Relativistic Ponderomotive Force Research Articles

High Dose‐Rate MeV Electron Beam from a Tightly‐Focused Femtosecond IR Laser in Ambient Air

AbstractUltrashort electron beams with femtosecond to picosecond bunch durations offer unique opportunities to explore active research areas ranging from ultrafast structural dynamics to ultra‐high dose‐rate radiobiological studies. It presents a straightforward method to generate relativistic electron beams in ambient air via the tight focusing of a few‐cycle, mJ‐class femtosecond infrared laser. It demonstrates experimentally that electrons can reach up to 1.4 MeV at a dose‐rate of 0.15 Gy/s, providing enough dose rate for radiation therapy applications. 3D Particle‐In‐Cell simulations confirm that the acceleration mechanism is based on the relativistic ponderomotive force and show theoretical agreement with the measured electron energies and divergence. Relativistic peak intensities up to 1019 Wcm−2 are reached in ambient air due to a very low B‐integral accumulation during focusing, which prevents intensity clamping. Furthermore, it discusses the scalability of this method with the continuing development of mJ‐class high average power lasers, and providing a promising approach for FLASH radiation therapy.

Effect of relativistic ponderomotive force on shock waves in a relativistic degenerate plasma

Abstract We investigate the effect of relativistic ponderomotive force on the propagation of shock waves in relativistic degenerate plasma, which is relevant to high-intensity laser-plasma experiments aimed at replicating extreme conditions on white dwarfs. We derive the KdV-Burger’s equation by incorporating the density modification induced by the ponderomotive force and hence demonstrate that this equation is a suitable model for shock waves affected by ponderomotive force. Unlike previous studies that use ponderomotive force as a source of nonlinearity to derive the nonlinear Schrödinger equation for envelope solitons, our study focuses on the effect of ponderomotive force on shocks produced by the intense laser. We show that the ponderomotive force can significantly modify the strength and shape of shock waves, providing insight into the underlying physics of shock waves in relativistic degenerate plasmas which may help to better understand experimental observations in this regime.

Electron reflux dynamics in relativistically transparent plasma

The electron re-injection effect has revealed the great probability rate of photon generation due to the head-on collision between relativistic electrons and laser. We study the electron re-injection dynamics when the ultra-intense laser irradiates the near-critical-density plasma and successfully controls the photon radiation by means of the transversely tailored plasma. Starting from the relativistic corrected ponderomotive force, the critical strength of the laser field required by the refluxing effect is theoretically obtained. Then, the theoretical description of the wavefront formed by electron refluxing is given via plugging in the difference in the transverse phase velocity of the plasma wave. Simulation results display a curved surface of the refluxing electrons, which are in good agreement with the calculation results stemming from the physics model. The re-built phase space of the refluxing electrons illustrates that they gain energy mainly from the longitudinal electrostatic field on the re-injection path. Despite the energy of the refluxing electron being relatively low, it could radiate more photons via more efficient non-linear Compton scattering than the electron being accelerated in the positive direction. Furthermore, we employ a transverse density profile in the plasma and successfully achieve control of the electron re-injection effect and the properties of the resultant photons as well. Simulation results exhibit that overcritical electron beams are successively re-injected from the plasma density peaks. These backward electrons emit photons along the two maximal plasma densities as they collide with the laser pulse. Although the quality of the photons is not improved, their spatial distribution is changed, which is a big step toward manipulating light sources.

Revisiting Experimental Signatures of the Ponderomotive Force

The classical theory of single-electron dynamics in focused laser pulses is the foundation of both the relativistic ponderomotive force (RPF), which underlies models of laser-collective-plasma dynamics, and the discovery of novel strong-field radiation dynamics. Despite this bedrock importance, consensus eludes the community as to whether acceleration of single electrons in vacuum has been observed in experimental conditions. We analyze an early experiment on the RPF with respect to several features that were neglected in modeling and that can restore consistency between theory predictions and experimental data. The right or wrong pulse profile function, laser parameters, or initial electron distribution can each make or break the agreement between predictions and data. The laser phase at which the electron’s interaction with the pulse begins has a large effect, explaining why much larger energies are achieved by electrons liberated in the focal region by photoionization from high-Z atoms and by electrons ejected from a plasma mirror. Finally, we compute the difference in a typical electron spectrum arising from fluctuating focal spot size in state-of-the-art ultra-relativistic laser facilities. Our results emphasize the importance of thoroughly characterizing laser parameters in order to achieve quantitatively accurate predictions and the precision required for discovery science.

