Self‐focusing of a cosh‐Gaussian laser beam in magnetized plasma under relativistic‐ponderomotive regime

The combined effect of relativistic and ponderomotive nonlinearities on the self‐focusing of an intense cosh‐Gaussian laser beam (CGLB) in magnetized plasma have been investigated. Higher‐order paraxial‐ray approximation has been used to set up the self‐focusing equations, where higher‐order terms in the expansion of the dielectric function and the eikonal are taken into account. The effects of various lasers and plasma parameters viz. laser intensity (a₀), decentred parameter (b), and magnetic field (ω_c) on the self‐focusing of CGLB have been explored. The results are compared with the Gaussian profile of laser beams and relativistic nonlinearity. Self‐focusing can be enhanced by optimizing and selecting the appropriate laser‐plasma parameters. It is observed that the focusing of CGLB is fast in a nonparaxial region in comparison with that of a Gaussian laser beam and in a paraxial region in magnetized plasma. In addition, strong self‐focusing of CGLB is observed at higher values of a₀, b, and ω_c. Numerical results show that CGLB can produce ultrahigh laser irradiance over distances much greater than the Rayleigh length, which can be used for various applications.     

Non‐paraxial theory of self‐focusing/defocusing of Hermite cosh Gaussian laser beam in rippled density plasmas

Present research work focuses on study of self‐focusing and self‐trapping of Hermite cosh Gaussian (HchG) laser beams in rippled density plasma by considering relativistic non‐linearity. The coupled non‐linear differential equations for the beam width parameters (for modes m = 0, 1, and 2) were derived by employing higher‐order correction in comparison to paraxial ray theory by expanding dielectric function and eikonal up to r⁴ terms. It is observed that the inclusion of higher‐order terms significantly influence the off‐axial properties for m ≥ 1 mode indices. Furthermore, the effect of parameters including beam intensity, ripple factor, depth of density modulation, and decentred parameter on self‐focusing and self‐trapping is analysed and discussed both analytically and numerically.     

Ion‐ and positron‐acoustic solitons in magnetized dusty plasma with q‐non‐extensive electron and positron velocity distribution

In this study, the properties of ion‐ and positron‐acoustic solitons are investigated in a magnetized multi‐component plasma system consisting of warm fluid ions, warm fluid positrons, q‐non‐extensive distributed positrons, q‐non‐extensive distributed electrons, and immobile dust particles. To drive the Korteweg–de Vries (KdV) equation, the reductive perturbation method is used. The effects of the ratio of the density of positrons to ions, the temperature of the positrons, and ions to electrons, the non‐extensivity parameters q_e and q_p , and the angle of the propagation of the wave with the magnetic field on the potential of ion‐ and positron‐acoustic solitons are also studied. The present investigation is applicable to solitons in fusion plasmas in the edge of tokamak.     

Second Harmonic Generation of Self‐Focused Cosh‐Gaussian Laser Beam in Thermal Quantum Plasma by Excitation of an Electron Plasma Wave

This paper presents a scheme for second harmonic generation (SHG) of an intense Cosh‐Gaussian (ChG) laser beam in thermal quantum plasmas. Moment theory approach in W.K.B approximation has been adopted in deriving the differential equation governing the propagation characteristics of the laser beam with distance of propagation. The effect of relativistic increase in electron mass on propagation dynamics of laser beam has been incorporated. Due to relativistic nonlinearity in the dielectric properties of the plasma, the laser beam gets self‐focused and produces density gradients in the transverse direction. The generated density gradients excite electron plasma wave (EPW) at pump frequency that interacts with the incident laser beam to produce its second harmonics. Numerical simulations have been carried out to investigate the effects of laser parameters on selffocusing of the laser beam and hence on the conversion efficiency of its second harmonics. Simulation results predict that within a specific range of decentered parameter the ChG laser beams show smaller divergence as they propagate and, thus, lead to enhanced conversion efficiency of second harmonics. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Tunable nonlinear beam shaping by non‐collinear interactions

