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International audience; 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.

The study presented in this paper focuses on the analysis of rubbing interactions—including unilateral contact and dry friction—between a rotating fan blade and a rigid casing by frequency domain methods. Two previously published Harmonic Balance Method-based methodologies are assessed: (1) an approach relying on augmented Lagrangians and (2) a second method using a regularized penalty law combined with a Lanczos σ-approximation filter. As a reference point for this comparison, a time-domain numerical strategy relying on a Lagrange multiplier-based contact treatment is considered. All computations are run with the NASA rotor 67 fan blade, an open industrial blade geometry. As it undergoes structural contacts, this blade features an intricate dynamics response, thus making it a challenging case study for nonlinear iterative solvers. The contact scenario is chosen to be an ovalization of the casing with no external forcing. This scenario induces highly nonlinear responses of the blade and complex phenomena such as isolated frequency response curves. The results presented underline a very good agreement of the different strategies with the reference time marching approach. An in-depth comparison is made with an emphasis on nonlinear frequency response curves (NFRC) and time signals. Finally, a physical analysis of the encountered isolas is presented through an in-depth investigation of the main modal contributions for each computed solution. In the end, this paper provides new qualitative elements allowing for a better understanding of rubbing interactions that may not be efficiently obtained with time marching procedures.

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 study presented in this paper focuses on the analysis of rubbing interactions — including unilateral contact and dry friction — between a rotating fan blade and a rigid casing by frequency domain methods. Two previously published Harmonic Balance Method-based methodologies are assessed: 1) an approach relying on augmented lagrangians and 2) a second method using a regularized penalty law combined with a Lanczos σ-approximation filter. Asa reference point for this comparison, a time-domain numerical strategy relying on a Lagrange multiplier-based contact treatment is considered. All computations are run with the NASA rotor 67 fan blade, an open industrial blade geometry. As it undergoes structural contacts, this blade features an intricate dynamics response, thus making it a challenging case study for nonlinear iterative solvers. The contact scenario is chosen to be an ovalization of the casing with no external forcing. This scenario induces highly nonlinear reponses of the blade and complex phenomena such as isolated frequency response curves. The results presented underline a very good agreement of the different strategies with the reference time marching approach. An in-depth comparison is made with an emphasis on nonlinear frequency response curves and time signals. In order to investigate further onto the frequency domain strategies, a comparative analysis is carried out on isolated nonlinear frequency response curves, referred to as isolas. Finally, a physical analysis of these isolas is presented through an in-depth investigation of the main modal contributions for each computed solution. In the end, this paper provides new qualitative elements allowing for a better understanding of rubbing interactions that may not be efficiently obtained with time marching procedures.

This paper investigates the local stability analysis of periodic solutions corresponding to the nonlinear vibration response of an industrial compressor blade, NASA rotor 37, on which are applied different types of nonlinearities. These solutions are obtained using a harmonic balance method-based approach presented in a previous paper. It accounts for unilateral contact and dry friction of the rotating blade against a rigid casing through a regularized penalty law. A Lanczos filtering technique is also employed to mitigate spurious oscillations related to the Gibbs phenomenon thus enhancing the robustness of the solver. In addition, a component mode synthesis technique is used to reduce the dimension of the numerical model. Stability assessment of the computed solutions relies on Floquet theory. It is performed through the computation of the monodromy matrix as well as Hill's method. Both methodologies are applied and thoroughly compared as the severity of the nonlinearity is gradually increased from a cubic spring to three-dimensional contact conditions on a deformed casing. While the presented results underline the applicability of both stability assessment methodologies for all types of nonlinearities, they also put forward the much higher computational effort required when computing the monodromy matrix. Indeed, it is shown that Hill's method yields converged results for significantly lower values of both the number of retained harmonics and the considered number of time steps thus making it a far more efficient method when dealing with industrial models. It is also underlined that the presented results are in excellent agreement with reference solution points obtained with time domain solution methods. Specific implementation tweaks that were found to be of critical importance in order to efficiently assess the stability of computed solutions are also detailed in order to provide a comprehensive view of the challenges inherent to such numerical developments.

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.

We present a parametric scaling of hot electron (HE) generation at quarter critical density from the two-plasmon decay process. The study is conducted with the laser plasma simulation environment code, considering Langmuir decay instabilities (LDI) and laser pump depletion in 2D. The parameter scan is conducted as a function of electron temperature, ion–electron temperature ratio, drive strength, and density scale length. The scaling shows an hot electron (HE) conversion fraction up to 40%, HE fluxes up to [Formula: see text] [Formula: see text], and average temperatures in the range of 30 to 100 keV. The electron angular distributions exhibit two main regions: the plasma “bulk,” characterized by homogeneous emission, up to energies of [Formula: see text] keV depending on the individual laser–plasma conditions, and a HE tail after [Formula: see text] keV. The mid-energy electrons are homogeneously emitted toward the end of the plasma bulk and acquire energy through electron plasma wave (EPW) Landau damping from Langmuir wave collapse and LDI cascade. The HE tail has electrons emitted in the forward direction and at low divergence, due to turbulence and EPW Landau damping from multi-staged acceleration. Finally, the laser power transmitted through the quarter critical region reaches values from [Formula: see text] down to [Formula: see text] for increasing HE generation, with absorption due to EPW collisional damping in the range of [Formula: see text].

International audience; Investigating the potential benefits of the use of magnetic fields in inertial confinement fusion experiments has given rise to experimental platforms like the Magnetized Liner Inertial Fusion approach at the Z-machine (Sandia National Laboratories) or its laser-driven equivalent at OMEGA (Laboratory for Laser Energetics). Implementing these platforms at MegaJoule-scale laser facilities, such as the Laser MegaJoule (LMJ) or the National Ignition Facility (NIF), is crucial to reaching self-sustained nuclear fusion and enlarges the level of magnetization that can be achieved through a higher compression. In this paper, we present a complete design of an experimental platform for magnetized implosions using cylindrical targets at LMJ. A seed magnetic field is generated along the axis of the cylinder using laser-driven coil targets, minimizing debris and increasing diagnostic access compared with pulsed power field generators. We present a comprehensive simulation study of the initial B field generated with these coil targets, as well as two-dimensional extended magnetohydrodynamics simulations showing that a 5 T initial B field is compressed up to 25 kT during the implosion. Under these circumstances, the electrons become magnetized, which severely modifies the plasma conditions at stagnation. In particular, in the hot spot the electron temperature is increased (from 1 keV to 5 keV) while the density is reduced (from 40g/cm3 to 7g/cm3). We discuss how these changes can be diagnosed using x-ray imaging and spectroscopy, and particle diagnostics. We propose the simultaneous use of two dopants in the fuel (Ar and Kr) to act as spectroscopic tracers. We show that this introduces an effective spatial resolution in the plasma which permits an unambiguous observation of the B-field effects. Additionally, we present a plan for future experiments of this kind at LMJ.

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.

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.