Cross-beam Energy Transfer Research Articles

Development of an x-ray radiography platform to study laser-direct-drive energy coupling at the National Ignition Facility.

A platform has been developed to study laser-direct-drive energy coupling at the National Ignition Facility (NIF) using a plastic sphere target irradiated in a polar-direct-drive geometry to launch a spherically converging shock wave. To diagnose this system evolution, eight NIF laser beams are directed onto a curved Cu foil to generate Heα line emission at a photon energy of 8.4keV. These x rays are collected by a 100-ps gated x-ray imager in the opposing port to produce temporally gated radiographs. The platform is capable of acquiring images during and after the laser drive launches the shock wave. A backlighter profile is fit to the radiographs, and the resulting transmission images are Abel inverted to infer radial density profiles of the shock front and to track its temporal evolution. The measurements provide experimental shock trajectories and radial density profiles that are compared to 2D radiation-hydrodynamic simulations using cross-beam energy transfer and nonlocal heat-transport models.

The crossed-beam energy transfer model without empirical factor for multi-beam irradiation of a spherical laser target

Stimulated Brillouin scattering of laser radiation in an expanding plasma during compression of a spherical target can significantly reduce the fraction of absorbed energy. A model of CBET (crossed-beam energy transfer) stimulated scattering under multi-beam irradiation of a spherical target has been developed. The model does not contain empirical factor, unlike the model known in the literature. This makes it possible to use it in calculations for the conditions of planned experiments. Calculations of the fraction ΔCB of energy released from the plasma due to CBET scattering for experimental conditions at the OMEGA installation have been carried out. It is shown that this fraction depends on the factor fe of the electron heat flux limitation. With fe values in the range 0.04–0.06, the calculated values of ΔCB (0.12–0.084) are close to the value 0.1 obtained in the experiment and in numerical simulation at fe = 0.06.

3D Simulations Capture the Persistent Low-Mode Asymmetries Evident in Laser-Direct-Drive Implosions on OMEGA.

Spherical implosions in inertial confinement fusion are inherently sensitive to perturbations that may arise from experimental constraints and errors. Control and mitigation of low-mode (long wavelength) perturbations is a key milestone to improving implosion performances. We present the first 3D radiation-hydrodynamic simulations of directly driven inertial confinement fusion implosions with an inline package for polarized crossed-beam energy transfer. Simulations match bang times, yields (separately accounting for laser-induced high modes and fuel age), hot spot flow velocities and direction, for which polarized crossed-beam energy transfer contributes to the systematic flow orientation evident in the OMEGA implosion database. Current levels of beam mispointing, imbalance, target offset, and asymmetry from polarized crossed-beam energy transfer degrade yields by more than 40%. The effectiveness of two mitigation strategies for low modes is explored.

The development of a high-resolution Eulerian radiation-hydrodynamics simulation capability for laser-driven Hohlraums

Hohlraums are hollow cylindrical cavities with high-Z material walls used to convert laser energy into uniform x-ray radiation drives for inertial confinement fusion capsule implosions and high energy density physics experiments. Credible computational modeling of hohlraums requires detailed modeling and coupling of laser physics, hydrodynamics, radiation transport, heat transport, and atomic physics. We report on improvements to Los Alamos National Laboratory's xRAGE radiation-hydrodynamics code in order to enable hohlraum modeling. xRAGE's Eulerian hydrodynamics and adaptive mesh refinement make it uniquely well suited to study the impacts of multiscale features in hohlraums. In order to provide confidence in this new modeling capability, we demonstrate xRAGE's ability to produce reasonable agreement with data from several benchmark hohlraum experiments. We also use xRAGE to perform integrated simulations of a recent layered high density carbon capsule implosion on the National Ignition Facility in order to evaluate the potential impacts of the capsule support tent, mixed cell conductivity methodologies, plasma transport, and cross-beam energy transfer (XBT). We find that XBT, seeded by plasma flows in the laser entrance hole (LEH), causes a slight decrease in energy coupling to the capsule and that all of these impact the symmetry of the x-ray drive such that they have an appreciable impact on the capsule implosion shape.