A method is proposed for nonlinear beam shaping, employing a non‐collinear quasi phase‐matched interaction in a crystal whose nonlinear coefficient is encoded by a computer generated hologram pattern. In this method the same axis is used for both satisfying the phase‐matching requirements and encoding the holographic information, the result is a single shaped beam in the generated frequency. This allows to shape beams in one‐dimension using a very simple method to fabricate patterned nonlinear crystals and to shape beams in two‐dimensions with high conversion efficiency. The one‐dimensional case is experimentally demonstrated by converting a fundamental Gaussian beam into Hermite‐Gaussian beams at the second harmonic in a KTiOPO₄ crystal. The two‐dimensional case is demonstrated by generating Hermite‐Gaussian and Laguerre‐Gaussian beams in a stoichiometric lithium tantalate crystal. The suggested scheme enables broad wavelength tuning by simply tilting the crystal.     

Dust ion‐acoustic solitons with trapped q‐non‐extensive electrons,dissipative processes,and streaming ions

The characteristics of dust ion‐acoustic waves (DIAWs) that are excited because of streaming ions and hot q‐non‐extensive electrons obeying a vortex‐like distribution are investigated. By exploiting a pseudo‐potential technique, we have derived an energy integral equation. The presence of non‐extensive q‐distributed hot trapped electrons and a streaming ion beam has been shown to influence soliton structure quite significantly. The evolution of the soliton‐like perturbations in complex plasmas, taking into account the dissipation processes, are also investigated, obtained by numerically solving the modified Schamel, equation whose widths are dependant on electron trapping efficiency β. Our illustrations indicate that compressive DIAWs develop in this plasma. As the plasmas in reality have a relative flow, such an analysis can be used to understand the DIA solitary structures observed in the mesospheric noctilucent clouds.     

Variable‐size dust grains with generalized (r,q) electrons in a dusty plasma

The effect of the generalized (r, q) distribution on the non‐linear propagation of dust acoustic waves (DAWs) in a dusty plasma consisting of variable‐size dust grains is discussed. A Korteweg–de Vries (KdV) equation is derived using the reductive perturbation technique (RPT). The dust size obeys the power‐law dust size distribution (DSD). The present results reveal that rarefactive and compressive waves can propagate in the proposed plasma model. It is found that the spectral indices r and q influence the main properties of DAWs. Especially, the velocity, amplitude, and width of the DAW change drastically with r compared to changes in q.     

Effects of non‐extensive electrons on the sheath of dusty plasmas with variable dust charge

In this study, a detailed investigation of the problem of sheath is presented using the fluid model in a magnetized three‐component dusty plasma system comprising positive ions, dust grains with variable charge and q‐non‐extensive electrons (i.e., the electrons evolve far away from their Maxwellian thermodynamic equilibrium [q = 1]). The effects of q‐non‐extensivity parameter on the plasma sheath parameters are studied numerically. A significant change is observed in the quantities characterizing the sheath with the presence of the super‐extensive electrons (q < 1) and sub‐extensive electrons (q > 1). In addition, based on the orbital motion limited theory, by taking various forces acting on the dust particle into consideration, the dynamics of the dust located within the sheath, that is, the dust grain charging inside the sheath, is examined under different values of q. It is found that the q‐non‐extensivity has affected significantly the dynamics and the charging process of the dust grains in the sheath.     

