Intense Laser-plasma Interactions Research Articles

SPRAY: A smoothed particle radiation hydrodynamics code for modeling high intensity laser-plasma interactions

Here we report the development of SPRAY, a massively parallel GPU accelerated, smoothed particle hydrodynamics (SPH)-based, radiation hydrodynamics (RHD) code designed specifically for simulating high intensity laser-plasma interactions. When a target is irradiated by an intense laser, highly complex fluid deformation occurs due to instabilities, which is challenging to study numerically. SPRAY is particle-based, mesh-free, and Lagrangian, which addresses numerical issues that posed difficulties to existing methods. Its SPH formulations for RHD governing equations are tailored toward accurate and reliable simulations of laser-target irradiation phenomena, and are solved via a time-dependent, flux-limited diffusion method. A new laser energy coupling module, which is based on the Wentzel-Kramers-Brillouin (WKB) approximation, is implemented with a totally mesh-free ray-tracing scheme that is applicable for arbitrary geometry and dimensions. The accuracy and reliability of the code are demonstrated with a series of benchmark problems. To the authors' knowledge, this is the first attempt to employ SPH method for simulations of laser-plasma interactions in high energy density physics research. Possible expansions to the code, such as laser beam-beam interaction modeling and more sophisticated multi-group radiation transport are left for future development.

Nonlinear electrostatic kelvin-helmholtz shock waves in a viscous electron-positron-ion plasma with non-maxwellian distribution

A theoretical investigation is carried out for nonlinear electrostatic Kelvin-Helmholtz (K-H) shock waves in a magnetized electron-positron-ion viscous plasma in the presence of transport equations and non-Maxwellian particles by following the generalized (r, q) distribution function. The propagation of electrostatic K-H modes are studied both in the presence of trapped and free electrons. The nonlinear analysis with inclusion of plasma transport properties (magnetic viscosity and heat conduction) lead to nonlinear electrostatic K-H mode in the form of shock like waves by solving the modified Burgers’ equation. The electrostatic K-H shocks are investigated numerically with effect of different plasma parameters such as shear velocity and non-Maxwellian distributed particles. It is observed that the striking features (viz., amplitude and width of dissipative shock through the solution of Burgers’ equation) of the K-H mode are significantly modified by the effects of non-thermality of electrons and positrons both at shoulder and tails along with shear velocity due to viscosity. The relevancy of our work to the observations in space (viz., cometary comae and earth’s ionosphere), astrophysical (viz., pulsars) and laboratory (viz., solid-high intense laser plasma interaction experiments) plasmas is highlighted.

Study of particle acceleration by Laguerre–Gaussian ultra intense laser plasma interactions

In this work, simulations of multi-petawatt lasers in the range of ∼0.2 PW–∼100 PW with varying Laguerre–Gaussian (LG) azimuthal modes as well as linearly polarized (LP) and circularly polarized (CP) laser beams striking near critical density targets were studied by using three-dimensional particle in cell (PIC) codes. Particle acceleration mechanisms have a dependence on laser polarization and it affects the energy gained by the particles. It is known that laser pulses can be polarized helically by applying the LG distribution function to the fundamental Gaussian laser profile. In this study, differently polarized laser beams with varying powers were employed to study laser driven particle acceleration and compares accelerated charged particles’ energy spectra and angular distribution. It is seen that LG laser beams can accelerate higher energetic particles due to higher conversion efficiency compared to LP and CP laser beams. It is also seen that LG laser beams can collimate ions with a narrower spread compared to LP and CP beams. Furthermore, ions can have a smaller divergence angle with increasing azimuthal mode index when the laser is LG polarized. We also studied the energy deposition of these particles in a water cell obtained by the PIC codes for different laser parameters by using Geant4 Monte Carlo simulations which suggests that LG laser beam can be useful for the future hadron therapy applications.

Compton scattering of plasmons

We extend de concept of Compton scattering to the case of plasmons. This concept was originally applied to electrons in vacuum. Here, we consider electrons in a plasma, and study the scattering properties of photon-plasmon interactions. We show that a number n of plasmons with frequency ω ≃ ω p is scattered by an electron, for an incident photon with frequency , where ω p is the plasma frequency. We describe the general case of arbitrary n and assume that Compton scattering of plasmons is intrinsically a nonlinear process. Our theoretical model is based on Volkov solutions of the Klein–Gordon equation describing the state of relativistic electrons, when the spin is ignored. We derive the corresponding scattering probability, as well as the recoil formula associated with arbitrary final electron states. This process can be relevant to intense laser-plasma interactions.

