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.

Figure 1

(a) Ray- and (b) wave-based simulations of the magnitude of the enveloped electric fields for two beams (injected from the bottom and left) interacting in an azimuthally symmetric plasma. The critical surface is indicated by a white dashed line. (c) Line-outs of the fields from laser-plasma simulation environment (LPSE) (solid blue curve) and rays (red dashed curve). The location of the caustic is denoted by a vertical dashed black line.

Figure 2

The difference in field energy in the ray- and wave-based calculations for (a) CBET turned on and (b) CBET turned off in the ray-based calculation. A Gaussian filter with a $1\text{−}\mu \mathrm{m}$ standard deviation has been applied to smooth out differences resulting from phase mismatches in regions with high-frequency interference.

Figure 3

(Top) The first sheet of the two beams for the configuration shown in Fig. 1 overlaid on the Cartesian grid. (Bottom) A closeup of one of the grid cells. The filled gray region denotes the first sheet of the beam coming from the bottom. The ray trajectories correspond to the first sheet of the beam coming from the side. The solid red part of the ray trajectories shows where the rays would interact with the beam coming from the bottom without the CGT correction. The dashed blue part of the ray trajectories is the region where there is no interaction with the beam coming from the bottom. Note that finite sheets are shown for illustrative purposes; only the parabolic edge corresponds to a caustic. The other edges of the sheet are chosen such that the intensity is vanishingly small (for the sides) or outside the interaction region (for the injector).

Figure 4

The laser absorption (left column) and energy conservation error (right column) for the nominal (red circles) and CGT (blue squares) ray-trace algorithms as functions of grid resolution for [(a) and (b)] 2D two-beam calculations, [(c) and (d)] 2D 16-beam calculations, and [(e) and (f)] 3D 60-beam calculations. The 2D calculations are compared to the LPSE results, and the 3D calculations are compared to the OMEGA results (black dashed lines).