Liquid X‐ray scattering with a pink‐spectrum undulator

X‐ray scattering from a liquid using the spectrum from the undulator fundamental is examined as a function of the bandwidth of the spectrum. The synchrotron‐generated X‐ray spectrum from an undulator is `pink', i.e. quasi‐monochromatic but having a saw‐tooth‐shaped spectrum with a bandwidth from 1 to 15%. It is shown that features in S(q) are slightly shifted and dampened compared with strictly monochromatic data. In return, the gain in intensity is 250–500 which makes pink beams very important for time‐resolved experiments. The undulator spectrum is described by a single exponential with a low‐energy tail. The tail shifts features in the scattering function towards high angles and generates a small reduction in amplitude. The theoretical conclusions are compared with experiments. The r‐resolved Fourier transformed signals are discussed next. Passing from q‐ to r‐space requires a sin‐Fourier transform. The Warren convergence factor is introduced in this calculation to suppress oscillatory artifacts from the finite q_M in the data. It is shown that the deformation of r‐resolved signals from the pink spectrum is small compared with that due to the Warren factor. The q‐resolved and the r‐resolved pink signals thus behave very differently.     

Modeling of terahertz radiation emission from a free‐electron laser

In this article, we report the generation of terahertz (THz) radiation using the interaction of a laser‐modulated relativistic electron beam (REB) with a surface plasma wave. Two laser beams propagating through the modulator interact with the REB, leading to velocity modulation of the beam. This results in pre‐bunching of the REB. The pre‐bunched beam travels through the drift space, where the velocity modulation translates into density modulation. The density‐modulated beam, on interacting with the surface plasma pump wave, acquires an oscillatory velocity that couples with the modulated beam density to give rise to a nonlinear current density which acts as an antenna to give THz radiation. By optimizing the parameters of the beam and the wiggler, we obtain power of the order of 10⁻⁴ using the current scheme.     

Effect of non‐extensivity parameter q on the damping rate of dust ion acoustic waves in non‐extensive dusty plasma

Kinetic theory has been applied to study the damping characteristics of dust ion acoustic waves (DIAWs) in a dusty plasma comprising q‐non‐extensive distributed electrons and ions, while the dust particles are considered extensive following the Maxwellian velocity distribution function. It is found that the results of the three‐dimensional velocity distribution function are more accurate compared to the results of the one‐dimensional velocity distribution function. The numerical solution of the dispersion relation is carried out to study the effect of the non‐extensivity parameter q on the dispersion, the damping rate, and the range of the values of the normalized wavenumber ( k λ_D) for which the DIAWs are weakly damped. It is found that the change in the value of the electron non‐extensivity parameter q_e has a minor effect on the dispersion, the damping rate, and the range of the values of the normalized wavenumber ( k λ_D) for which the DIAWs are weakly damped, while on the other hand, ion non‐extensivity parameter q_i has a strong effect on these arguments. The effect of other parameters, such as the ratio of electron to ion number density and ratio of electron to ion temperature, on the damping characteristics of DIAWs is also highlighted.     

The (3+1)‐dimensional dust‐acoustic waves in multi‐components magneto‐plasmas

A three‐dimensional four components magneto‐plasma system consists of super‐thermal κ‐distributed electrons and positrons, Maxwellian ions, and inertial massive negatively charged dust grains is considered to examine the modulational instability (MI) of the dust‐acoustic waves (DAWs), which propagates in such a magneto‐plasma system. The reductive perturbation method, which is valid for small but finite amplitude DAWs, is employed to derive the (3 + 1)‐dimensional non‐linear Schrödinger equation (NLSE). The NLSE leads to the MI of DAWs as well as the formation of dust‐acoustic rogue waves (DARWs) which are formed due to the effects of non‐linearity in the propagation of the DAWs. It is found that the basic features (viz. amplitude and width) of the DAWs and DARWs (which is formed in the unstable region) are significantly modified by the various plasma parameters such as κ‐distributed electrons and positrons, temperatures, and number densities of plasma species, and so on. The application of the results in both space and laboratory magneto‐plasma systems is briefly discussed.     

