Ponderomotive Nonlinearity Research Articles

Propagation and cross-focusing of hollow Gaussian laser beams in plasma

This paper presents the cross focusing of two high power Hollow Gaussian laser beams (HGLB) by considering ponderomotive nonlinearity in a collisionless plasma. On account of the nonlinearity present in the plasma the two laser beams affect the dynamics of each other and cross-focusing takes place. The expressions for the laser beam intensities by using the eikonal method have been derived and the beam width parameter is calculated in the case when only ponderomotive nonlinearity is operative. The numerical appreciation of the cross focusing has been presented graphically by plotting beam-width parameter vs. dimensionless distance of propagation. Theself focusing of one laser beam is affected due to the optical inhomogeneities introduced by another copropagatingHGLBin the plasma. It is observed thatthe presence of one HGLBalso affects the self focusing of different order's (n) of the other HGLB.

THz generation by self-focusing of hollow Gaussian laser beam in magnetised plasma

A scheme of terahertz (THz) generation is proposed by the self-focusing of a high-power laser beam having hollow Gaussian intensity profile in a collissionless magnetized plasma, where ponderomotive nonlinearity is operative. THz waves are resonantly excited at the difference frequency of laser and electron plasma wave (EPW) satisfying the proper phase matching conditions. In this paper first we have investigated the filamentation of the circularly polarized hollow Gaussian beam (HGB) propagating parallel to the direction of a static background magnetic field within the paraxial approximation, subsequently this filamented HG laser beam interplay with the electron plasma wave to generate a nonlinear current in the transverse direction, thereby producing THz radiations. The intensity of the emitted radiations are found to be highly sensitive to the order of the HGB. For the current scheme the power level of THz wave comes out to be gigawatts.

Nonlinear interaction of 3‐D kinetic Alfvén wave and fast magnetosonic wave

AbstractThe nonlinear interaction of 3‐D kinetic Alfvén wave and fast magnetosonic wave for the intermediate‐β plasma in magnetopause has been considered in the present study. A set of dimensionless equations has been derived taking ponderomotive nonlinearity into account due to kinetic Alfvén wave in the fast magnetosonic wave dynamics. In order to analyze the nonlinear coupling of fast magnetosonic wave and kinetic Alfvén wave and also to study its effect on the turbulent power spectrum, we have numerically solved these coupled equations using pseudo‐spectral method of simulation. The results show the appearance of localized structures of kinetic Alfvén wave, which may be accountable for the heating and acceleration of plasma. The obtained results are consistent with the recent observations by Time History of Events and Macroscale Interactions during Substorms spacecraft in magnetopause.

Nonlinear coupling of left and right handed circularly polarized dispersive Alfvén wave

The nonlinear phenomena are of prominent interests in understanding the particle acceleration and transportation in the interplanetary space. The ponderomotive nonlinearity causing the filamentation of the parallel propagating circularly polarized dispersive Alfvén wave having a finite frequency may be one of the mechanisms that contribute to the heating of the plasmas. The contribution will be different of the left (L) handed mode, the right (R) handed mode, and the mix mode. The contribution also depends upon the finite frequency of the circularly polarized waves. In the present paper, we have investigated the effect of the nonlinear coupling of the L and R circularly polarized dispersive Alfvén wave on the localized structures formation and the respective power spectra. The dynamical equations are derived in the presence of the ponderomotive nonlinearity of the L and R pumps and then studied semi-analytically as well as numerically. The ponderomotive nonlinearity accounts for the nonlinear coupling between both the modes. In the presence of the adiabatic response of the density fluctuations, the nonlinear dynamical equations satisfy the modified nonlinear Schrödinger equation. The equations thus obtained are solved in solar wind regime to study the coupling effect on localization and the power spectra. The effect of coupling is also studied on Faraday rotation and ellipticity of the wave caused due to the difference in the localization of the left and the right modes with the distance of propagation.

Strong self-focusing of a cosh-Gaussian laser beam in collisionless magneto-plasma under plasma density ramp

The effect of plasma density ramp on self-focusing of cosh-Gaussian laser beam considering ponderomotive nonlinearity is analyzed using WKB and paraxial approximation. It is noticed that cosh-Gaussian laser beam focused earlier than Gaussian beam. The focusing and de-focusing nature of the cosh-Gaussian laser beam with decentered parameter, intensity parameter, magnetic field, and relative density parameter has been studied and strong self-focusing is reported. It is investigated that decentered parameter “b” plays a significant role for the self-focusing of the laser beam as for b=2.12, strong self-focusing is seen. Further, it is observed that extraordinary mode is more prominent toward self-focusing rather than ordinary mode of propagation. For b=2.12, with the increase in the value of magnetic field self-focusing effect, in case of extraordinary mode, becomes very strong under plasma density ramp. Present study may be very useful in the applications like the generation of inertial fusion energy driven by lasers, laser driven accelerators, and x-ray lasers. Moreover, plasma density ramp plays a vital role to enhance the self-focusing effect.

