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 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.     

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.     

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.     

Relativistic Self-Focusing of Hermite-cosine-Gaussian Laser Beam in Collisionless Plasma with Exponential Density Transition

This work reveals an exploration of self-focusing of Hermite-cosine-Gaussian laser beam in a collisionless plasma under relativistic nonlinearity. Self-focusing along with self-trapping of Hermite-cosine-Gaussian laser beam are analyzed for different values of laser intensity, plasma density, and decentered parameters. Mathematical analysis displays that these parameters play a major role in achieving the stronger and earlier self-focusing. Further, a comparative study between self-focusing of Hermite-cosine-Gaussian laser beam with and without exponential density ramp profile is introduced. Plasma density transition with exponential profile is found to be more effective in order to have stronger self-focusing. The present analysis may lead to very useful applications in the field of efficient harmonic generation, laser driven fusion etc.     

Non-paraxial theory of self-defocusing/focusing of a laser pulse in a multiple-ionizing gas

The self-focusing of a laser pulse through a tunnel ionizing gas (helium) has been studied in both non-relativistic and relativistic regimes, relaxing the near-axis approximation. In the non-relativistic regime, the laser pulse produces multiple ionization of the gas and faces strong defocusing due to the steep radial density gradient caused by the same. The uneven defocusing of paraxial and marginal rays leads to a beam acquiring a ring shaped intensity distribution. In the relativistic regime, the laser pulse produces fully ionized plasma within a few wave periods, subsequently the relativistic mass effect and the ponderomotive force induced electron cavitation cause periodic self-focusing. PACS 52.38.Hb; 42.65.Jx     

Growth of a laser ripple in a magnetoplasma and its effect on plasma wave excitation

Summary This paper presents an investigation of the growth of a radially symmetrical ripple, superimposed on a Gaussian laser beam in a collisionless magnetoplasma. The effect of the magnetic field and the intensity of the laser on the growth of the ripple is presented in some detail. The effect of the presence of the ripple on the excitation of an electron plasma wave is also investigated. Coupling of a weak plasma wave with the main laser beam is through the modified background density. The combined effect of increased intensity of the laser beam and magnetic field is observed to suppress the growth of the ripple as well as the excitation of the plasma wave. The authors of this paper have agreed to not receive the proofs for correction.     

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.     

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     

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.     

Experimental tests of the new paradigm for laser filamentation in gases

Since their discovery in the mid-1990s, ultrafast laser filaments in gases have been described as products of a dynamic balance between Kerr self-focusing and defocusing by free electric charges that are generated via multiphoton ionization on the beam axis. This established paradigm has been recently challenged by a suggestion that the Kerr effect saturates and even changes sign at high intensity of light and that this sign reversal, not free-charge defocusing, is the dominant mechanism responsible for the extended propagation of laser filaments. We report qualitative tests of the new theory based on electrical and optical measurements of plasma density in femtosecond laser filaments. Our results consistently support the established paradigm.     

Growth and stabilization of a laser ripple on laser beam in a collisionless unmagnetized plasma

Summary In this paper we have studied the growth and stabilization of a radially symmetric ripple superimposed on a laser beam in a collisionless unmagnetized plasma. The saturation of the growth rate is due to pump depletion effect. On acoount of the nonuniform intensity distribution of the main beam, a d.c. component of the ponderomotive force becomes finite and it redistributes the carriers in the plasma in a plane transverse to the beam propagation. We have set up and solved the wave equations for main beam and ripple by using the WKB and paraxial ray approximations. As the ripple grows in the plasma, it draws energy from the background laser field. It is seen that the relative intensity of the laser ripple becomes critical due to the counteracting behaviour of the self-focusing and depletion of the main beam. To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.     

