Cross-beam Energy Transfer Research Articles

Optimization Methodology of Polar Direct-Drive Illumination for the National Ignition Facility.

Improved laser illumination uniformity drives shocks and implosions to create more extreme high energy density environments. Predominantly, the geometry of experiments that can be performed is dictated by the layout of beams at laser facilities, limiting interfacility and multiscale investigations. This Letter presents the first automated, algorithmic approach for generating illumination configurations for high energy density experiments. The method is demonstrated in comparison to a polar direct-drive solid target experiment at the National Ignition Facility. The new illumination configuration is simulated to create greater than ×3 higher peak pressure and almost ×2 higher density by maintaining better shock uniformity. The optimization process is performed with reduced computational expense and isotropic plasma profiles while accounting for the impact of cross-beam energy transfer.

Spatial-temporal modulation method of nanosecond laser for the double-cone ignition scheme

In order to improve the stability of the pulse, realize the high requirements of the direct drive ignition design for the uniformity of the target irradiation, reduce the interference of laser plasma instability, and improve the laser-target coupling efficiency, a nanosecond laser spatial-temporal modulation of high-power laser driver for double-cone ignition (DCI) research was proposed. Under the premise of satisfying the near-isentropic compression waveform of driving implosion, the time-power curves of all sub-beams in the facility are redistributed to reduce the waveform contrast ratio of each sub-beam. A fewer number of sub-beams are utilized to generate low-power foot pulses, which are focused on the target surface of the initial radius. And the remaining sub-beams are utilized to generate high-power driving main pulses, which are focused on a relatively small target surface. It is shown that the stability of the time-power curve of each sub-beam and the power balance control ability can be effectively improved by redistributing. At the same time, the variable focal spot control can be realized to reduce the influence of cross-beam energy transfer (CBET).

Design and modeling of indirectly driven magnetized implosions on the NIF

The use of magnetic fields to improve the performance of hohlraum-driven implosions on the National Ignition Facility (NIF) is discussed. The focus is on magnetically insulated inertial confinement fusion, where the primary field effect is to reduce electron-thermal and alpha-particle loss from the compressed hotspot (magnetic pressure is of secondary importance). We summarize the requirements to achieve this state. The design of recent NIF magnetized hohlraum experiments is presented. These are close to earlier shots in the three-shock, high-adiabat (BigFoot) campaign, subject to the constraints that magnetized NIF targets must be fielded at room-temperature, and use ≲1 MJ of laser energy to avoid the risk of optics damage from stimulated Brillouin scattering. We present results from the original magnetized hohlraum platform, as well as a later variant that gives a higher hotspot temperature. In both platforms, imposed fields (at the capsule center) of up to 28 T increase the fusion yield and hotspot temperature. Integrated radiation-magneto-hydrodynamic modeling with the Lasnex code of these shots is shown, where laser power multipliers and a saturation clamp on cross-beam energy transfer are developed to match the time of peak capsule emission and the P2 Legendre moment of the hotspot x-ray image. The resulting fusion yield and ion temperature agree decently with the measured relative effects of the field, although the absolute simulated yields are higher than the data by 2.0−2.7×. The tuned parameters and yield discrepancy are comparable for experiments with and without an imposed field, indicating the model adequately captures the field effects. Self-generated and imposed fields are added sequentially to simulations of one BigFoot NIF shot to understand how they alter target dynamics.

How numerical simulations helped to achieve breakeven on the NIF

The inertial confinement fusion program relies upon detailed simulations with inertial confinement fusion (ICF) codes to design targets and to interpret the experimental results. These simulations treat as much physics from essential principles as is practical, including laser deposition, cross beam energy transfer, x-ray production and transport, nonlocal thermal equilibrium kinetics, thermal transport, hydrodynamic instabilities, thermonuclear burn, and transport of reaction products. Improvements in radiation hydrodynamic code capabilities and vast increases in computing power have enabled more realistic, accurate 3D simulations that treat all known asymmetry sources. We describe how numerical simulations helped to guide the program, assess the impediments to breakeven, and optimize every aspect of target design. A preshot simulation of the first National Ignition Facility experiment that surpassed breakeven predicted an increased yield that matches the experimental result, within the preshot predicted uncertainty, with a target gain of 1.5. We will cover the key developments in Lawrence Livermore National Laboratory ICF codes that enabled these simulations and give specific examples of how they helped to guide the program.

