Ponderomotive Nonlinearity Research Articles

Pulse-compression and self-focusing of Gaussian laser pulses in plasma having relativistic–ponderomotive nonlinearity

AbstractThe mathematical model for the propagation of intense laser pulse in a plasma having Gaussian profile is investigated. The model has been formulated considering that the relativistic–ponderomotive nonlinearity dominates over other nonlinearities in the plasma. Model equation for self-compression and self-focusing properties of the laser pulse has been set up and solved by both semi-analytical and numerical methods. The result indicates that due to the effect of group velocity dispersion, diffraction of the laser pulse and the nonlinearity of medium, the pulse width parameter as well as beam width parameter of pulse gets focused at a different normalized distance, and hence the normalized intensity is also deferred at those points. Numerical simulation shows an oscillatory behavior of intensity during propagation in the plasma either having minimum beam radius (r0) or having minimum pulse duration (t0) depending on the normalized distance.

Propagation characters of multi-Gaussian beam with large eccentric displacement in collisionless plasma: Higher order paraxial theory

The multiple coherent identical Gaussian beams with symmetry distribution are abbreviated as multi-Gaussian beam, of which the propagation characters in collisionless plasma are studied with the WKB method and higher order paraxial theory. The initial beam profile presents the flat top like or hollow like distribution when the eccentric displacement is large enough. Based on the derived nonlinear propagation equations, the initial condition analyses are performed, and the impact of eccentric displacement on the free propagation effect and ponderomotive nonlinearity is thoroughly discussed. The propagation characters of dimensionless beam width parameter, spot intensity, and spatial distribution of plasma electron density are presented. Results show that the initial spot intensity is expanding outwards along the propagation and the ring structure of electron evacuation in plasmas is generated.

Nonlinear evolution of 3D whistler waves in space plasmas

The present model is proposed to study the nonlinear effects related to quasi-transverse 3D whistler waves in three different regions of space plasmas which are Earth's radiation belt, magnetopause, and solar wind plasma at 1 A.U. We have analysed the effect of considering the third dimension in the dynamics of whistler waves on Localization of whistler waves and associated magnetic field power spectra. Three dimensionally propagating oblique whistler waves get localized due to background density perturbation. This background density modulation is supposed to be originating due to the propagation of low frequency kinetic Alfven waves in the background. The ponderomotive nonlinearity originating due to high amplitude whistler waves has been taken into account to develop the model equations. Next, these coupled model equations have been solved numerically using the pseudo-spectral method. Simulation results are investigated to study the process of field localization and magnetic field power spectrum. The resulting magnetic field power spectrum is discussed in detail in view of their observation in all the three above mentioned regions of space plasmas.

Absorption of the S-polarized short laser pulse in underdense plasma by considering the electrons ohmic heating and the laser pulse ponderomotive force effects

With the advent of ultrashort high intensity laser pulses, laser absorption during laser-plasma interactions has received significant attention during the past two decades since it is related to a variety of applications of high intensity lasers, including the hot electron production for fast ignition of fusion targets, bright X-ray and gamma-ray sources, ion acceleration, compact neutron sources, and generally the creation of high energy density matters. Although some absorption mechanisms appear for short laser pulses with nanosecond duration time, they usually appear for some nonlinear phenomena as electron ohmic heating and laser pulse ponderomotive force are not considered. In this paper, the absorption of the S-polarized laser pulse through an interaction with an underdense plasma in attendance of electron ohmic heating and ponderomotive nonlinearities is analyzed. It is shown that, due to the effect of the ponderomotive force in both isothermal and non-isothermal plasmas, the increasing laser radiation angle leads to the increasing electric field wavelength. Also, since the ponderomotive force modifies the electron density and temperature distribution, it is shown that the decreasing radiation angle leads to the steepening of the electron density profile and the narrowing of electron bunching. Furthermore, by increasing the radiation angle, the absorption coefficient is decreased strongly. It is found that due to the heat of the plasma at the expanse of the wave energy in the case of a non-thermal plasma, the absorption coefficient is increased intensively in comparison to a collisional plasma.

