Cross-beam Energy Transfer Models Research Articles

Enhanced sensitivity to target offset when using cross-beam energy transfer mitigation techniques in direct-drive inertial confinement fusion implosions

In direct-drive inertial confinement fusion, target offset from the target chamber center (or center of beam convergence) may lead to significant implosion asymmetry and fusion yield degradation. In addition, cross-beam energy transfer (CBET) has been shown to be a significant source of laser energy scattering and leads to a reduction in implosion velocity and yield. To improve energy coupling and implosion performance, several techniques for CBET mitigation have been proposed. Recent simulations, however, have shown that CBET also substantially mitigates the effect of target offset on implosion asymmetry and yield [Anderson et al., Phys. Plasmas 27, 112713 (2020)]. Furthermore, the inclusion of CBET models in radiation-hydrodynamics codes was shown to greatly improve agreement between simulations and experiments involving substantial target offset distances. This paper explores the intensity dependence of this CBET–offset effect. In addition, it is shown that enhanced sensitivity to target offset can be expected when CBET-mitigation techniques are used in direct-drive implosions. This is shown through simulations of two such CBET-mitigation techniques on the OMEGA laser: (1) decreased beam-to-target radius, and (2) beam-to-beam frequency detuning. For the typical target offset distances (<15 μm) observed in experiments on OMEGA, however, overall yield is still anticipated to be substantially higher when CBET-mitigation techniques are employed.

Ray-based cross-beam energy transfer modeling for broadband lasers

Broadband lasers have the potential to mitigate cross-beam energy transfer (CBET) in direct-drive inertial confinement fusion (ICF) experiments. A quantitative assessment of the bandwidth required for CBET mitigation necessitates the development of broadband ray-based CBET models that can be implemented in the radiation-hydrodynamic codes that are used to design ICF experiments. Two different approaches to broadband ray-based CBET modeling (discrete and fixed spectrum) are developed and compared to wave-based calculations. Both approaches give good agreement with wave-based calculations in ICF-relevant configurations. Full-scale 3D calculations show that the bandwidth required for adequate CBET mitigation increases with increasing scale and drive intensity.

Time-dependent saturation and physics-based nonlinear model of cross-beam energy transfer

The nonlinear physics of cross-beam energy transfer (CBET) for multi-speckled laser beams is examined using large-scale particle-in-cell simulations for a range of laser and plasma conditions relevant to indirect-drive inertial confinement fusion (ICF) experiments. The time-dependent growth and saturation of CBET involve complex, nonlinear ion and electron dynamics, including ion trapping-induced enhancement and detuning, ion acoustic wave (IAW) nonlinearity, oblique forward stimulated Raman scattering (FSRS), and backward stimulated Brillouin scattering (BSBS) in a CBET-amplified seed beam. Ion-trapping-induced detuning of CBET is captured in the kinetic linear response by a new δf-Gaussian-mixture algorithm, enabling an accurate characterization of trapping-induced non-Maxwellian distributions. Ion trapping induces nonlinear processes, such as changes to the IAW dispersion and nonlinearities (e.g., bowing and self-focusing), which, together with pump depletion, FSRS, and BSBS, determine the time-dependent nature and level of CBET gain as the system approaches a steady state. Using VPIC simulations at intensities at and above the onset threshold for ion trapping and the insight from the time-dependent saturation analyses, we construct a nonlinear CBET model from local laser and plasma conditions that predicts the CBET gain and the energy deposition into the plasma. This model is intended to provide a more accurate, physics-based description of CBET saturation over a wide range of conditions encountered in ICF hohlraums compared with linear CBET gain models with ad hoc saturation clamps often used in laser ray-based methods in multi-physics codes.

Validation of ray-based cross-beam energy transfer models

Ray-based cross-beam energy transfer (CBET) models have become a common feature of the radiation-hydrodynamic codes used to simulate inertial confinement fusion experiments. These models are necessary for achieving better agreement with experimental measurements, but their detailed implementation can vary widely between the codes and often rely on artificial multipliers. To address this, a series of 2D and 3D test cases has been developed with validated solutions from wave-based calculations. Comparisons of various ray-based CBET models to the wave-based calculations highlight the essential physics that is required for accurate ray-based CBET modeling. Quantitative comparison metrics and/or field data from the wave-based calculations have been made available for use in the validation of other ray-based CBET codes.

