On the influence of optical smoothing techniques on cross-beam energy transfer

Abstract

In the context of inertial confinement fusion (ICF) experiments, spatial and temporal laser beam smoothing techniques are used to control the beams propagation in hohlraum plasmas. Currently, spatial and temporal smoothing are either neglected or not properly taken into account in the inline cross beam energy transfer (CBET) models included in the hydrodynamic codes dedicated to the design of these experiments. In some cases, which we will highlight in this study, this simplification leads to important errors in the power transfer of importance for the implosion symmetry of the capsule, either in the direct or indirect drive ICF configurations. In a recent study [A. Oudin et \textit{al}., Phys. Plasmas \textbf{32}, 042706 (2025)], we demonstrated the necessity of accounting for spatial smoothing when modeling CBET, provided that the beams do not have the same wavelength. This work presents a linear kinetic model compared with Hera paraxial fluid simulations and compared with the Smilei particle-in-cell code, demonstrating the important influence of smoothing by spectral dispersion on CBET. Moreover, we demonstrate the importance of accounting for the plasma velocity profile, the beam modulation bandwidth, and the spectral dispersion to better predict the power exchanged between the beams. Additionally, we reveal a strong sensitivity of this power transfer to the synchronization of the phase modulators.

Figures (11)

• Figure 1: FIG 0: Envelope of the ponderomotive (Eq. \ref{['pondero beat']}) and acoustic gratings (Eq. \ref{['dne']}) along the acoustic-wave propagation direction $(Oy)$ in a monospeckle configuration ($\phi_{\mathbf{n}_1} \equiv 0$ and $\phi_{\mathbf{n}_2} \equiv 0$), normalized to their maximum values. The case in which the beams have the same wavelength and intersect in a plasma with any flow along the $(Oy)$ direction is represented by the green dashed line. Situations where the plasma is stationary and when there is a frequency detuning, $\omega/kc_s = 0.8, 1.0$, between the beams are represented by the red dash-dotted curves and blue dotted curves, respectively. We consider a carbon plasma and use: $N = 30$, $\theta = 12^\circ$, $\lambda_0 = 0.351\,\mu\text{m}$, $\textbf{u}_1 \parallel \textbf{u}_2$ and $f_\sharp=8$ (see Sec. \ref{['III Modele']}).
• Figure 2: FIG 1: Maps in the $(xOy)$ plane of the RPP ($M=0$) ponderomotive grating envelope (a), the RPP acoustic grating envelope for two beams with the same wavelength crossing in a carbon plasma drifting at the sound speed along $(Oy)$ (b), plasma drifting in the $(xOy)$ plane (c), and for the case where a wavelength detuning is imposed between the RPP beams (d). The only parameter that differs from Fig. \ref{['Delocalisation']} is $N = 10$, and the laser vector potential $A_{0,i} = 9.32 \times 10^{-6} \, \text{T} \cdot \text{m}$ (see Sec. \ref{['III Modele']}).
• Figure 3: FIG 2: Maps in the $(xOy)$ plane of the TSSD ponderomotive beat envelope (a), and of the TSSD acoustic grating envelope (b) for beams with the same central frequency crossing in a plasma drifing at the sound speed in the main IAW direction $(Oy)$. The only parameters that differ from Fig. \ref{['RPP pondero acoustique vdy']} are: $M = 3.9$, $\Delta=\lceil M\rceil$, $\nu_d=17\,\text{GHz}$, $N_c=1$ and $t_0=0$ (see Sec. \ref{['III.1 Champs rpp ssd']}).
• Figure 4: FIG 3: Simplified scheme of the temporal smoothing applied on the laser chain. Spatial smoothing is provided by a random phase plate (RPP, green). Temporal smoothing is achieved through the combination of a frequency modulator (orange) and spectral dispersion, implemented using a dispersive grating for transverse smoothing and a focusing grating for longitudinal smoothing (both shown in purple in panels (a) and (b), respectively). In the case of transverse smoothing, the temporally and spatially out-of-phase wavelets are focused by a converging lens (black). The reference frame $(Oxyz)$ is defined, with the transverse plane $(Oyz)$ centered on the RPP and the $(Ox)$ axis oriented orthogonally to it.
• Figure 5: FIG 4: Schematic of the spatially and TSSD-smoothed beam crossing configuration in a plasma drifting in the $(xOy)$ plane of the laboratory. The two beams ($i=1,2$) propagate along the $(Ox_i)$ directions (red dashed arrows) and are inclined by an angle $\theta$ with respect to the longitudinal $(Ox)$ direction of the laboratory frame $(Oxyz)$ (black dashed arrows). Plasma moves at $\textbf{v}_d$ in the laboratory (light red).