Experimental investigation on cross-beam energy transfer between P-polarized lasers at 45-deg incidence

In this paper, we report the first experimental results on cross-beam energy transfer (CBET) at the Shengguang-II laser facility, in which two p-polarized laser beams irradiated planar targets at 45-deg incidence orthogonally. Frequency shifts of 0 and 0.06% were added between the two beams to investigate the relation of CBET to the degree of frequency shift. Enhancement of scattering was observed in the two-beam configuration with respect to the sum of the two single-beam configurations, indicating CBET was developed by the interaction of the two beams in the cases both with and without the frequency shift. When time delays were added between the seed and the pump pulses, scatter from the seed was enhanced, which further confirmed the existence of CBET in the experiments. The amplifications of the seed light by CBET with and without the frequency shift were sequentially ∼3.3 and ∼2.0 when the two beams were synchronized, and the energy loss due to CBET within the full aperture of the final optics of the pump to the total laser energy was ∼4% with the frequency shift. Calculations suggest that a more than 0.2% frequency shift may be needed to mitigate CBET under experimental laser-plasma conditions.

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.

Control of laser-plasma instabilities by non-collinear polychromatic light

Normal broadband lasers with collinear polychromatic components have immense potential for mitigating laser plasma instabilities (LPIs). However, the projection complexity of collinear polychromatic light (CPL) is a significant challenge owing to the demand for a large bandwidth and beamlet number. Here, we propose a theoretical LPI model and optical design for non-collinear polychromatic light (NCPL), which has a small angle ∼4∘ and large frequency difference ∼1% between the double-color beamlets. LPI models of the NCPL demonstrate a decoupling threshold for the shared daughter waves under a multibeam configuration. Compared with the CPL, the wavevector couplings of LPIs are further reduced by the introduced angle. Therefore, both the growth rate and saturation level of LPIs are greatly mitigated by using the NCPL. The two- and three-dimensional simulation results indicate that the NCPL reduces the absolute and convective decoupling thresholds of the CPL and is sufficient to effectively mitigate the reflectivity, hot-electron generation, and intensity of cross-beam energy transfer. An optical design for the efficient generation of ultraviolet NCPL has been presented based on the unsaturated optical parametric amplification and non-collinear sum-frequency generation.

Effects of ion trapping and fluctuations of electron temperature and plasma flow on cross-beam energy transfer

The influences of ion trapping and fluctuations of electron temperature and plasma flow on cross-beam energy transfer (CBET) are examined using two- and three-dimensional particle-in-cell simulations in parameter regimes relevant to recent CBET experiments at the OMEGA laser facility. In mid-Z plasma irradiated by an intense pump beam and weaker probe beam, ion trapping, collisional de-trapping, and plasma flow induced by thermal effects are shown to affect the CBET gain. Ion trapping can enhance or detune the CBET resonance [Nguyen et al., Phys. Plasmas 28, 082705 (2021)]. Collisional de-trapping can affect the CBET gain at low seed beam intensity near the onset threshold for ion trapping. Thermal-effects-induced flow can also detune the CBET resonance at a level comparable to that from trapping at low seed beam intensity. As a consequence, the CBET gain is sensitive to collisions and dimensionality at low seed beam intensity where ion trapping is weak but is insensitive to collisions and dimensionality at high seed beam intensity where ion trapping is strong.

Laser-direct-drive fusion target design with a high-Z gradient-density pusher shell.