Real time reconstruction of the fast electron spectrum from high intensity laser plasma interaction using gamma counting technique

X-ray and gamma fluxes from the high intensity laser-plasma interaction are extremely short, well beyond temporal resolution of any detectors. If laser pulses come repetitively, the single photon counting technique allows to accumulate the photon spectra, however, its relation to the spectrum of the initial fast electron population in plasma is not straightforward. We present efficient and fast approach based on the Geant4 package that significantly reduces computer time needed to re-construct the high energy tail of electron spectrum from experimental data accounting for the pileup effect. Here, we first tabulate gamma spectrum from monoenergetic electron bunches of different energy for a given experimental setup, and then compose the simulated spectrum. To account for the pileups, we derive analytical formula to reverse the data. We also consider errors coming from the approximation of the initial electron spectrum by the sum of monoenergetic impacts, the finite range of the electron spectrum, etc. and give estimates on how to choose modelling parameters to minimize the approximation errors. Finally, we present an example of the experimental data treatment for the case of laser-solid interaction using 50 fs laser pulse with intensity above 1018 W/cm2.

Nonlinear interaction of the fast magnetosonic wave with the extraordinary mode laser and ion-scaled turbulence generation in the magnetized plasma

This study introduces a nonlinear wave-wave coupling model to understand the nature of the turbulence generation at the ion scale observed in the interaction of high-intensity laser with plasma. For this nonlinear coupling of waves, the fast magnetosonic wave and the extraordinary mode laser are taken into account, along with the nonlinear ponderomotive force. The model dynamical equations have been developed for the extraordinary mode laser and the fast magnetosonic wave. Laboratory simulations have been employed to solve the obtained model equations utilizing the finite difference and pseudo-spectral methods. The simulation results show the initiation of the nonlinear progression of the laser beam at an early time and its turbulent nature at a later time. The background density perturbation, along with the cavity and hump caused by the ponderomotive force, has also been studied. The simulation results demonstrate that the propagation angle of the fast magnetosonic wave affects the magnitudes of the localization of the laser beam (pump wave) and the perturbed background density. The turbulent power spectra (ensemble-averaged) have also been studied for the different propagation angles of the fast magnetosonic wave. The turbulent spectra demonstrate that the plasma turbulence is MHD-type at small-scale lengths and ion-dominated at larger-scale lengths. This study also observed that the simulation results have some resemblance with the experimental results reported by Chatterjee et al.12 in the intense laser-plasma interaction experiment at a laboratory astrophysical scale.

The effect of longitudinal static magnetic field on the radiation efficiency of high harmonics from overdense plasma

The effect of the magnetic field applied along the laser propagation direction on the radiation efficiency of high-order harmonics generated from laser-irradiated overdense plasma is investigated theoretically and numerically. We find that the external magnetic field can increase the transmittance of the overdense target, thereby dramatically enhancing the energy coupling between the laser and target. While for high-order harmonics of the laser reflected from the oscillating target, the radiation efficiency reaches the maximum when the cyclotron frequency of the electrons in the magnetized target approaches the laser frequency. This conclusion applies only to overdense plasmas targets. For targets with low reflectivity, the application of the magnetic field reduces the harmonic radiation efficiency due to the decrease of both the oscillating coherence and opacity of the target. This work provides a reasonable approach to improving the radiation efficiency of high-order harmonics and a method to estimate the magnitude of the self-generated magnetic field during intense laser–plasma interactions.

Effect of trapping in coupled kinetic Alfven-acoustic waves in a partially degenerate plasma with quantizing magnetic field

Inclusion of a quantizing magnetic field in a partially degenerate plasma has interesting effects on the propagation of solitary and nonlinear periodic structures in coupled kinetic Alfven acoustic waves. In this paper, we use two-potential theory to investigate the nonlinear structures using Sagdeev potential approach and further analyze it using nonlinear dynamical methods. It is shown that the existence of solitary structure is sensitive to small temperature effects and quantizing magnetic field in a dense plasma with adiabatically trapped electrons. The work presented here is useful in understanding the low frequency wave propagation in a dense astrophysical environment like white dwarf stars and in low beta laboratory plasmas e.g. intense laser-plasma interactions.