Brillouin backward scattering in the nonlinear interaction of a short-pulse laser with an underdense transversely magnetized plasma with nonextensive distribution

Nonlinear Brillouin backward scattering of a linearly polarized short laser pulse propagating through a homogenous nonextensive distributed plasma in the presence of a uniform magnetic field perpendicular to both the direction of propagation and electric vector of the radiation field is investigated theoretically when ponderomotive relativistic and nonlinearity effects up to third order are taken into account. The governing equations for nonlinear wave in the context of nonextensive statistics are given, and the nonextensive coupled equations describing the nonlinear Brillouin backward scattering instability are solved by the Fourier transformation method, and the growth rate of the nonlinear Brillouin backward scattering instability is obtained. The results in the case q→1 are consistent with those in the framework of the Maxwellian distribution. It is found that the instability growth rate increases on increasing plasma density, radiation field amplitude, and nonextensive parameter, while the instability growth rate shows a decrease due to the presence of external magnetic field.

Effect of pump depletion and cross-focusing on twisted terahertz radiation generation

In this paper, the pump depletion and cross-focusing effects on the generation of twisted terahertz radiation are investigated. Based on the beating of two Laguerre-Gaussian lasers in a radial plasma channel, a twisted terahertz radiation can be produced. In the presence of pump depletion, the lasers power is consumed. So, the ponderomotive force nonlinearity decreases and the output terahertz field approaches to a saturation value. Under competition between the diffraction and nonlinearity effects, the amplitude of laser beam width oscillation grows. When the incident laser beams have non-similar topological charge numbers, the normalized generated terahertz amplitude is low and the pump depletion effect on the laser beam width evolution is ignorable.

Growth of spike in relativistic Gaussian laser beam in a plasma and its effect on third-harmonic generation

AbstractA paraxial ray formalism is developed to study the evolution of an on axis intensity spike on a Gaussian laser beam in a plasma dominated by relativistic and ponderomotive non-linearities. Ion motion is taken to be frozen. A single beam width parameter characterizes the evolution of the spike. The spike introduces two competing influences: diffraction divergence and self-convergence. The former grows with the reduction in spot size of the spike, while the latter depends on the gradient in non-linear permittivity. Parameter δ = (ωpr00/c) a00/(3.5 r00/r01) characterizes the relative importance of the two, where r01 and r00 are the spike and main beam radii, ωp is the plasma frequency, and a00 is the normalized laser amplitude. For δ > 1, the intensity ripple causes faster self-focusing of the beam; higher the ripple amplitude stronger the focusing. In the opposite limit, diffraction divergence increases more rapidly, slowing down the self-focusing of the beam. As the beam intensity rises due to self-focusing, it causes stronger generation of the third harmonic.

Effect of the transverse magnetic field on spatiotemporal dynamics of quadruple Gaussian laser beam in plasma in weakly relativistic and ponderomotive regime

The spatiotemporal dynamics of a quadruple Gaussian laser beam in plasma is studied in the presence of an external magnetic field by taking into account the relativistic and ponderomotive nonlinearities. Using the paraxial approximation approach, two coupled equations for longitudinal (in time) and transverse (in space) beam width parameters are derived. Their evolution determines the pulse dynamics in time and space. The effects of the initial laser parameters, such as the lateral separation and laser intensity on self-focusing and self-compression mechanisms, are discussed. The results illustrate that the laser beam is focussed and compressed in an enhanced manner in the presence of an external magnetic field. The three dimensional spatiotemporal profile of the normalized intensity of the pulse is studied at different positions where the beam is either focussed or compressed. A three dimensional portrait of the normalized intensity as a function of distance and time is also shown.