Laser-direct-drive fusion target designs with solid deuterium-tritium (DT) fuel, a high-Z gradient-density pusher shell (GDPS), and a Au-coated foam layer have been investigated through both 1D and 2D radiation-hydrodynamic simulations. Compared with conventional low-Z ablators and DT-push-on-DT targets, these GDPS targets possess certain advantages of being instability-resistant implosions that can be high adiabat (α≥8) and low hot-spot and pusher-shell convergence (CR_{hs}≈22 and CR_{PS}≈17), and have a low implosion velocity (v_{imp}<3×10^{7}cm/s). Using symmetric drive with laser energies of 1.9 to 2.5MJ, 1D lilac simulations of these GDPS implosions can result in neutron yields corresponding to ≳50-MJ energy, even with reduced laser absorption due to the cross-beam energy transfer (CBET) effect. Two-dimensional draco simulations show that these GDPS targets can still ignite and deliver neutron yields from 4 to ∼10MJ even if CBET is present, while traditional DT-push-on-DT targets normally fail due to the CBET-induced reduction of ablation pressure. If CBET is mitigated, these GDPS targets are expected to produce neutron yields of >20MJ at a driven laser energy of ∼2MJ. The key factors behind the robust ignition and moderate energy gain of such GDPS implosions are as follows: (1) The high initial density of the high-Z pusher shell can be placed at a very high adiabat while the DT fuel is maintained at a relatively low-entropy state; therefore, such implosions can still provide enough compression ρR>1g/cm^{2} for sufficient confinement; (2) the high-Z layer significantly reduces heat-conduction loss from the hot spot since thermal conductivity scales as ∼1/Z; and (3) possible radiation trapping may offer an additional advantage for reducing energy loss from such high-Z targets.

Exploration of cross-beam energy transfer mitigation constraints for designing an ignition-scale direct-drive inertial confinement fusion driver

The compression of direct-drive inertial confinement fusion (ICF) targets is strongly impacted by cross-beam energy transfer (CBET), a laser-plasma instability that limits ablation pressure by redirecting laser energy outward and that is projected to be mitigated by laser bandwidth. Here, we explore various CBET mitigation constraints to guide the design of future ICF facilities. First, we find that the flat, Gaussian, and Lorentzian spectral shapes have similar CBET mitigation properties, and a flat shape with nine spectral lines is a good surrogate for what can be obtained with other spectral shapes. Then, we conduct a comprehensive study across energy scales and ignition designs. 3D hydrodynamic simulations are used to derive an analytical model for the expected CBET mitigation as a function of laser and plasma parameters. From this model, we study the bandwidth requirements of conventional and shock ignition designs across four different energy scales and find that they require between 0.5 and 3±0.2% relative bandwidth. Best mitigation is achieved when the beam radius over critical radius Rb/Rc is kept low during the drive while the plasma temperature is kept high. In a steady state, we find that the bandwidth required to mitigate 85% of CBET scales as (Rb/Rc)2.15Ln−0.58I0.7, where Ln is the density scale length, and I the laser intensity. Finally, we find that the chamber beam port layout does not influence CBET mitigation. In the case of a driver using many monochromatic beamlets, we find that ∼10 beamlets per port is required, with diminishing returns above ∼20.

Cross-beam energy transfer in conditions relevant to direct-drive implosions on OMEGA

In cross-beam energy transfer (CBET), the interference of two laser beams ponderomotively drives an ion-acoustic wave that coherently scatters light from one beam into the other. This redirection of laser beam energy can severely inhibit the performance of direct-drive inertial confinement fusion (ICF) implosions. To assess the role of nonlinear and kinetic processes in direct-drive-relevant CBET, the energy transfer between two laser beams in the plasma conditions of an ICF implosion at the OMEGA laser facility was modeled using particle-in-cell simulations. For typical laser beam intensities, the simulations are in excellent agreement with linear kinetic theory, indicating that nonlinear processes do not play a role in direct-drive implosions. At higher intensities, CBET can be modified by pump depletion, backward stimulated Raman scattering, or ion trapping, depending on the plasma density.

Suppressing parametric instabilities in direct-drive inertial-confinement-fusion plasmas using broadband laser light