Effect of collisional frequency on the relativistic solitons in the intense laser-plasma interaction

Short and intense laser pulses in laser-plasma interaction stimulate various local structures like solitary waves in the plasma. Relative salitons should be given special attention because the amplitude of the electromagnetic field is intense enough to set plasma electrons in relativistic motions. In the interaction of intense laser with plasma, collisions can play an important role in the physical phenomena. In this paper, the effect of the collision on the emission of solitons is investigated by considering the interaction of an intense laser with plasma. Then, the NLS equation is numerically solved and the different results are compared with each other. Also, the stability conditions of individual waves and the effect of the collision on these waves are investigated.

Correction of intense laser–plasma interactions by QED vacuum polarization in collision of laser beams

The influence of vacuum polarization effects on the interactions of multiple ultra-intense lasers with plasmas is discussed. The nonlinear paraxial monochromatic model of the interactions has been improved by considering the Heisenberg–Euler Lagrangian density of two laser processes. Comparing the corrections of vacuum polarization effects in the collision of laser beams with one generated by a single intense laser, we find that the former has a higher order of magnitude correction. The laser collision also produces variations in the propagation direction and polarization direction of the lasers propagating in the plasma. In addition, the strong-field quantum electrodynamic (QED) effects can be enhanced by increasing the laser intensity or frequency difference, or by adjusting the incident angles of the two laser beams.

Shocks and solitons in collisional dense laser produced plasmas

The characteristics of nonlinear electron-acoustic waves such as shocks and solitons, are investigated in a three component, dense laser produced plasma consisting of ions and two distinct groups of electrons, using the quantum hydrodynamic model and the standard reductive perturbation method. The modified Korteweg-deVries (mKdV) and Korteweg-deVries-Burgers (KdVB) equations have been derived for the electron-acoustic waves in the plasma. The dependence of both shocks and solitons on various parameters has been extensively studied. It is observed that whenever the density crosses the limit from the classical to the quantum range, the effective potential remains invariant for the solitary profiles; but shows a slight variation for the shock profiles. The collisional effect plays a significant role in the dissipation of solitary waves and the dissipation is larger for higher values of collision frequencies. The results obtained could prove helpful for understanding the parametric dependence of nonlinear waves in highly intense laser plasma interactions.

Achieving record hot spot energies with large HDC implosions on NIF in HYBRID-E

HYBRID-E is an inertial confinement fusion implosion design that increases energy coupled to the hot spot by increasing the capsule scale in cylindrical hohlraums while operating within the current experimental limits of the National Ignition Facility. HYBRID-E reduces the hohlraum scale at a fixed capsule size compared to previous HYBRID designs, thereby increasing the hohlraum efficiency and energy coupled to the capsule, and uses the cross-beam energy transfer (CBET) to control the implosion symmetry by operating the inner (23° and 30°) and outer (44° and 50°) laser beams at different wavelengths (Δλ> 0). Small case to capsule ratio designs can suffer from insufficient drive at the waist of the hohlraum. We show that only a small amount of wavelength separation between the inner and outer beams (Δλ 1–2 Å) is required to control the symmetry in low-gas-filled hohlraums (0.3 mg/cm3 He) with enough drive at the waist of the hohlraum to symmetrically drive capsules 1180 μm in outer radius. This campaign is the first to use the CBET to control the symmetry in 0.3 mg/cm3 He-filled hohlraums, the lowest gas fill density yet fielded with Δλ> 0. We find a stronger sensitivity of hot spot P2 in μm per Angstrom (40–50 μm/Å wavelength separation) than observed in high-gas-filled hohlraums and previous longer pulse designs that used a hohlraum gas fill density of 0.6 mg/cm3. There is currently no indication of transfer roll-off with increasing Δλ, indicating that even longer pulses or larger capsules could be driven using the CBET in cylindrical hohlraums. We show that the radiation flux symmetry is well controlled during the foot of the pulse, and that the entire implosion can be tuned symmetrically in the presence of the CBET in this system, with low levels of laser backscatter out of the hohlraum and low levels of hot electron production from intense laser–plasma interactions. Radiation hydrodynamic simulations can accurately represent the early shock symmetry and be used as a design tool, but cannot predict the late-time radiation flux symmetry during the peak of the pulse, and semi-empirical models are used to design the experiments. Deuterium–tritium (DT)-layered tests of 1100 μm inner radius implosions showed performance close to expectations from simulations at velocities up to ∼360 km/s, and record yields at this velocity, when increasing the DT fuel layer thickness to mitigate hydrodynamic mixing of the ablator into the hot spot as a result of defects in the ablator. However, when the implosion velocity was increased, mixing due to these defects impacted performance. The ratio of measured to simulated yield for these experiments was directly correlated with the level of observed mixing. These simulations suggest that reducing the mixing, e.g., by improving the capsule defects, could result in higher performance. In addition, future experiments are planned to reduce the coast time at this scale, delay between the peak compression and the end of the laser, to increase the hot spot convergence and pressure. To reduce the coast time by several hundred ps compared to the 1100 μm inner radius implosions, HYBRID-E has also fielded 1050 μm inner radius capsules, which resulted in higher hot spot pressure and a fusion energy yield of ∼170 kJ.