Self-focusing and defocusing phenomena of super-Gaussian laser beams in plasmas carrying density gradient

Considering nonlinearities due to relativistic mass variation and ponderomotive force driven depression in the electron density, a model is developed for the self-focusing of a super-Gaussian laser beam in inhomogeneous plasmas. Since paraxial ray approximation is not appropriate for the beams of super-Gaussian profile, the formulation is developed based on the moment theory. To have an in-depth understanding of self-focusing and defocusing phenomena and to develop generalized treatment, three different types of plasma density profiles namely linear, tangent and exponential density profiles, are considered and the results are compared. Due to the saturating nature of nonlinear permittivity with laser intensity, the beam is found to undergo periodic focusing because of competition between the diffraction divergence and nonlinear self-focusing effects. The ponderomotive nonlinearity enhances the self-focusing. As the super-Gaussian beam moves into higher density plasma region up to several Rayleigh lengths, stronger self-focusing is achieved and the value of minimum spot size decreases.

Dynamics of resonant self‐focusing on second harmonic generation of Gaussian laser beam in a rippled density plasma

AbstractResonant second harmonic generation by a Gaussian laser beam in a rippled density plasma is studied using the moment theory approach. The nonlinearity arises through the relativistic mass effect and ponderomotive forces. The laser beam creates a plasma channel and gives rise to electron density perturbation at the laser frequency. The density perturbation beats with electron quiver velocity to produce second harmonics. The ripple provides phase matching and makes the process a resonant one. The second harmonic power efficiency is increased effectively with density ripple. Self‐focusing causes enhancement in the efficiency of harmonic generation.

A Mathematical Modelling with Zakharov System for Langmuir Wave in Unmagnetized Plasma

In this article we present a discussion and overview of mathematical result of the self-focusing of a Langmuir wave which governs Zakharov system and has studied the self- focusing of a Langmuir wave following by Gaussian distribution. Langmuir wave propagates through uncharged plasma which governed by Zakharov systems. The phenomenon plays a vital role in the Dynamics. We present the article mathematical model with effect of Landou damping. Relativistic mass oscillation and ponderomotive force on electrons of the ionized plasma encouraged the Langmuir wave which resists the self-focusing effect when damping is ignored. The Beam radius gets narrow. when it further propagates considering the paraxial ray’s approximation, the self-focusing length Rn. It shows that characteristics of varying bandwidth distance of propagation in relativistic plasma.

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

AbstractThe 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.

Modulational instability of ultraintense laser pulses in electron-positron-ion plasmas including vacuum polarization effect

A non-linear equation for describing the dynamics of slowly varying envelope of ultra-intense lasers in electron-positron-ion plasmas is derived, taking into account the vacuum polarization effect. Then the modulation instability of ultra-intense laser pulses in the plasmas is investigated. Theoretical results show that the growth rate of modulation instability is originated from the relativistic ponderomotive force of lasers and the vacuum polarization effect. In the regime of different physical parameters, there is an interplay of the two effects. The dependence of the growth rate on the intensity of lasers, the temperature of electrons (positrons), the component of plasmas and the vacuum polarization effect is numerically studied.

Enhancement of target normal sheath acceleration in laser multi-channel target interaction

Target-normal sheath acceleration (TNSA) of ions by >100-fs relativistic laser pulses irradiating a multichannel target consisting of a row of parallel long wires and a plane back foil is studied. Two-dimensional particle-in-cell simulations show that the laser light pulls out from the wires a large number of dense hot attosecond electron bunches, which are synergetically accelerated forward by the relativistic ponderomotive force of the laser as well as the longitudinal electric field of a transverse magnetic mode that is excited in the vacuum channels between the wires. These electrons are characterized by a distinct two-temperature energy spectrum, with the temperature of the more energetic electrons close to twice the ponderomotive potential energy. After penetrating through the foil, they induce behind its rear surface a sheath electric field that is both stronger and frontally more extended than that without the channels. As a result, the TNSA ions have much higher maximum energy and the laser-to-ion energy conversion efficiency is also much higher. It is found that a laser of intensity 1.37 × 1020 W/cm2, duration 165 fs, and energy 25.6 J can produce 85 MeV protons and 31 MeV/u carbon ions, at 30% laser-to-ion energy conversion efficiency. The effects of the channel size and laser polarization on the TNSA ions are also investigated.