Growth of ring ripple in a collisionless plasma in relativistic-ponderomotive regime and its effect on stimulated Raman backscattering process

A theoretical and numerical study has been made of the propagation of a ring rippled laser beam in collisionless plasma with dominant relativistic ponderomotive nonlinearity and its effect on the excitation of electron plasma wave and stimulated Raman backscattering process. The growth of ring ripple, riding on an intense Gaussian laser beam in plasma has also been studied. A paraxial-ray and WKB approximation has been invoked to understand the nature of propagation of the ring rippled Gaussian laser beam in plasma, electron plasma wave and back reflectivity under the influence of both nonlinearities. The growth rate and focusing of a ring rippled beam is found to be considerably affected by the power of the main beam and the phase angle between the electric vectors of the main beam and the ring ripple. It has also been observed that the focusing is released by the coupling of relativistic and ponderomotive nonlinearities, which significantly affected the dynamics of the excitation of electron plasma wave and back reflectivity of stimulated Raman scattering (SRS). Due to the strong coupling between ring rippled laser beam and the excited electron plasma wave, back reflectivity of SRS is enhanced. It has been observed from the computational results that the effect of the increased intensity leads to suppression of SRS back reflectivity. The results have been presented for established laser and plasma parameters.

Ponderomotive self-focusing of Gaussian laser beam in warm collisional plasma

The propagation characteristics of a Gaussian laser beam through warm collisional plasma are investigated by considering the ponderomotive force nonlinearity and the complex eikonal function. By introducing the dielectric permittivity of warm unmagnetized plasma and using the WKB and paraxial ray approximations, the coupled differential equations defining the variations of laser beam parameters are obtained and solved numerically. Effects of laser and plasma parameters such as the collision frequency, the initial laser intensity and its spot size on the beam width parameter and the axis laser intensity distribution are analyzed. It is shown that, self-focusing of the laser beam takes place faster by increasing the collision frequency and initial laser spot size and then after some distance propagation the laser beam abruptly loses its initial diameter and vastly diverges. Furthermore, the modified electron density distribution is obtained and the collision frequency effect on this distribution is studied.

SPM and XPM nonlinear effects in plasmonic directional couplers, considering the ponderomotive metal nonlinearity.

In this paper, a two-dimensional nonlinear plasmonic directional coupler (2D-NPDC), with 90° waveguide bends, has been numerically analyzed by the finite-difference time-domain (FDTD) method, considering the nonlinear response of metal due to the ponderomotive force. It has been shown that the required switching power of the 2D-NPDC is 0.05% of that when only the dielectric is nonlinear and the nonlinearity of metal is neglected. Also, the cross-phase modulation (XPM) nonlinear effect has been investigated, which the power for switching is decreased significantly compared to the one with the self-phase modulation (SPM) effect.

Effects of relativistic and ponderomotive nonlinearties on the beat wave generation of electron plasma wave and particle acceleration in non-paraxial region

In this communication, the combined effect of relativistic and ponderomotive nonlinearities on the generation of electron plasma wave by cross focusing of two intense laser beams at difference frequency (Δω ≈ ω1 − ω2 ≈ ωp) and acceleration of electrons in laser produced homogeneous plasma is analysed in the non-paraxial region. On account of these nonlinearities, two laser beams affect the dynamics of each other, and cross focusing takes place. It is observed that the focusing of laser beams becomes fast in the non-paraxial region by expanding the eikonal and other relevant quantities up to the fourth power of the radial distance (r). Modified coupled equations for the beam width of laser beams, electric field amplitude of the excited electron plasma wave and energy gain at beat wave frequency are derived, when relativistic and ponderomotive nonlinearities are operative. These coupled equations are solved analytically and numerically to study the cross focusing of two intense laser beams in plasma and its effect on the variation of the amplitude of the electron plasma wave and energy gain. It is observed from the results that both nonlinearities significantly affect the amplitude of plasma wave excitation and particle acceleration in the non-paraxial region in comparison to the paraxial region.