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.

Enhanced direct-drive implosion performance on NIF with wavelength separation

Cross-beam energy transfer (CBET) can significantly affect the energy coupling and symmetry of direct-drive implosions. We report on a series of direct-drive shots with 2.1 mm outer diameter capsules conducted on NIF for diagnostic development and calibration in which the wavelength separation (Δλ) between the inner and outer cone beams was varied. We observe a strong improvement in performance as Δλ is applied, with the nuclear yield increasing by up to a factor of 4×. Other data including the nuclear bang time and implosion symmetry suggest that increasing Δλ suppresses CBET and improves both the energy coupling and drive symmetry. These results provide a strong and important benchmark for CBET models applicable to direct-drive ignition designs.

Ray-based modeling of cross-beam energy transfer at caustics

Cross-beam energy transfer (CBET) is a laser-plasma instability that significantly impacts laser energy deposition in laser-driven inertial confinement fusion (ICF) experiments. Radiation-hydrodynamics simulations, which are used to design and tune ICF implosions, use ray-based CBET models, but existing models require artificial multipliers to conserve energy and to obtain quantitative agreement with experiments. The discretization of the ray trajectories in traditional ray-based CBET models does not account for the rapid variation in CBET gain as rays pass through caustics. We introduce a model that allows one to treat caustics much more accurately and greatly improves energy conservation. The ray-based CBET calculations show excellent agreement with laser absorption from two-dimensional wave-based calculations (0.3% difference) and a three-dimensional 60-beam OMEGA implosion (2.4% difference) without artificial multipliers.

Properties of hot-spot emission in a warm plastic-shell implosion on the OMEGA laser system

A warm plastic-shell implosion is performed on the OMEGA laser system. The measured corona plasma evolution and shell trajectory in the acceleration phase are reasonably simulated by the one-dimensional lilac simulation including the nonlocal and cross-beam energy transfer models. The results from analytical thin-shell model reproduce the time-dependent shell radius by lilac simulation and also the hot-spot x-ray-emissivity profile at stagnation predicted by spect3d. In the spect3d simulations within a clean implosion, a U-shaped hot-spot radius evolution can be observed with the Kirkpatrick-Baez microscope response (the photon energy is from 4 to 8 keV). However, a fading-away hot-spot radius evolution is measured in OMEGA warm plastic-shell implosion because of mixings. To recover the measured hot-spot x-ray emissivity profile at stagnation, a nonisobaric hot-spot model is built and the normalized hot-spot temperature, density, and pressure profiles (normalized to the corresponding target-center values) are obtained.

Isolating and quantifying cross-beam energy transfer in direct-drive implosions on OMEGA and the National Ignition Facility

The angularly resolved mass ablation rates and ablation-front trajectories for Si-coated CH targets were measured in direct-drive inertial confinement fusion experiments to quantify cross-beam energy transfer (CBET) while constraining the hydrodynamic coupling. A polar-direct-drive laser configuration, where the equatorial laser beams were dropped and the polar beams were repointed from a symmetric direct-drive configuration, was used to limit CBET at the pole while allowing it to persist at the equator. The combination of low- and high-CBET conditions observed in the same implosion allowed for the effects of CBET on the ablation rate and ablation pressure to be determined. Hydrodynamic simulations performed without CBET agreed with the measured ablation rate and ablation-front trajectory at the pole of the target, confirming that the CBET effects on the pole are small. The simulated mass ablation rates and ablation-front trajectories were in excellent agreement with the measurements at all angles when a CBET model based on Randall's equations [C. J. Randall et al., Phys. Fluids 24, 1474 (1981)] was included into the simulations with a multiplier on the CBET gain factor. These measurements were performed on OMEGA and at the National Ignition Facility to access a wide range of plasma conditions, laser intensities, and laser beam geometries. The presence of the CBET gain multiplier required to match the data in all of the configurations tested suggests that additional physics effects, such as intensity variations caused by diffraction, polarization effects, or shortcomings of extending the 1-D Randall model to 3-D, should be explored to explain the differences in observed and predicted drive.