CBETor: a hybrid-kinetic particle-in-cell code for cross-beam energy transfer simulation

The parametric instability related to ion motion and the resulting cross-beam energy transfer are important aspects in the physics of inertial confinement fusion. The numerical simulation of the above physical problems still faces great technical challenges. This paper introduces a 2D hybrid-kinetic particle-in-cell (PIC) code, CBETor. In this code, the motion of ions is described by the kinetic method, the motion of electrons is described by the simplified fluid method and the propagation of laser in plasma is described by solving the wave equation. We use CBETor and the popular fully kinetic PIC code EPOCH to simulate the stimulated Brillouin scattering and cross-beam energy transfer process, respectively. The physical images are in good agreement, but CBETor can significantly reduce the amount of calculation. With the premise of correctly simulating the ion dynamics, our hybrid-kinetic code can effectively suppress the noise of numerical simulation and significantly expand the simulation scale of physical problems. CBETor is very suitable for simulating the physical process dominated by ion motion in the interaction of medium intensity laser and underdense plasma.

Beam Spray Thresholds in ICF-Relevant Plasmas.

Beam spray measurements suggest thresholds that are a factor of ≈2 to 15× less than expected based on the filamentation figure of merit often quoted in the literature. In this moderate-intensity regime, the relevant mechanism is forward stimulated Brillouin scattering. Both weak ion acoustic wave damping and thermal enhancement of ion acoustic waves contribute to the low thresholds. Forward stimulated Brillouin scattering imparts a redshift to the transmitted beam. Regarding the specific possibility of beam spray occurring outside the laser entrance holes of an indirectly driven hohlraum, this shift may be the most concerning feature owing to the high sensitivity of crossed-beam energy transfer to the interacting beam wavelengths in the subsequent overlap region.

Understanding and controlling capsule symmetry in near vacuum hohlraums at the National Ignition Facility

The near vacuum hohlraum platform is an inertial confinement fusion design at the National Ignition Facility (NIF) that uses the lowest practical density of helium gas of 30 μg/cc to fill the hohlraum, which is ten times lower than now used routinely. This has several advantages, such as high laser coupling; however, the inability to understand and simulate the symmetry of the imploded capsule has limited the use of this platform. This work presents the first simulations that are able to accurately capture the highly prolate implosion seen experimentally without unphysical, ad hoc model changes. While previous investigations attributed this asymmetry to multi-species interpenetration in the hohlraum, we find that this alone has little effect on symmetry. Instead, it is the presence of crossed-beam energy transfer (CBET), occurring with no applied wavelength shift between the laser beams, that increases the laser power to the inner cones and causes a more prolate implosion. The effect of CBET is increased in the simulation model when the hohlraum laser entrance hole hardware is included. Using this understanding, CBET is exploited by shifting the inner-beam wavelength by −0.75 Å (at 1ω) with respect to the outer-beams. This transfers laser power to the outer-beams in contrast to positive wavelength shifts as done routinely on NIF and produces a round capsule implosion in our simulations. This work shows the possibility of the near vacuum hohlraum as a viable experimental platform.

Cross-beam energy transfer in direct-drive ICF. I. Nonlinear and kinetic effects

Results are presented from a series of simulations examining the susceptibility of the cross-beam energy transfer (CBET) instability to nonlinear processes in the context of direct-drive inertial confinement fusion experiments on the OMEGA laser facility. These form the basis for the second paper of this series [A. G. Seaton, L. Yin, R. Follett, B. J. Albright, and A. Le, “Cross-beam energy transfer in direct-drive ICF. II. Theory and simulation of mitigation through increased laser bandwidth,” Phys. Plasmas 29, 042707 (2022)], where we examine the efficacy of increases in laser bandwidth at suppressing CBET. We choose laser and plasma conditions for the simulations that are favorable to CBET and promote nonlinearity. Through a comparison of outputs from the particle-in-cell code vector particle in cell (VPIC) and the linearized fluid code laser-plasma simulation environment (LPSE), a series of nonlinear effects have been identified in the kinetic simulations that include particle trapping, the two-ion wave decay, and ion-acoustic wave self-focusing. These effects produce time-dependent energy transfer, in contrast to the linearized fluid simulations in which a steady state is reached after an initial transient. Ion trapping is shown to allow for increased energy transfer relative to fluid simulations, with the remaining nonlinear processes acting to reduce the energy transfer. Nonlinear dynamics is contrasted for low- and high-intensity beams as well as between speckled and planar beams. For the parameters under consideration, beam profile has a significant effect on nonlinear dynamics, though the greatest sensitivity is to beam intensity.