Generation of terahertz radiation from beating of two intense cosh-Gaussian laser beams in magnetized plasma

AbstractAn analytical and numerical study has been carried out for the generation of terahertz (THz) radiation by beating of two intense cosh-Gaussian laser beams (decentered Gaussian beams) in the rippled density magnetized plasma under the relativistic–ponderomotive regime. In this process, both laser beams exert a relativistic–ponderomotive force on plasma electrons at the beat frequency and impart them an oscillatory velocity in the presence of a static magnetic field. Due to coupling between this nonlinear oscillatory velocity with density ripple, nonlinear current is generated that excites the THz radiation at the different frequency. Higher-order paraxial-ray approximation (non-paraxial theory) has been used in this study. The effects of the decentered parameter, magnetic field, and density ripple on the THz radiation generation in ripple density magnetized plasma have been investigated. Further, the effect of beating of laser beams on the THz field amplitude and the efficiency of THz radiation have been studied. The amplitude and efficiency of the emitted radiation are found to be highly sensitive to the decentered parameter, magnetic field, and density ripple. It has been found that the amplitude and efficiency of the generated THz radiation increase significantly with increasing the values of decentered parameter, magnetic field, and density ripple.

Nonlinear space charge dynamics and modulational instability in the interaction of intense laser pulses with electron-positron plasmas

Nonlinear space charge dynamics and modulational instability in the interaction between ultrashort, intense laser pulses and electron-positron pair plasmas are investigated taking into account the relativistic ponderomotive force and the relativistic mass of electrons and positrons. By coupling Maxwell's equations and hydrodynamic model, the electron and positron density distributions and the dispersion relation for the modulational instability are obtained. Moreover, two coupled nonlinear equations for the scalar and vector potentials are derived and numerically solved. The results show that the growth rate of instability increases with the decrease in the electron and positron temperatures. Moreover, it is shown that when the temperatures of electrons and positrons are not equal to each other, the profiles of scalar potential are similar to bright-like or dark-like solitons.

High intensity laser beam propagation through a relativistic warm magnetoplasma

In this work, nonlinear aspects of a circularly polarized high intensity Gaussian laser beam propagating in a relativistic warm magnetized plasma are studied, taking into account the relativistic ponderomotive force. The differential equation governing the dimensionless beam width parameter is achieved and numerically solved by introducing the dielectric permittivity of such plasma and using the paraxial ray approximation. The effects of entrance laser intensity and its polarization state, external magnetic field, and electron temperature on the laser spot size evolution are studied. It is found that for both right and left-handed polarization states increasing initial laser intensity deteriorates the self-focusing mechanism while rising electron temperature improves it. It is also observed that enhancing magnetic field leads to faster and stronger self-focusing in the case of right-handed polarization and an attenuation in the self-focusing process in the case of left-handed one. In addition, the spatial distribution of normalized modified electron density as well as laser intensity profiles as a function of plasma length and beam radius is plotted and discussed for three self-focusing, self-trapping, and defocusing regimes.

Relativistic ponderomtive force acceleration of electrons in weak inhomogenous underdense plasma

In the paper, relativistic ponderomotive force acceleration of electrons in weak inhomogenous underdense plasma is investigated. The results shown that, in interaction of ultraintense laser and the plasma, due to the influence of relativistic ponderomotive force, laser beam presents self-focusing, and electrons are accelerated obviously. Initially, electron energy presents a fluctuation variation along the propagation distance, then the fluctuation will weaken gradually, finally it trend to a steady state and the electrons acquire a high net energy. Compared with homogeneous plasma, electron energy would increase and its vibration length becomes short in weak inhomogeneous underdense plasma. Moreover, the high-energy electrons can be easily extracted by the relativistic ponderomotive force, the results may offer some useful theoretical proof for the design of new accelerators.