Rogue waves in multi‐pair plasma medium

The non‐linear propagation of ion acoustic (IA) waves, which is governed by the non‐linear Schrödinger equation, in multi‐pair plasmas (MPPs) containing adiabatic positive and negative ion fluids as well as non‐extensive (q‐distributed) electrons and positrons is theoretically investigated. It is observed that the MPP under consideration supports two types of modes, namely fast and slow IA modes, and the modulationally stable and unstable parametric regimes for the fast and slow IA modes are determined by the sign of the ratio of the dispersive coefficient to the non‐linear one. It is also found that the modulationally unstable regime generates highly energetic IA rogue waves (IARWs), and the amplitude as well as the width of the IARWs decreases with increase in the value of q (for both q > 0 and q < 0 limits). These new striking features of the IARWs are found to be applicable in the space (i.e., D‐region [], and F‐region [H⁺, H^?] of the Earth's ionosphere) and laboratory MPPs (i.e., fullerene [C⁺, C^?]).     

Polycapillary‐optics‐based micro‐XANES and micro‐EXAFS at a third‐generation bending‐magnet beamline

A focusing system based on a polycapillary half‐lens optic has been successfully tested for transmission and fluorescence µ‐X‐ray absorption spectroscopy at a third‐generation bending‐magnet beamline equipped with a non‐fixed‐exit Si(111) monochromator. The vertical positional variations of the X‐ray beam owing to the use of a non‐fixed‐exit monochromator were shown to pose only a limited problem by using the polycapillary optic. The expected height variation for an EXAFS scan around the Fe K‐edge is approximately 200 µm on the lens input side and this was reduced to ～1 µm for the focused beam. Beam sizes (FWHM) of 12–16 µm, transmission efficiencies of 25–45% and intensity gain factors, compared with the non‐focused beam, of about 2000 were obtained in the 7–14 keV energy range for an incoming beam of 0.5 × 2 mm (vertical × horizontal). As a practical application, an As K‐edge µ‐XANES study of cucumber root and hypocotyl was performed to determine the As oxidation state in the different plant parts and to identify a possible metabolic conversion by the plant.     

Ultra‐short and ultra‐intense X‐ray free‐electron laser single pulse in one‐dimensional photonic crystals

The propagation within a one‐dimensional photonic crystal of a single ultra‐short and ultra‐intense pulse delivered by an X‐ray free‐electron laser is analysed with the framework of the time‐dependent coupled‐wave theory in non‐linear media. It is shown that the reflection and the transmission of an ultra‐short pulse present a transient period conditioned by the extinction length and also the thickness of the structure for transmission. For ultra‐intense pulses, non‐linear effects are expected: they could give rise to numerous phenomena, bi‐stability, self‐induced transparency, gap solitons, switching, etc., which have been previously shown in the optical domain.     

The effects of tilt corrected residual aberration on the detection probability of single-photon propagation in a slant path turbulent atmosphere

Based on the assumption of a pulse laser beam with an initial Gaussian temporal shape and a collimated fundamental-model Gaussian beam, the Rytov approximation and Kolmogorov spectrum model for the index-of-refraction fluctuation of atmosphere, the effect of turbulence on the probability density, acquisition transmittance probability, transmittance probability density, acquisition probability of single-photon propagation in atmospheric communication channel with z-tilt and centroid-tilt aberration corrected are studied theoretically. The probability density, acquisition transmittance probability, transmittance probability density and acquisition probability models for single-photon propagation in uplink path and downlink path are derived. Our results shown that the detection probability and the acquisition transmittance probability of the single-photon are obvious increase, when the beams are propagation in the z-tilt corrected communication channel.     

Role of the wall ablation in the operation of a 46.9 nmAr capillary discharge soft x‐ray laser

A capillary discharge pumped soft x‐ray laser operating at 46.9 nm on the 3p–3s transition of the Ne‐like Ar has been realized by pumping the active medium with a relatively slow current pulse (dI/dt ≈ 6 · 10¹¹ A/s). In order to study the role of the ablation in the production of the laser effect, the intensity of the amplified 46.9 nm line has been investigated using the same pumping current pulses in the plastic (polyacetal) and ceramic (Al₂O₃). We showed that the ablation of the capillary walls is unfavorable both for the compression and stability of the plasma and consequently for the soft x‐ray laser production. The amplification and lasing effects are observed only in the ceramic channel. The measurements of the line intensity at 46.9 nm showed the lasing with a gain‐length product of ≈ 9, a laser pulse energy of ≈ 5 μJ, a pulse duration of 1.3 ns and a beam divergence of ≈ 3.5 mrad. In addition, effect of the scaling of the time of lasing with the initial plasma diameter was demonstrated experimentally and compared with a one‐dimensional MHD model.     