Early-Time Symmetry Tuning in the Presence of Cross-Beam Energy Transfer in ICF Experiments on the National Ignition Facility

On the National Ignition Facility, the hohlraum-driven implosion symmetry is tuned using cross-beam energy transfer (CBET) during peak power, which is controlled by applying a wavelength separation between cones of laser beams. In this Letter, we present early-time measurements of the instantaneous soft x-ray drive at the capsule using reemission spheres, which show that this wavelength separation also leads to significant CBET during the first shock, even though the laser intensities are 30× smaller than during the peak. We demonstrate that the resulting early drive P2/P0 asymmetry can be minimized and tuned to <1% accuracy (well within the ±7.5% requirement for ignition) by varying the relative input powers between different cones of beams. These experiments also provide time-resolved measurements of CBET during the first 2 ns of the laser drive, which are in good agreement with radiation-hydrodynamics calculations including a linear CBET model.

Towards an integrated model of the NIC layered implosions

A detailed simulation-based model of the June 2011 National Ignition Campaign (NIC) cryogenic DT experiments is presented. The model is based on integrated hohlraum-capsule simulations that utilize the best available models for the hohlraum wall, ablator, and DT equations of state and opacities. The calculated radiation drive was adjusted by changing the input laser power to match the experimentally measured shock speeds, shock merger times, peak implosion velocity, and bangtime. The crossbeam energy transfer model was tuned to match the measured time-dependent symmetry. Mid-mode mix was included by directly modeling the ablator and ice surface perturbations up to mode 60. Simulated experimental values were extracted from the simulation and compared against the experiment. The model adjustments brought much of the simulated data into closer agreement with the experiment, with the notable exception of the measured yields, which were 15-40% of the calculated yields.

A high-resolution integrated model of the National Ignition Campaign cryogenic layered experiments

A detailed simulation-based model of the June 2011 National Ignition Campaign cryogenic DT experiments is presented. The model is based on integrated hohlraum-capsule simulations that utilize the best available models for the hohlraum wall, ablator, and DT equations of state and opacities. The calculated radiation drive was adjusted by changing the input laser power to match the experimentally measured shock speeds, shock merger times, peak implosion velocity, and bangtime. The crossbeam energy transfer model was tuned to match the measured time-dependent symmetry. Mid-mode mix was included by directly modeling the ablator and ice surface perturbations up to mode 60. Simulated experimental values were extracted from the simulation and compared against the experiment. Although by design the model is able to reproduce the 1D in-flight implosion parameters and low-mode asymmetries, it is not able to accurately predict the measured and inferred stagnation properties and levels of mix. In particular, the measured yields were 15%–40% of the calculated yields, and the inferred stagnation pressure is about 3 times lower than simulated.

Increasing Hydrodynamic Efficiency by Reducing Cross-Beam Energy Transfer in Direct-Drive-Implosion Experiments

A series of experiments to determine the optimum laser-beam radius by balancing the reduction of cross-beam energy transfer (CBET) with increased illumination nonuniformities shows that the hydrodynamic efficiency is increased by ∼35%, which leads to a factor of 2.6 increase in the neutron yield when the laser-spot size is reduced by 20%. Over this range, the absorption is measured to increase by 15%, resulting in a 17% increase in the implosion velocity and a 10% earlier bang time. When reducing the ratio of laser-spot size to a target radius below 0.8, the rms amplitudes of the nonuniformities imposed by the smaller laser spots are measured at a convergence ratio of 2.5 to exceed 8 μm and the neutron yield saturates despite increasing absorbed energy, implosion velocity, and decreasing bang time. The results agree well with hydrodynamic simulations that include both nonlocal and CBET models.