Cross-beam energy transfer in direct-drive ICF. II. Theory and simulation of mitigation through increased laser bandwidth

The response of the cross-beam energy transfer instability (CBET) to laser bandwidth is investigated through a combination of theory and simulation. Existing linear theory is generalized to treat broadband lasers, demonstrating that CBET is most effectively suppressed when the bandwidth exceeds the ion-acoustic wave (IAW) frequency. It is shown that for such bandwidths, reverse (seed to pump) transfer becomes possible, which reduces the net energy transfer rapidly as bandwidth is increased. The CBET gain exponent in this regime scales with bandwidth (Δω) as Δω−3 for Gaussian or Lorentzian laser spectra with different scalings possible for other spectra. Comparison of our theory with linearized fluid and particle-in-cell simulations, performed with the laser-plasma simulation environment (LPSE) and vector particle in cell (VPIC) codes, respectively, finds that the model is accurate in the absence of nonlinear processes. However, linear analysis also finds that the IAW energy density scales as Δω−1, implying that nonlinear effects may be more difficult to control than the CBET scaling would suggest. Indeed, nonlinear effects are found to be present in VPIC simulations with high-intensity lasers, despite minimal apparent CBET. Nonlinear processes in the VPIC cases include particle trapping, the two-ion wave decay, and ion wave self-focusing. In some high intensity VPIC cases, these effects lead to net energy transfer from seed to pump and increases to backscatter stimulated Brillouin scattering reflectivities. Finally, for a given bandwidth, we show that improved control of nonlinear processes can be achieved via smoothing by spectral dispersion.

Cross-beam energy transfer saturation: ion heating and pump depletion

Cross-beam energy transfer (CBET) was measured in two regimes where the energy transfer saturation mechanism was determined by the plasma and laser beam conditions. Linear kinetic CBET theory agrees well with the measured energy transfer in all experimental configurations and at all probe beam intensities when accounting for pump depletion and the plasma conditions measured using Thomson-scattering. Simultaneous CBET and Thomson-scattering measurements enabled uncertainties in the plasma conditions to be isolated from CBET theory, which allowed the saturation mechanisms to be identified. In the perpendicular-beam configuration the saturation mode was through ion heating, which resulted from ion trapping in the driven waves and subsequent ion-ion collisional heating. In the co-propagating beam configuration there was minimal ion heating and the saturation mode was through pump depletion.

Potential continuous zooming scheme based on high-power broadband laser

Continuous zooming is efficient in mitigating the cross-beam energy transfer effect and improving implosion hydrodynamic efficiency in the application of inertial confinement fusion. In this paper, a novel continuous zooming scheme is proposed, based on the chromatic aberration effect of the lens groups to gradually reduce the size of the focal spot at the target position by focusing the broadband laser pulse. This scheme is simulated theoretically on the Shenguang-II upgrade (SG-II UP) facility, and the results show that the focal spot size is positive and linear for the beam wavelength. When the fundamental wave bandwidth was 5 nm, the focal spot radius was reduced by 15.21% without changing the geometric parameters of the SG-II upgrade, and the focal spot radius was reduced by 27.73% after optimization. In addition, the conversion efficiency is compensated for in the harmonic converter. This paper supports a new perspective for the realization of high-power laser zooming.

Reduction of Cross-Beam Energy Transfer by a Speckle Pattern.

