propagation of intense laser beam through the plasma is derived. This nonlinear equation is numerically solved and the distributions of electromagnetic fields in the plasma, the variations of electron density, and plasma refractive index are investigated for two different background electron density profiles. The results show that the amplitude of the electric field and electron density oscillations gradually increase and decrease, during propagation in the inhomogeneous warm plasma with linear and exponential density profiles, respectively, and the distribution of electron density becomes extremely sharp in the presence of intense laser beam. It is also indicated that the electron temperature and initial electron density have an impact on the propagation of the laser beam in the plasma and change the plasma refractive index and the oscillations' amplitude and frequency. The obtained results indicate the importance of a proper choice of laser and plasma parameters on the electromagnetic field distributions, density steepening, and plasma refractive index variations in the interaction of an intense laser beam with an inhomogeneous warm plasma.     

Self-Focusing of Quadruple Gaussian Laser Beam in an Inhomogenous Magnetized Plasma with Ponderomotive Non-Linearity: Effect of Linear Absorption

The propagation of quadruple Gaussian laser beam in a plasma characterized by axial inhomogeneity and nonlinearity due to ponderomotive force in the paraxial ray approximation is investigated. An appropriate expression for the nonlinear dielectric constant has been developed in the presence of external magnetic field, with linear absorption and due to saturation effects for arbitrary large intensity. The effects of different types of plasma axial inhomogeneities on self-focusing of laser beam have been studied with the typical laser and plasma parameters. Self-focusing of quadruple Gaussian laser beam in the presence of externally applied magnetic field and saturating parameter is found significantly improved in the case of extraordinary mode. Our results reveal that initially converging beam shows oscillatory convergence whereas initially diverging beam shows oscillatory divergence. The beam is more focussed at lower intensity in both cases viz. extraordinary and ordinary mode.     

黑腔中高斯型激光束偏折的模拟研究

利用三维激光等离子体相互作用流体程序LAP3D数值模拟研究了高斯光束在均匀等离子体传播过程中的激光束偏折现象,分别考察了激光强度变化和等离子体横向流的流速变化对束偏折的影响。模拟结果表明:当流速接近离子声速时,激光束偏折效应最明显,此时激光偏折程度与激光强度成正比;当流速逐渐小于离子声速时,激光束偏折行为受抑制逐渐减弱;而当流速逐渐大于离子声速时,激光光强包络的变化以衍射效应为主。     

Performance comparison of self-focusing with 1053- and 351-nm laser pulses

Hole boring characteristics of laser beams are studied using two different laser wavelengths in preformed plasmas with overdense regions. We have shown that a whole beam self-focusing is created in plasma with a considerable density scale length using a 1 microm wavelength laser. The whole beam self-focusing of this type could be used for guiding the ultrahigh intense laser pulse to a highly compressed core for studying the feasibility of a fast ignitor. There is a clear difference in the hole-boring characteristics between two laser wavelengths at 1053 and 351 nm, both in the experiment and the simulation. Using the third-harmonic laser, a whole beam self-focusing is never created. The 351-nm laser beam broke up into filaments resulting in plasma jets observed in our interferogram.     

Enhanced Raman Scattering of Elliptical Laser beam in a Collisional Plasma

This paper presents the Enhanced Raman scattering of a elliptical laser beam in a collisional plasma. We have considered the mechanism of non‐uniform heating of carriers along the wave‐front, which is important in collisional plasma. The nonlinearity arising through non‐uniform heating leads to redistribution of carriers, which modifies the background plasma density profile in a direction transverse to pump beam axis. This modification in density effects the incident laser beam, plasma wave and back‐scattered beam. Non‐linear differential equations for the beam width parameters of pump laser beam, plasma wave and back‐scattered beam are set up and solved numerically. Numerical results predict the effect of self‐focusing of waves on the back‐scattered beam (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)