It has long been recognized that broadband laser light has the potential to control parametric instabilities in inertial-confinement-fusion (ICF) plasmas. Here, we use results from laser-plasma-interaction simulations to estimate the bandwidth requirements for mitigating the three predominant classes of instabilities in direct-drive ICF implosions: cross-beam energy transfer (CBET), two-plasmon decay (TPD), and stimulated Raman scattering (SRS). We find that for frequency-tripled, Nd:glass laser light, a bandwidth of 8.5 THz can significantly increase laser absorption by suppressing CBET, while ∼13 THz is needed to mitigate absolute TPD and SRS on an ignition-scale platform. None of the glass lasers used in contemporary ICF experiments, however, possess a bandwidth greater than 1 THz and reaching larger values requires the use of an auxiliary broadening technique such as optical parametric amplification or stimulated-rotational-Raman scattering. An arguably superior approach is the adoption of an argon-fluoride (ArF) laser as an ICF driver. Besides having a broad bandwidth of ∼10 THz, the ArF laser also possesses the shortest wavelength (193 nm) that can scale to the high energy/power required for ICF—a feature that helps to mitigate parametric instabilities even further. We show that these native properties of ArF laser light are sufficient to eliminate nearly all CBET scattering in a direct-drive target and also raise absolute TPD and SRS thresholds well above those for broadband glass lasers. The effective control of parametric instabilities with broad bandwidth is potentially a “game changer” in ICF because it would enable higher laser intensities and ablation pressures in future target designs.

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.

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.

Cross beam energy transfer and backward stimulated Brillouin scattering in double-cone ignition experiment

&lt;sec&gt;In the research of direct-drive laser fusion, laser irradiation of a target pellet can stimulate various laser plasma instabilities, such as stimulated Brillouin scattering (SBS) and cross-beam energy transfer (CBET), which significantly reduce the energy coupling efficiency between the laser and target pellet as well as the laser irradiation uniformity, leading the implosion quality to degrade. In the double-cone ignition (DCI) scheme of laser fusion scheme, the diagnosis of SBS and CBET is important owing to the different target configurations and oblique incident laser irradiation from the traditional spherically symmetric direct-drive central ignition scheme. In this paper, a simple and reliable backscattering diagnostic system is developed and applied to the diagnosis of the time-resolved backscattering spectrum at wavelength near 351 nm in a DCI experiment on the Shenguang-II upgrade (SG-IIU) facility. We use the system to carry out an experimental study of the SBS process and CBET process in DCI.&lt;/sec&gt;&lt;sec&gt;The backscattering diagnostic system collects the backscattered light signal through the scattered light by reflector mirror via an optical fiber. The signal is dispersed by a spectrometer and then recorded by a streak camera. The signal contains both the laser reference signal from the frequency doubling crystal and the backscattered light. With the help of the reference signal, the diagnostic system can reliably give the energy fraction of backscattered light. The experimental results show that the energy fraction of backscattered light around 351 nm is not higher than 3%, which is significantly lower than the experimental result of the spherically symmetric irradiation direct-drive central ignition scheme.&lt;/sec&gt;&lt;sec&gt;By analyzing the correlation between the backscattered signal and the laser irradiation conditions and combining the results of a set of comparative experiments, we determine that the backscattered signal contains both CBET and SBS. There is a significant difference in the CBET fraction between the backscattered signal of the #5 laser and the backscattered signal of the #7 laser. By combining the polarisation state of the laser beams, we confirm that this phenomenon is related to the polarisation angle between the laser beams. This finding provides a reference for designing subsequent large-scale laser fusion devices.&lt;/sec&gt;

3D simulations of inertial confinement fusion implosions part 1: inline modeling of polarized cross beam energy transfer and subsequent drive anomalies on OMEGA and NIF

Inertial confinement fusion experiments are sensitive to cross-beam energy transfer (CBET), a laser-plasma instability that redistributes laser energy in the coronal plasma through self-generated ion acoustic wave (IAW) gratings. The detailed CBET coupling depends on the polarization state of the crossing wavefields. CBET itself can also scramble the beam polarizations by inducing ellipticity through the IAW grating, and rotating the seed polarization toward that of the pump. We develop a ray-based model that describes the polarized CBET coupling and that is compatible with the framework of 3D inline radiative hydrodynamics simulations. The model is implemented in the ASTER/IFRIIT code and verified against an academic test case and an offline polarized CBET post-processor. It is then applied to the detailed configuration of the distributed polarization rotator system on OMEGA, where results highlight how polarized CBET induces significant low modes in the collisional absorption source term. Finally, the modeling is applied to a simple indirect-drive configuration, comparing CBET calculations with 96 unpolarized or polarized beams with 24 unpolarized quads. It is shown that these cases produce similar power amplification per cone of beams grouped with similar polar angles. However, the 96 beam geometry itself is found to reduce azimuthal variations in quad power after the interaction and favors beams with larger polar angles within the cones, an effect that is amplified by the polarized CBET. Application of the model to inline calculations of OMEGA implosions are presented in a companion paper.