Temperature Effect on Self-Focusing and Defocusing of Gaussian Laser Beam Propagation Through Plasma in Weakly Relativistic Regime

The propagation characters of an intense Gaussian laser beam in underdense plasma are investigated taking into account the combined effects of relativistic and ponderomotive nonlinearities. The nonlinear second-order differential equation of the dimensionless beamwidth parameter is obtained and numerically solved. The effect of initial electron temperature on self-focusing and defocusing of Gaussian laser beam propagation in plasma are studied. Moreover, the behavior and variation of modified electron density and laser beam intensity as a function of plasma length in both self-focusing and defocusing regimes are discussed.

Localization of circularly polarized dispersive Alfvén wave and effect on solar wind turbulence

AbstractSolar wind turbulence at large inertial scales is well known for decades and believed to consist of Alfvén cascade. At scales of the order of proton inertial length, Alfvén cascade excites kinetic Alfvén wave, fast wave, or whistler wave that carries wave energy to smaller scales. Despite supporting the kinetic Alfvén wave cascade to elucidate the steeper spectra at the kinetic scales, we here present another model, the localization of longitudinally propagating dispersive Alfvén wave (DAW) with finite frequency correction to illustrate the same. Inclusion of this finite frequency in Alfvén wave makes them dispersive. In this approach, the dynamical equation of the wave in the presence of ponderomotive nonlinearity of the pump is obtained and then solved numerically to study the evolution of the turbulence. The ponderomotive force accounts for the coupling between the DAW and ion acoustic wave. Taking the adiabatic case, we have first studied the localization of DAW. To have the physical insight of the dynamical system, the equation is also studied semi‐analytically.

Increasing the upper-limit intensity and temperature range for thermal self-focusing of a laser beam by using plasma density ramp-up

This work is devoted to improving relativistic and ponderomotive thermal self-focusing of the intense laser beam in an underdense plasma. It is shown that the ponderomotive nonlinearity induces a saturation mechanism for thermal self-focusing. Therefore, in addition to the well-known lower-limit critical intensity, there is an upper-limit intensity for thermal self-focusing above which the laser beam starts to experience ponderomotive defocusing. It is indicated that the upper-limit intensity value is dependent on plasma and laser parameters such as the plasma electron temperature, plasma density, and laser spot size. Furthermore, the effect of the upward plasma density ramp profile on the thermal self-focusing is studied. Results show that by using the plasma density ramp-up, the upper-limit intensity increases and the self-focusing temperature range expands.

Role of 3d-dispersive Alfven waves in coronal heating

Coronal heating is one of the unresolved puzzles in solar physics from decades. In the present paper we have investigated the dynamics of vortices to apprehend coronal heating problem. A three dimensional (3d) model has been developed to study propagation of dispersive Alfven waves (DAWs) in presence of ion acoustic waves which results in excitation of DAW and evolution of vortices. Taking ponderomotive nonlinearity into account, development of these vortices has been studied. There are observations of such vortices in the chromosphere, transition region and also in the lower solar corona. These structures may play an important role in transferring energy from lower solar atmosphere to corona and result in coronal heating. Nonlinear interaction of these waves is studied in view of recent simulation work and observations of giant magnetic tornadoes in solar corona and lower atmosphere of sun by solar dynamical observatory (SDO).

Formation of the localized structures and the generation of turbulence by 3-dimensional kinetic Alfvén waves in solar wind plasmas

In the present paper, we have investigated nonlinear interaction of three dimensional kinetic Alfven wave with perpendicularly propagating magnetosonic wave for intermediate β-plasma (m e /m i ≪β≪1). We have developed the set of dimensionless equations in the presence of ponderomotive nonlinearity due to three dimensional kinetic Alfven wave in the dynamics of perpendicularly propagating magnetosonic wave. Numerical simulation has been carried out to study the effect of nonlinear coupling of three dimensional kinetic Alfven wave with perpendicularly propagating magnetosonic wave on power spectrum for the plasma parameters applicable to solar wind around 1 AU. Relevance of the obtained results is pointed out with observation received by Cluster spacecraft for the solar wind around 1 AU.

Exact surface plasmon dispersion relation with ponderomotive nonlinearity in a metal/dielectric structure

The nonlinear effects in a metal due to the ponderomotive potential, which is induced by a steep spatial gradient in the electric field intensity, on the surface plasmon dispersion relation at a planar metal/dielectric interface are studied exactly. Previous studies invoked an approximation that amounts to keeping only the lowest order Kerr-like term in the metal dielectric constant. Comparing the exact result with the Kerr approximation reveals that the Kerr approximation often overestimates a cutoff frequency for the existence of surface waves and gives erroneous results in the range of frequencies below the overestimated cutoff and the real cutoff. Our result thus sheds light on the applicability of the Kerr approximation. Properly expanding the exact results recovers the standard linear results and the results starting with a Kerr-like approximation.