Effect of self-focused cosh Gaussian laser beam on the excitation of electron plasma wave and particle acceleration

AbstractThis work presents an investigation of the self-focusing of a high-power laser beam having cosh Gaussian intensity profile in a collissionless plasma under weak relativistic-ponderomotove (RP) and only relativistic regimes and its effect on the excitation of electron plasma wave (EPW), and particle acceleration process. Nonlinear differential equations have been set up for the beam width and intensity of cosh Gaussian laser beam (CGLB) and EPW using the Wentzel-Kramers-Brillouin and paraxial-ray approximations as well as fluid equations. The numerical results are presented for different values of decentered parameter ‘b’ and intensity parameter ‘a’ of CGLB. Strong self-focusing is observed in RP regime as compared with only relativistic nonlinearity. Numerical analysis shows that these parameters play crucial role on the self-focusing of the CGLB and the excitation of EPW. It is also found that the intensity/amplitude of EPW increases withbanda. Further, nonlinear coupling between the CGLB and EPW leads to the acceleration of electrons. The intensity of EPW and energy gain by electrons is significantly affected by including the ponderomotive nonlinearity. The energy of the accelerated electrons is increased by increasing the value of ‘b’. The results are presented for typical laser and plasma parameters.

Role of nonlinear localized structures and turbulence in magnetized plasma

In the present study, we have analyzed the field localization of kinetic Alfven wave (KAW) due to the presence of background density perturbation, which are assumed to be originated by the three dimensionally propagating low frequency KAW. These localized structures play an important role for energy transportation at smaller scales in the dispersion range of magnetic power spectrum. For the present model, governing dynamic equations of high frequency pump KAW and low frequency KAW has been derived by considering ponderomotive nonlinearity. Further, these coupled equations have been numerically solved to analyze the resulting localized structures of pump KAW and magnetic power spectrum in the magnetopause regime. Numerically calculated spectrum exhibits inertial range having spectral index of \(-3/2\) followed by steeper scaling; this steepening in the turbulent spectrum is a signature of energy transportation from larger to smaller scales. In this way, the proposed mechanism, which is based on nonlinear wave-wave interaction, may be useful for understanding the particle acceleration and turbulence in magnetopause.

Spatiotemporal dynamics of Gaussian laser pulse in a multi ions plasma

Spatiotemporal evolutions of Gaussian laser pulse propagating through a plasma with multiple charged ions are studied, taking into account the ponderomotive nonlinearity. Coupled differential equations for beam width and pulse length parameters are established and numerically solved using paraxial ray approximation. In one-dimensional geometry, effects of laser and plasma parameters such as laser intensity, plasma density, and temperature on the longitudinal pulse compression and the laser intensity distribution are analyzed for plasmas with singly and doubly charged ions. The results demonstrate that self-compression occurs in a laser intensity range with a turning point intensity in which the self-compression process has its strongest extent. The results also show that the multiply ionized ions have different effect on the pulse compression above and below turning point intensity. Finally, three-dimensional geometry is used to analyze the simultaneous evolution of both self-focusing and self-compression of Gaussian laser pulse in such plasmas.

Propagation of two intense cosh-Gaussian laser beams in plasma in the relativistic-ponderomotive regime

This work presents an investigation of the propagation of two intense cosh-Gaussian laser beams (CGLBs) in collisionless plasma taking into account the combined effects of relativistic and ponderomotive nonlinearities. Due to mutual interaction of two CGLBs, the self-focusing of one beam is affected by the presence of another beam in plasma, and cross-focusing takes place. A paraxial-like approach has been used to investigate the cross-focusing of CGLBs in plasma. An appropriate expression for the nonlinear dielectric constant of plasma has been evaluated in the presence of relativistic-ponderomotive force and used to study the propagation of CGLBs in plasma. The effect of various well-established laser and plasma parameters on the cross-focusing of two beams in plasma has been explored and the results are compared with only relativistic nonlinearity and the Gaussian profile of laser beams. Numerical results show that the decentered parameter (b) plays a crucial role in the cross-focusing of the CGLBs. It is observed that CGLBs focused earlier than Gaussian beams. This study is useful in beat wave excitation of electron plasma wave and collective laser particle accelerators.