A particle-in-cell code comparison for ion acceleration: EPOCH, LSP, and WarpX

There are now more Particle-in-Cell (PIC) codes than ever before that researchers use to simulate intense laser–plasma interactions. To date, there have been relatively few direct comparisons of these codes in the literature, especially for relativistic intensity lasers interacting with thin overdense targets. To address this, we perform a code comparison of three PIC codes: EPOCH, LSP, and WarpX for the problem of laser-driven ion acceleration in a 2D(3v) geometry for a 1020 W cm−2 intensity laser. We examine the plasma density, ion energy spectra, and laser–plasma coupling of the three codes and find strong agreement. We also run the same simulation 20 times with different random seeds to explore statistical fluctuations of the outputs. We then compare the execution times and memory usage of the codes (without “tuning” to improve performance) using between 1 and 48 processors on one node. We provide input files to encourage larger and more frequent code comparisons in this field.

Formation and evolution of post-solitons following a high intensity laser-plasma interaction with a low-density foam target

The formation and evolution of post-solitons has been discussed for quite some time both analytically and through the use of particle-in-cell (PIC) codes. It is however only recently that they have been directly observed in laser-plasma experiments. Relativistic electromagnetic (EM) solitons are localised structures that can occur in collisionless plasmas. They consist of a low-frequency EM wave trapped in a low electron number-density cavity surrounded by a shell with a higher electron number-density. Here we describe the results of an experiment in which a 100 TW Ti:sapphire laser (30 fs, 800 nm) irradiates a TMPTA foam target with a focused intensity . A third harmonic ( nm) probe is employed to diagnose plasma motion for 25 ps after the main pulse interaction via Doppler-Spectroscopy. Both radiation-hydrodynamics and 2D PIC simulations are performed to aid in the interpretation of the experimental results. We show that the rapid motion of the probe critical-surface observed in the experiment might be a signature of post-soliton wall motion.

Ion acceleration at two collisionless shocks in a multicomponent plasma.

Intense laser-plasma interactions are an essential tool for the laboratory study of ion acceleration at a collisionless shock. With two-dimensional particle-in-cell calculations of a multicomponent plasma we observe two electrostatic collisionless shocks at two distinct longitudinal positions when driven with a linearly polarized laser at normalized laser vector potential a_{0} that exceeds 10. Moreover, these shocks, associated with protons and carbon ions, show a power-law dependence on a_{0} and accelerate ions to different velocities in an expanding upstream with higher flux than in a single-component hydrogen or carbon plasma. This results from an electrostatic ion two-stream instability caused by differences in the charge-to-mass ratio of different ions. Particle acceleration in collisionless shocks in multicomponent plasma are ubiquitous in space and astrophysics, and these calculations identify the possibility for studying these complex processes in the laboratory.

Particle integrator for particle-in-cell simulations of ultra-high intensity laser-plasma interactions

Particle-in-cell codes are the most widely used simulation tools for kinetic studies of ultra-intense laser-plasma interactions. Using the motion of a single electron in a plane electromagnetic wave as a benchmark problem, we show surprising deterioration of the numerical accuracy of the PIC algorithm with increasing normalized wave amplitude for typical time-step and grid sizes. Two significant sources of errors are identified: strong acceleration near stopping points and the temporal field interpolation. We propose adaptive electron sub-cycling coupled with a third order temporal interpolation of the magnetic field and electric field as an efficient remedy that dramatically improves the accuracy of the particle integrator.

