Three-dimensional particle-in-cell modeling of parametric instabilities near the quarter-critical density in plasmas

The nonlinear regime of laser-plasma interactions including both two-plasmon decay (TPD) and stimulated Raman scattering (SRS) instabilities has been studied in three-dimensional (3D) particle-in-cell simulations with parameters relevant to the inertial confinement fusion (ICF) experiments. SRS and TPD develop in the same region in plasmas, and the generation of fast electrons can be described accurately with only the full model including both SRS and TPD. The growth of instabilities in the linear stage is found to be in good agreement with analytical theories. In the saturation stage the low-frequency density perturbations driven by the daughter waves of the SRS side scattering can saturate the TPD and consequently inhibit the fast-electron generation. The fast-electron flux in 3D modeling is up to an order of magnitude smaller than previously reported in 2D TPD simulations, bringing it close to the results of ICF experiments.

Figure 1

The integrated energy of different field components in the simulation region as a function of time for the (a) 2D $p$-polarized simulation, (b) 2D $s$-polarized simulation, and (d) 3D simulation. The wave-vector diagram for TPD and SRS is shown in (c).

Figure 2

(a) Plasma-wave spectra in the linear instability stage as a function of plasma density and the wave frequency normalized to laser frequency in 2D PP, (b) 2D SP, and (c) 3D simulation for modes with $0\le k_z/k_0<0.2$ and (d) $0.2\le k_z/k_0<3$. The overlaid solid black lines and the dashed black lines represent the dispersion relations satisfying the matching conditions for TPD and SRS, respectively.

Figure 3

Plasma-wave spectra in the saturation stage in the 2D (from 3.3 to 4.1 ps) and 3D (from 2.3 to 3.1 ps) simulations as a function of plasma density and the wave frequency. Each panel displays the same quantity as in Fig. 2.

Figure 4

(a) The spectrum of plasmons in the saturation stage of 3D simulation at densities lower than $0.23n_c$ plotted in the $k_x\text{−}{k}_y$ plane and (b) the $k_x\text{−}{k}_z$ plane. (c) The spectrum of ion density fluctuation plotted in the $k_x\text{−}{k}_z$ plane on a logarithmic scale. (d) Lower panel: Ion density fluctuation rms (root-mean-square average over the transverse direction and time) normalized to background density (black solid line), longitudinal electric field rms (blue dashed line), and caviton correlator $C_{E,n}$ (blue dotted line). Upper panel: The ratio of the electric field amplitude of the TPD plasmons with a larger wave vector between 2D PP and 3D simulations.