Combined effect of relativistic and ponderomotive nonlinearity on self-focusing of Gaussian laser beam in a cold quantum plasma

AbstractIn the present paper, we have investigated self-focusing of Gaussian laser beam in relativistic ponderomotive (RP) cold quantum plasma. When de Broglie wavelength of charged particles is greater than or equal to the inter particle distance or equivalently the temperature is less than or equal to the Fermi temperature, quantum nature of the plasma constituents cannot be ignored. In this context, we have reported self-focusing on account of nonlinear dielectric contribution of RP plasma by taking into consideration the impact of quantum effects. We have setup the nonlinear differential equation for the beam-width parameter by paraxial ray and Wentzel Kramers Brillouin approximation and solved it numerically by the Runge Kutta Fourth order method. Our results show that additional self-focusing is achieved in case of RP cold quantum plasma than relativistic cold quantum plasma and classical relativistic case. The pinching effect offered by quantum plasma and the combined effect of relativistic and ponderomotive nonlinearity greatly enhances laser propagation up to 20 Rayleigh lengths.

Nonlinear interaction of kinetic Alfvén waves and ion acoustic waves in coronal loops

Over the years, coronal heating has been the most fascinating question among the scientific community. In the present article, a heating mechanism has been proposed based on the wave–wave interaction. Under this wave–wave interaction, the high frequency kinetic Alfvén wave interacts with the low frequency ion acoustic wave. These waves are three dimensionally propagating and nonlinearly coupled through ponderomotive nonlinearity. A numerical code based on pseudo-spectral technique has been developed for solving these normalized dynamical equations. Localization of kinetic Alfvén wave field has been examined, and magnetic power spectrum has also been analyzed which shows the cascading of energy to higher wavenumbers, and this cascading has been found to have Kolmogorov scaling, i.e., k−5/3. A breakpoint appears after Kolmogorov scaling and next to this spectral break; a steeper scaling has been obtained. The presented nonlinear interaction for coronal loops plasmas is suggested to generate turbulent spectrum having Kolmogorov scaling in the inertial range and steepened scaling in the dissipation range. Since Kolmogorov turbulence is considered as the main source for coronal heating; therefore, the suggested mechanism will be a useful tool to understand the mystery of coronal loop heating through Kolmogorov turbulence and dissipation.

Laser-pulse compression in a collisional plasma under weak-relativistic ponderomotive nonlinearity

We present theory and numerical analysis which demonstrate laser-pulse compression in a collisional plasma under the weak-relativistic ponderomotive nonlinearity. Plasma equilibrium density is modified due to the ohmic heating of electrons, the collisions, and the weak relativistic-ponderomotive force during the interaction of a laser pulse with plasmas. First, within one-dimensional analysis, the longitudinal self-compression mechanism is discussed. Three-dimensional analysis (spatiotemporal) of laser pulse propagation is also investigated by coupling the self-compression with the self-focusing. In the regime in which the laser becomes self-focused due to the weak relativistic-ponderomotive nonlinearity, we provide results for enhanced pulse compression. The results show that the matched interplay between self-focusing and self-compression can improve significantly the temporal profile of the compressed pulse. Enhanced pulse compression can be achieved by optimizing and selecting the parameters such as collision frequency, ion-temperature, and laser intensity.

Nonlinear Evolution of a 3D Inertial Alfvén Wave and Its Implication in Particle Acceleration

A simulation based on a pseudo-spectral method has been performed in order to study particle acceleration. A model for the acceleration of charged particles by field localization is developed for the low-\(\upbeta\) plasma. For this purpose, a fractional diffusion approach has been employed. The nonlinear interaction between a 3D inertial Alfven wave and a slow magnetosonic wave has been examined, and the dynamical equations of these two waves in the presence of ponderomotive nonlinearity have been solved numerically. The nonlinear evolution of the inertial Alfven wave in the presence of slow magnetosonic wave undergoes a filamentation instability and results in field intensity localization. The results obtained show the localization and power spectrum of inertial Alfven wave due to nonlinear coupling. The scaling obtained after the first break point of the magnetic power spectrum has been used to calculate the formation of the thermal tail of energetic particles in the solar corona.