Уединённая правополяризованная электромагнитная волнав релятивистской плазме

In this paper of the nonlinear laser wave propagation in the hot plasma along the strong exter-nal magnetic field under the electron cyclotron resonance conditions is investigated. The strongnonlinearity of such a process is caused by the relativistic electron movement and resonancewave ponderomotive force acting on the electrons. The system of equations for the enveloperight hand polarized laser pulse is derived using the hydrodynamics and Maxwell’s equations.The numerical integration of this system for the cold plasma case discovered the soliton solu-tions. This kind of solutions take a form of the envelope solitons containing inside them the plasma oscillations. The analytical expression for the energy density integral in a cold plasma isderived. It follows from the numerical results that for a hot plasma under cyclotron resonanceconditions the soliton solution becomes unstable. In this case the energy density conservationbreaks down, but electron momentum density conserves. It is concluded that the nonlinear sat-uration of the field amplitude is due to the plasma charge separation under electromagneticradiation pressure. In this case the discrete set of the envelope soliton carrier frequency is de-termined by the ratio of the frequency of the nonlinear longitudinal electron oscillations to theLangmuir frequency of plasma. For the low density plasma the discrete frequency spectrumobtained by the numerical integration transforms to the continuous one.

Retraction: Higher-Order Nonlocal Effects of a Relativistic Ponderomotive Force in High-Intensity Laser Fields [Phys. Rev. Lett. 112, 035002 (2014)

Retraction of DOI: 10.1103/PhysRevLett.112.035002.

Self-focusing of super-Gaussian laser beam inmagnetized plasma under relativistic and ponderomotive regime

In this paper, we have investigated the propagation characteristics of super-Gaussian laser beam in magnetized plasma. Self-focusing of short pulse laser propagating along the direction of ambient magnetic field in plasma is studied. The nonlinearity arises through the combined effect of relativistic mass variation and ponderomotive force induced electron cavitation. An appropriate nonlinear Schro¨dinger equation has been solved analytically using variational approach. Self-phase modulation is also studied under variety of parameters. Further, the effect of magnetic field on self-focusing of the beam have been explored.

Weakly relativistic and space charge effects in interaction of high-power microwave with plasma

In the present work, numerical studies on the effects of weakly relativistic ponderomotive force and space charge in the nonlinear interaction of a high-power microwave beam with a plasma are carried out. It is shown that, the profiles of the electron density and dielectric permittivity contain high peaks, and modulation of wavelength occurs in electron density distribution by increasing the microwave energy flux. In addition, it is indicated that the profiles of the electric and magnetic fields in relativistic regime are lengthened more than non-relativistic regime by increasing the initial electron density and the relativistic effects cause the increase in oscillation wavelength of electron density, dielectric permittivity and space charge field, in comparison with the non-relativistic regime. Finally, the results of the research show that the steepening in electron density distributions and their oscillation wavelength are enhanced, when the relativistic effects appear.

Relativistic ponderomotive forces in the field of intense laser radiation

The motion of a relativistic charged particle in the presence of the field of high-power laser radiation represented in the form of a Gaussian beam of arbitrary mode is analyzed. The vector potential of the radiation field is expanded in terms of a small parameter (the ratio of the wavelength to the Gaussian beam waist). A specific feature of averaging with respect to the phases of the high-mode Gaussian beams is demonstrated. The averaged equations for the motion of particle and a general expression for the ponderomotive relativistic force for the circularly polarized radiation are derived. It is demonstrated that relativistic effects suppress the averaged action of high-power laser radiation on the particle.

Laser pulse distortion in a plasma of the weakly relativistic regime

We present particle-in-cell simulations to demonstrate laser pulse distortion by incorporating the role of plasma electron temperature, where the laser pulse propagates in the weakly relativistic regime. A high-intensity laser pulse gives rise to a relativistic ponderomotive force on the electrons and redistributes the plasma density, so the refractive index of the plasma changes. The electron temperature also contributes to the nonlinearity and it results in distortion of the laser pulse. As the laser pulse becomes self-focused, the front part of the pulse acquires higher group velocity compared to the tail part. As a result, the laser pulse shape changes. Our simulation shows that the plasma electron temperature plays a key role in the laser pulse distortion phenomena in the weakly relativistic regime.