Theoretical model for the effect of dust grains on self‐filamentation of a gaussian electromagnetic beam in a fully ionized plasma

A theoretical model for the effect of dust grains on the self‐filamentation of a Gaussian electromagnetic beam propagating in a fully ionized plasma has been developed by employing the energy balance of the plasma constituents, perturbed electron and ion concentrations, and temperature. In this model, neutral atom ionization, re‐integration and accumulation of electrons and ions, photoelectric emission of electrons from the surface of dust grains, as well as elastic and charging collisions have also been considered. The effective dielectric constant in the presence of dust grains has been constructed. The effect of temporal growth of dust grains on various plasma parameters for different values of the dust density has been explored. The variation of the beam width with the normalized channel of propagation has been observed for distinct dust densities and dust charge states. It is observed that the non‐linearity induced by the effective dielectric constant in the presence of dust grains increases the self‐filamentation of the beam, thus enhancing the effective critical power with the dust density. Some of the outcomes of our approach are in line with experimental observations. These outcomes may be useful for explaining space and laboratory plasma experiments as well as for future studies in complex plasmas.     

Theoretical analysis of planar and non‐planar electron ‐ acoustic shock waves in electron‐positron‐ion plasma

The propagation properties of planar and non‐planar electron acoustic shock waves composed of stationary ions, cold electrons, and q‐non‐extensive hot electrons and positrons are studied in unmagnetized electron‐positron‐ion plasma. In this model, the Korteweg‐de Vries Burgers equation is obtained in the planar and non‐planar coordinates. We have investigated the combined action of the dissipation, non‐extensivity, density ratio of hot to cold electrons, concentration of positrons, and temperature difference of cold electrons, hot electrons, and positrons. It was found that the amplitude of shock wave in e‐p‐i plasma increases when the positron concentration and temperature increase. The same effect is observed in the case of kinematic viscosity η. Furthermore, it is noticed that spherical wave moves faster in comparison to the shock waves in cylindrical geometry. This difference arises due to the presence of the geometry term m/2τ. It should be noted that the contribution of the geometry factor comes through the continuity equation. Results of our work may be helpful to illustrate the different properties of shock wave features in different astrophysical and space environments like supernova, polar regions, and in the vicinity of black holes.     

Nonlinear ion‐acoustic cnoidal wave in electron‐positron‐ion plasma with nonextensive electrons

Effects of plasma nonextensivity on the nonlinear cnoidal ion‐acoustic wave in unmagnetized electron‐positron‐ion plasma have been investigated theoretically. Plasma positrons are taken to be Maxwellian, while the nonextensivity distribution function was used to describe the plasma electrons. The known reductive perturbation method was employed to extract the KdV equation from the basic equations of the model. Sagdeev potential, as well as the cnoidal wave solution of the KdV equation, has been discussed in detail. We have shown that the ion‐acoustic periodic (cnoidal) wave is formed only for values of the strength of nonextensivity (q). The q allowable range is shifted by changing the positron concentration (p) and the temperature ratio of electron to positron (σ). For all of the acceptable values of q, the cnoidal ion‐acoustic wave is compressive. Results show that ion‐acoustic wave is strongly influenced by the electron nonextensivity, the positron concentration, and the temperature ratio of electron to positron. In this work, we have investigated the effects of q, p, and σ on the characteristics of the ion‐acoustic periodic (cnoidal) wave, such as the amplitude, wavelength, and frequency.