Electron plasma wave excitation by beating of two q-Gaussian laser beams in collisionless plasma

AbstractThis paper presents a scheme for excitation of an electron-plasma wave (EPW) by beating two q-Gaussian laser beams in an underdense plasma where ponderomotive nonlinearity is operative. Starting from nonlinear Schrödinger-type wave equation in Wentzel–Kramers–Brillouin (WKB) approximation, the coupled differential equations governing the evolution of spot size of laser beams with distance of propagation have been derived. The ponderomotive nonlinearity depends not only on the intensity of first laser beam, but also on that of second laser beam. Therefore, the dynamics of one laser beam affects that of other and hence, cross-focusing of the two laser beams takes place. Due to nonuniform intensity distribution along the wavefronts of the laser beams, the background electron concentration is modified. The amplitude of EPW, which depends on the background electron concentration, is thus nonlinearly coupled with the laser beams. The effects of ponderomotive nonlinearity and cross-focusing of the laser beams on excitation of EPW have been incorporated. Numerical simulations have been carried out to investigate the effect of laser and plasma parameters on cross-focusing of the two laser beams and further its effect on EPW excitation.

Beat wave excitation of electron plasma wave by cross-focusing of intense cosh-Gaussian laser beams in collisionless plasma with upward density ramp

This paper presents theoretical investigation of the effect of cross-focusing of two coaxial cosh-Gaussian (ChG) laser beams on beat wave excitation of electron plasma wave (EPW) in an under dense plasma with upward density ramp. The plasma wave is generated on account of beating of two coaxial laser beams of frequencies ω1 and ω2. The mechanism for laser induced nonlinearity is assumed to be a ponderomotive force. Following moment theory approach in Wentzel–Kramers–Brillouin (W.K.B) approximation nonlinearly coupled differential equations governing the evolution of spot size of the laser beams with distance of propagation have been derived. The ponderomotive nonlinearity depends not only on the intensity of first laser beam but also on that of second beam. Therefore, the behavior of first laser beam affects that of second laser beam and hence cross focusing of two laser beams takes place. By changing the decentred parameter, the peak intensity of the laser beam can be shifted in the transverse direction and a noticeable change is observed on the cross-focusing of the two laser beams as well as on the power of generated plasma wave. The results are presented in the form of graphs for typical set of laser-plasma parameters.

Nonlinear Interaction of High Power Elliptical Laser Beam with Cold Collisionless Plasma

In the present paper, nonlinear interaction of high power elliptical laser beam with cold collisionless plasma is investigated by taking in to account ponderomotive nonlinearity. 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 laser intensity, plasma density and plasma temperature on the beam width parameters are also analyzed.

Second harmonic generation by self-focusing of intense hollow Gaussian laser beam in collisionless plasma

The effect of self focused hollow Gaussian laser beam (HGLB) (carrying null intensity in center) on the excitation of electron plasma wave (EPW) and second harmonic generation (SHG) has been investigated in collisionless plasma, where relativistic-ponderomotive and only relativistic nonlinearities are operative. The relativistic change of electron mass and the modification of the background electron density due to ponderomotive nonlinearity lead to self-focusing of HGLB in plasma. Paraxial ray theory has been used to derive coupled equations for the self focusing of HGLB in plasma, generation of EPW, and second harmonic. These coupled equations are solved analytically and numerically to study the laser intensity in the plasma, electric field associated with the excited EPW, and the power of SHG. Second harmonic emission is generated due to nonlinear coupling between incident HGLB and EPW satisfying the proper phase matching conditions. The results show that the effect of including the ponderomotive nonlinearity is significant on the generation of EPW and second harmonic. The electric field associated with EPW and the power of SHG are found to be highly sensitive to the order of the hollow Gaussian beam.