Relativistic nonlinearity and wave-guide propagation of rippled laser beam in plasma

In the present paper we have investigated the self-focusing behaviour of radially symmetrical rippled Gaussian laser beam propagating in a plasma. Considering the nonlinearity to arise from relativistic phenomena and following the approach of Akhmanov et al, which is based on the WKB and paraxial-ray approximation, the self-focusing behaviour has been investigated in some detail. The effect of the position and width of the ripple on the self-focusing of laser beam has been studied for arbitrary large magnitude of nonlinearity. Results indicate that the medium behaves as an oscillatory wave-guide. The self-focusing is found to depend on the position parameter of ripple as well as on the beam width. Values of critical power has been calculated for different values of the position parameter of ripple. Effects of axially and radially inhomogeneous plasma on self-focusing behaviour have been investigated and presented here.     

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.     

Plasma channel formed by ultraviolet laser pulses at 193 nm in air

The propagation of picosecond deep ultraviolet laser pulse at wavelength of 193 nm in air is numerically investigated. Long plasma channel can be formed due to the competition between Kerr self-focusing and ionization induced defocusing. The plasma channel with electron density of above 10^13/cm^3 can be formed over 70 m by 50-ps, 20-mJ laser pulses. The fluctuation of laser intensity and electron density inside ultraviolet （UV） plasma channel is significantly lower UV laser by air is considered in the simulation and it the limit of the length of plasma channel. than that of infrared pulse. The linear absorption of is shown that the linear absorption is important for the limit of the length of plasma channel.     

Self-defocusing/focusing of a relativistic laser pulse in a multiple-ionizing gas

A fast rising flattop high power laser pulse, with Gaussian intensity distribution along its wavefront, causes single and double ionizations of the gas through which it propagates. The foot of the pulse causes single ionization of the gas and creates a sharp radial density profile resulting in strong defocusing of the front part of the pulse. After a little while, single state ionization saturates, creating a flat density profile in the axial region and weakening the divergence of the pulse. As the intensity of the pulse rises further, second state ionization occurs, causing strong defocusing of the beam. Later in time when the second state ionization saturates, the relativistic mass nonlinearity together with the electron cavitation tends to focus the pulse.     

Quadruple Gaussian Laser Beam Profile Dynamics in Collisionless Magnetized Plasma

This paper presents an investigation of self-focusing of a quadruple Gaussian laser beam in collisionless magnetized plasma. The nonlinearity due to ponderomotive force which arises on account of nonuniform intensity distribution of the laser beam is considered. The nonlinear partial differential equation governing the evaluation of complex envelope in the slowly varying envelope approximation is solved using a paraxial formalism. The self-focusing mechanism in magnetized plasma, in the presence of self-compression mechanism will be analyzed in contrast to the case in which it is absent. It can be observed that, in case of ponderomotive nonlinearity, the self-compression mechanism obstructs the pulse self-focusing above a certain intensity value. The effect of an external magnetic field is to generate pulses with smaller spot size and shorter compression length. The lateral separation parameter and the initial intensity of the laser beam play a crucial role on focusing and compression parameters. Also, the three-dimensional analysis of pulse propagation is presented by coupling the self-focusing equation with the self-compression one.     

Quadruple Gaussian Laser Beam Profile Dynamics in Collisionless Magnetized Plasma

This paper presents an investigation of self-focusing of a quadruple Gaussian laser beam in collisionless magnetized plasma. The nonlinearity due to ponderomotive force which arises on account of nonuniform intensity distribution of the laser beam is considered. The nonlinear partial differential equation governing the evaluation of complex envelope in the slowly varying envelope approximation is solved using a paraxial formalism. The self-focusing mechanism in magnetized plasma, in the presence of self-compression mechanism will be analyzed in contrast to the case in which it is absent. It can be observed that, in case of ponderomotive nonlinearity, the self-compression mechanism obstructs the pulse self-focusing above a certain intensity value. The effect of an external magnetic field is to generate pulses with smaller spot size and shorter compression length. The lateral separation parameter and the initial intensity of the laser beam play a crucial role on focusing and compression parameters. Also, the three-dimensional analysis of pulse propagation is presented by coupling the self-focusing equation with the self-compression one.