Self-focusing and stimulated Brillouin back-scattering of a long intense laser pulse in a finite temperature relativistic plasma

The nonlinear dynamics of electromagnetic waves propagating through a plasma considering the effects of relativistic mass and ponderomotive nonlinearities is investigated. The modified electron density distribution, the dispersion relation, and the spatial profiles of electromagnetic wave amplitude in the plasma are obtained. It is shown that the cut-off frequency decreases, and there is an intensity range in which the ponderomotive self-focusing takes place. In the upper limit of this range, the laser beam is defocused due to the relativistic ponderomotive force. In addition, the stability of electromagnetic waves to stimulated Brillouin scattering is studied, and the backscattered wave resulting from decay of high power electromagnetic beam is resolved in relativistic regime. The study of effects of electron density and temperature on the growth rate of backscattered wave has been shown that by increasing these effects, the growth rate of instability increases.

Nonlinear Interaction of 3D Kinetic Alfvén Waves and Ion Acoustic Waves in Solar Wind Plasmas

We have investigated the nonlinear interaction between a 3D kinetic Alfven wave (KAW) and an ion acoustic wave (IAW) in solar wind plasmas. A set of dimensionless equations was developed that describes the pump KAW perturbed by a low-frequency ion acoustic wave. The dependence of the growth rate of the modulational instability on the perturbation wave number was studied. We simulated numerically the dynamical equation of KAW with a pseudo-spectral method, taking ponderomotive nonlinearity into account. The 3D KAW itself propagates in the form of a vortex beam in a magnetised plasma, which manifests the presence of orbital angular momentum of the wave eigenmodes. We discuss the evolution of these vortex structures. Our results reveal that the Kolmogorov scaling is followed by a steeper scaling of power spectra, which is consistent with the solar wind observations by the Cluster spacecraft. We discuss the relevance of our investigation for solar wind plasmas.

Turning point temperature and competition between relativistic and ponderomotive effects in self-focusing of laser beam in plasma

The propagation characters of Gaussian laser beam in collisionless plasma are investigated by considering the ponderomotive and relativistic nonlinearities. The second-order differential equation of dimensionless beam width parameter is solved numerically, taking into account the effect of electron temperature. The results show that the ponderomotive force does not facilitate the relativistic self-focusing in all intensity ranges. In fact, there exists a certain intensity value that, if below this value, the ponderomotive nonlinearity can contribute to the relativistic self-focusing, or obstruct it, if above. It is also indicated that there is a temperature interval in which self-focusing can occur, while the beam diverges outside of this region. In addition, the results represent the existence of a “turning point temperature” in the mentioned interval that the self-focusing has the strongest power. The value of the turning point is dependent on laser intensity in which higher intensities result in higher turning point.

Self-focusing of a Gaussian electromagnetic beam in a multi-ions plasma

In this paper, the authors have developed a formulation for the dependence of electron and ion densities on the irradiance of an electromagnetic beam in a plasma with multiply charged ions, corresponding to collisional, ponderomotive, and relativistic-ponderomotive nonlinearities and different electron/ion temperatures; consequently, the corresponding expressions for the electron density modification in the presence of an electromagnetic (em) field have been derived. Paraxial approach in the vicinity of intensity maximum has been adopted to analyze the propagation characteristics of an em beam in such plasmas; on the basis of this analysis, critical curves and self-focusing curves have been computed numerically and graphically illustrated. For a numerical appreciation of the analysis, we have specifically carried out the computations for the simultaneous presence of singly and doubly charged ions in the plasma. As an important outcome, it is seen that the nonlinear effects (and hence self-focusing) get suppressed in the presence of multiply ionized ions; the conditions for the three modes of em-beam propagation viz. oscillatory focusing/defocusing and steady divergence have been discussed.

Effect of laser beam filamentation on coexisting stimulated Raman and Brillouin scattering

This paper presents the study of stimulated Raman scattering (SRS) and stimulated Brillouin scattering (SBS) when both of these processes are coexisting and pump laser beam initial power is more than filamentation threshold. On account of the ponderomotive nonlinearity, the pump laser beam gets filamented, and both the scattering processes (SRS and SBS) get affected. Simultaneous presence of SRS and SBS (five wave interaction case) also affect the pump filamentation process due to pump depletion. Both the scattering processes (SRS and SBS) are enhanced due to filamentation of laser beam. Results are also compared with the three wave interaction case (either SRS or SBS) with and without filamentation.