Investigation of QED Effects With Varying Z in Thin Foil Targets

Quantum electrodynamics (QED) effects in intense laser–plasma interaction were investigated using particle-in-cell (PIC) simulations, specifically the generation of electron–positron pairs. Linearly polarized intense laser pulses were used to irradiate a thin foil (1- $\mu \text{m}$ ) with an intensity of $4\times 10^{23}$ W cm−2. A scan of targets with varying $Z$ (Al, Cu, and Au) is investigated to determine the effect of target $Z$ /density on electron–positron pair production. The total number of pairs created for Al and Cu targets is 1014 and 1013, respectively. In the case of Au, we did not observe any pair production to occur. We have also calculated the variation in electron energy in these targets. The results indicate that target $Z$ plays a very important role with the laser interaction in the pair production process, which will be explained in this article.

Stability of ion-acoustic solitons in a multi-ion degenerate plasma with the effects of trapping and polarization under the influence of quantizing magnetic field

ABSTRACT Multi-dimensional instability of ion acoustic solitary waves (IASWs) in a magnetized, collisionless, degenerate multi-ion plasma system with trapping distributed electrons in the presence of a quantizing magnetic field has been theoretically investigated. The dispersion properties of the linear IASWs are discussed. The dynamics of the nonlinear Zakharo-Kuznetsov (ZK) equation is also analyzed for investigation of the solitary waves. The effects of the trapped electrons, the electron temperature and the mass-to-charge for positive to negative ions on the phase velocity are discussed. Only compressive solitary waves are produced, those are affected by the system parameters like the number density ratio of negative to positive ions and the polarization effect. The waves growth rate is calculated. The effects of the previous plasma parameters on the instability growth rate are also discussed. The present investigation could be helpful in understanding the propagation and the instability of the detected IASWs waves in magnetized multi-ion plasmas which are observed in dense quantum plasmas such as those existing in white dwarfs and in the intense-laser plasma interactions where the trapping and the polarization effects are important.

The dependency of the stochastic heating to the pulse shape in intense laser-plasma interaction

Stochastic heating is a generic mechanism in the production of energetic electrons during the interaction of intense short laser pulse with under-dense plasma. In this paper, we employ fully kinetic 1D-3 V particle-in-cell (PIC) simulations to examine the effects of the pulse shape in the performance of the stochastic heating. To correctly characterize the local plasma temperature, we exploit the proper (relativistically invariant) stress tensor,Pij, which decouples the bulk motion from stochastic fluctuations. Our results reveal a strong dependence of heating performance on the pulse shape parameter. It is represented that the pulse rise-time is one of the main factors affecting the type of heating mechanism of electrons. In this regard, the possibility of stochastic heating is confirmed in the smooth shape pulse. It is shown that unlike the pulses with quickly rising time, when the pulse rise-time is initially smooth, Raman backscattered fields can act as a second counter-propagating wave and provide the necessary condition for the stochastic heating. In these pulses, the stochastic heating threshold time is dependent on the pulse rise-time. So that, decreasing the pulse rise-time, down to a definite value, leads to the stronger initiation of the backward Raman scattering, whence, faster onset of the stochastic heating.

Generation and regulation of electron vortices in an underdense plasma by Laguerre-Gaussian laser pulses

An analytical model is presented to control the angular momentum of electrons by impinging Laguerre-Gaussian (LG) laser beam in an underdense warm plasma. During intense laser-plasma interaction, radiative effects of intense long laser pulses become important, which are analyzed under quasi-static approximation. It is shown that the spot size of the laser beam controls the depth of doughnut-shaped ion-channel created in the plasma. Due to inhomogeneity of plasma density, the nonlinear beating of two fast-time-scale laser fields results in the generation of slow-time-scale “dc” magnetic fields. These fields confine the fast electrons in relativistic laser channel and support their direct coupling with the lasers’ fields. Inside the doughnut-shaped channel, the electrons are found to execute transverse betatron oscillations. At resonance, the laser field efficiently transfers the energy and momentum to the plasma electrons which can be controlled by the lasers and plasma parameters. The angular momentum of the electrons is also found to be dependent on the magnitude of the quasi-static axial magnetic field. Moreover, regulation of the electron angular momentum can explore various interesting areas including coherent vortex beam generation via synchrotron radiation process.