In this Letter, we show that cross-beam energy transfer (CBET), ubiquitous in inertial confinement fusion (ICF) experiments, may be strongly modified by the speckle pattern of the beams. This is demonstrated by the means of two-dimensional particle in cell simulations, supported by a linear model. In particular, we show that, although they would be the same in a plane wave model, the exchange rates of energy may be significantly different whether there is a plasma flow, or a wavelength shift, especially when the waves are weakly damped. When the crossed laser beams have different frequencies, the energy exchange rate is substantially reduced compared with the predictions of the plane wave model, widely used in the hydrodynamic codes that model and interpret ICF experiments. Such effects can partly explain the disagreement of the CBET predictions compared with experimental results.

Nonuniform Absorption and Scattered Light in Direct-Drive Implosions Driven by Polarization Smoothing.

Laser-direct-drive symmetric implosions on OMEGA illuminate a target with 60 laser beams and are designed to produce spherical implosions. Each beam is smoothed using orthogonal polarizations obtained by passing the laser beams through distributed polarization rotators (DPRs). Observations of light scattered from OMEGA implosions do not show the expected symmetry and have much larger variation than standard predictions. For the first time, we have quantified the scattered-light nonuniformity from individual beams and identified the DPRs as the source of the enhanced nonuniformity. An instrument was invented that isolated and measured the variation in the intensity and polarization of the light scattered from each OMEGA beam. The asymmetric intensity and polarization measurements are explained when the on-target offsets between the two orthogonal polarizations produced by the DPRs are modeled using a 3D cross-beam energy transfer (CBET) code that tracks the polarizations of each beam. The time-integrated nonuniformity in laser absorption and scattered light due to CBET and the DPR polarization offsets during high-performance OMEGA implosions is predicted to be significant and dominated by low spherical harmonic mode numbers. The nonuniformity is predicted to be greatly reduced by replacing the DPRs with new optics that create smaller offsets.

Cross-beam energy transfer saturation by ion trapping-induced detuning

The performance of direct-drive inertial confinement fusion implosions relies critically on the coupling of laser energy to the target plasma. Cross-beam energy transfer (CBET), the resonant exchange of energy between intersecting laser beams mediated by ponderomotively driven ion-acoustic waves (IAWs), inhibits this coupling by scattering light into unwanted directions. The variety of beam intersection angles and varying plasma conditions in an implosion results in IAWs with a range of phase velocities. Here, we show that CBET saturates through a resonance detuning that depends on the IAW phase velocity and that results from trapping-induced modifications to the ion distribution functions. For smaller phase velocities, the modifications to the distribution functions can rapidly thermalize in the presence of mid-Z ions, leading to a blueshift in the resonant frequency. For larger phase velocities, the modifications can persist, leading to a redshift in the resonant frequency. Ultimately, these results may reveal pathways toward CBET mitigation and inform reduced models for radiation hydrodynamics codes to improve their predictive capability.

Inverse ray tracing on icosahedral tetrahedron grids for non-linear laser plasma interaction coupled to 3D radiation hydrodynamics

A novel approach to efficiently model 3-D laser plasma interactions at fluid scales is presented. This method, implemented in the IFRIIT propagation code developed at CELIA, relies on inverse ray tracing to compute laser fields at arbitrary locations in a plasma. This enables to describe the fields at high order in space compared to standard forward ray tracing approaches. In addition, inverse ray tracing enables the use of etalon integral methods to reconstruct caustic fields and greatly speeds up calculations of cross-beam energy transfer by decoupling the ray amplitude and ray phase calculations. A comparison of the inverse and forward methods for 3-D calculations of fields in presence or not of cross-beam energy transfer illustrates the significant advantages of the inverse method. Conversely, while the inverse method is well suited to most spherical plasma profiles, it currently cannot treat concave profiles or target holders. The coupling of IFRIIT with the 3-D ASTER radiative hydrodynamics code developed at the Laboratory for Laser Energetics is then presented. ASTER and IFRIIT resolve their respective equations on separate grids which communicate through interpolation. As such, IFRIIT uses a dedicated laser grid adapted to the computations at play, which also allows to use different parallelization methods for both codes: block decomposition for the hydrodynamics versus domain duplication for the laser. Applications to direct-drive implosions for inertial confinement fusion are presented, for which a geodesic icosahedron grid is implemented in IFRIIT. The performances of the ASTER/IFRIIT coupling are demonstrated by conducting simulations of cryogenic implosions performed on the OMEGA laser system, in presence of various sources of 3-D effects; laser port geometry, cross-beam energy transfer, beam imbalance and target mis-alignment. Comparison with neutron data, measured through bang-time, for a cryogenic implosion experiment shows an excellent agreement for the laser-plasma coupling.

