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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.

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.

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.

Experiments have been conducted on the OMEGA EP laser facility to study the effect of density scale length and overlapping beam geometry on laser-plasma instabilities near and below the quarter-critical density. Experiments were conducted in both planar geometry (density scale length [Formula: see text] [Formula: see text] 190 to 300 [Formula: see text]m) and spherical geometry ([Formula: see text] [Formula: see text] 150 [Formula: see text]m) with up to four overlapping beams and were designed to have overlapped intensities and density scale lengths comparable to OMEGA spherical experiments, but with many fewer beams. In comparison with previous experiments on OMEGA and National Ignition Facility, it is confirmed that shorter density scale lengths favor the two-plasmon decay (TPD) instability, while longer density scale lengths favor stimulated Raman scattering (SRS). In addition, for experiments at the same scale length and overlapped laser intensity, higher single-beam intensities favor SRS, while a larger number of overlapping beams favor TPD.

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].

The independent-hot-spot model is used to develop an analytic formulation for multibeam laser-plasma instabilities in inhomogeneous plasmas. The model is applied to the absolute two-plasmon-decay instability and shows good agreement with simulations and experiments. The success of the model indicates the emergence of single-speckle behavior for sufficiently large speckles sizes.

Target preheat by superthermal electrons from laser-plasma instabilities is a major obstacle to achieving thermonuclear ignition via direct-drive inertial confinement fusion at the National Ignition Facility (NIF). Polar-direct-drive surrogate plastic implosion experiments were performed on the NIF to quantify preheat levels at an ignition-relevant scale and develop mitigation strategies. The experiments were used to infer the hot-electron temperature, energy fraction, and divergence, and to directly measure the spatial hot-electron energy deposition profile inside the imploding shell. Silicon layers buried in the ablator are shown to mitigate the growth of laser-plasma instabilities and reduce preheat, providing a promising path forward for ignition designs at an on-target intensity of about 10^{15}W/cm^{2}.

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.

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 ([Formula: see text]) as [Formula: see text] 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 [Formula: see text], 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 (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.