3D simulations of inertial confinement fusion implosions part 2: systematic flow anomalies and impact of low modes on performances in OMEGA experiments

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, which were used to assess the impact of the current distributed polarization rotators (DPRs) on OMEGA as well as other known sources of asymmetry. Applied to OMEGA implosions, the simulations predict bang times with no need for ad hoc multipliers, as well as yields—if you separately account for the impacts of imprint and fuel age. The magnitude of the flow is well reproduced when the low mode sources are large, whereas the modeling of the stalk is thought to be required to match the flow magnitude in the remaining cases. For the cases explored in more detail, polarized cross-beam energy transfer (CBET)—the only known systematic drive asymmetry, brought the results closest to the measured flow vectors. The remaining discrepancies are shown to be stemming from the limited knowledge of the laser pointing modes. For typical current levels of beam mispointing, power imbalance, target offset, and asymmetry caused by polarized CBET, low modes degrade the yield by more than 40%. The current strategy of attempting to compensate the mode-1 asymmetry with a preimposed target offset recovers only about one-third of the losses caused by the low modes due to the dynamic nature of the multiple asymmetries and the presence of low modes other than l = 1. Therefore, addressing the root causes of the drive asymmetries is apt to be more beneficial. To that end, one possible solution to the specific issue of polarized CBET (10 µm DPRs) is shown to work well.

Cross-beam energy transfer between spatially smoothed laser beams

The crossing of two spatially smoothed laser beams amounts to the crossings of a large number of speckles. The energy transfer between two of these speckles is mediated by laser induced electron/ion density ripples that act as a Bragg grating. In a weakly Landau-damped plasma, this ion acoustic wave (IAW) may propagate from one crossing region to another, hence perturbing the local electron/ion grating [Oudin et al. Phys. Rev. Lett. 127, 265001 (2021)] even without phase shift between IAWs. In this paper, we investigate how the phase-shifted IAWs generated at the speckle scale interfere and affect the overall energy exchange. To this aim, we perform 2D particle-in-cell simulations with in-phase and out-of-phase Gaussian beams. In the latter situation, which better matches a smoothed laser beam, we find that the destructive interferences between the ion waves significantly reduce the energy exchange compared to the plane wave case. Additional 2D particle-in-cell simulations with random phase plate smoothed laser beams confirm the relevance of this effect in carbon plasma. A second effect is that cross-beam energy transfer (CBET) inhibition persists in strongly damped plasmas when the speckle radius is comparable with the IAW damping distance. There, the reduction in the IAW amplitude is attributed to the smallness of the speckle's envelop. These results are supported by a simple model that analytically estimates the CBET and clearly shows that neglecting the inhomogeneities in the laser intensity would usually lead to an overestimate of the energy exchange.

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.

Optimization of Backscatter and Symmetry for Laser Fusion Experiments Using Multiple Tunable Wavelengths

A new additional wavelength-tuning capability has been implemented on the National Ignition Facility (NIF) laser allowing for unprecedented control of crossed-beam energy transfer (CBET) between all groups of beams for better performance of indirect-drive inertial confinement fusion (ICF) ignition experiments. In particular, this advance allows for negation and reversal of flow-induced CBET and the rebalancing of the intensity of different groups of beams within an indirect-drive (ICF) hohlraum. Experiments conducted at the NIF using a 1.1 MJ laser pulse with peak power of 390 TW demonstrate this high level of control through measurements of the precise changes to stimulated Brillouin scattering, typically driven by flow-induced CBET at the end of the pulse. Additionally, this new capability is shown to be able to predictably control gold-wall plasma expansion in the target driven by early-time flow-induced CBET. Estimates of early-time CBET from the wall expansion are shown to be consistent with simulation expectations. This new additional capability to control symmetry and backscatter expands the design space of current experiments and provides extra margin for increased laser energy in near-future experiments.