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.

Trending low mode asymmetries in NIF capsule drive using a simple viewfactor metric *

The mode-1 x-ray drive asymmetry of indirect-drive Inertial Confinement Fusion(ICF) implosions at the National Ignition Facility(NIF) has been estimated using a simple static ViewFactor model. The model takes as input measured laser performance data in the foot and peak, the hohlraum configuration, and laser to hohlraum pointing. These estimates are compared with neutron time-of-flight measurements of directionality and magnitude of the resultant hotspot bulk velocity (~20–100 μm/ns) for 39 NIF shots using High Density Carbon (HDC) ablators and show strong correlation on a statistically significant number of shots. The most important factors identified so far are random quad-to-quad peak power laser imbalances, the presence of lossy diagnostic windows and gaps on the hohlraum waist, capsule sag and capsule thickness mode 1. Typical mode-1 asymmetry in drive is currently ~0.5% for many of these sources on their own and, when summed, can lead to a neutron hotspot velocity of up to 100 μm /ns and a reduction in yield of 35% for current NIF DT layered implosions. Our goal is to identify, quantify and mitigate all potential sources of mode-1 asymmetry (which also include target and laser alignment imperfections, foot power and Cross Beam Energy Transfer imbalances) to enable higher quality implosions on NIF.

Unabsorbed light beamlets for diagnosing coronal density profiles and absorption nonuniformity in direct-drive implosions on OMEGA.

Laser light scattered from a target is the most-direct measurement for diagnosing laser absorption in a direct-drive implosion. The 3ω gated optical imager beamlets diagnostic images unabsorbed light from all 60 OMEGA beams as distinct "beamlet" spots for each beam. The implosion can be diagnosed using the position and intensity of these beamlets. The position of each beamlet in the image is determined by refraction and can be used to fit the coronal plasma density profile of the implosion. The inferred plasma density profiles are comparable to the profiles predicted by the 1D hydrodynamics code LILAC but suggest that the predictions underestimate the density farther out in the corona. The intensity of light in each spot depends on the cumulative effects of absorption and cross-beam energy transfer along the beamlet's path through the corona. The measured variation in intensity and polarization between similar spots indicates that absorption during OMEGA implosions is less uniform than previously known.

A transmitted-beam diagnostic for the wavelength-tunable UV drive beam on OMEGA.

A transmitted-beam diagnostic (P9TBD) was developed as part of a new experimental platform used to study laser-plasma interactions on OMEGA. Located in the opposing port to the wavelength-tunable (350nm to 353nm) UV drive beam, the P9TBD characterizes the beam after it propagates through an undersense plasma. The instrument consists of a large-aperture window that allows light to exit the target chamber and project onto a thin sheet of semi-transparent diffuser material. Light transmitted through the diffuser is recorded using a time-integrated camera and a fiber-optically coupled streaked spectrometer, providing measurements of the energy, power, fluence, polarization, and spectrum of the transmitted beam. The diagnostic enables direct observation of a variety of cross-beam energy transfer phenomena, such as wavelength detuning, polarization effects, and gain saturation.

Cross-Beam Energy Transfer Saturation by Ion Heating.

We measure cross-beam energy transfer (CBET) saturation by ion heating in a gas-jet plasma characterized using Thomson scattering. A wavelength-tunable ultraviolet (UV) probe laser beam interacts with four intense UV pump beams to drive large-amplitude ion-acoustic waves. For the highest-intensity interactions, the power transfer to the probe laser drops, demonstrating ion-acoustic wave saturation. Over this time, the ion temperature is measured to increase by a factor of 7 during the 500-ps interaction. Particle-in-cell simulations show ion trapping and a subsequent ion heating consistent with measurements. Linear kinetic CBET models are found to agree well with the observed energy transfer when the measured plasma conditions are used.