Three-dimensional particle-in-cell simulations of ion-driven parametric instabilities

HERCULES, a massively parallel three-dimensional hybrid particle-in-cell (PIC) code, implemented on the CRAY-T3D, is presented. The code is based on a physical model, described in a previous report, where the electrons are modeled as an adiabatic fluid with an arbitrary ratio of specific heats γ, and the electromagnetic field model is based on a temporal WKB approximation. On a CRAY-T3D with 512 processors, the code requires about 0.6 μs/particle/time step. The largest test problem performed with this code consists of a computational mesh of 4096×64×64 (16 million) cells, and a total of 256 million particles, and corresponds to a plasma volume of 250 μm×62.5 μm×62.5 μm. This code is the first PIC code capable of simulating ion-driven parametric instabilities in a large plasma volume, and it offers a unique opportunity for examining issues that are potentially vital to inertial confinement fusion (ICF), e.g., nonlinear ion kinetic effects and their role in nonlinear saturation mechanisms. Applications of HERCULES in simulations of Gaussian f/4 diffraction-limited lasers with and without transverse plasma flows are presented. Simulation parameters are chosen to correspond to actual experimental conditions, and the simulations are performed over a substantial portion of the actual laser pulse. The simulations indicate that while the transmitted laser beam can be significantly deflected by transverse flows, the SBS-reflected beam does not necessarily exhibit the same behavior. Furthermore, the total SBS reflectivity appears to be insensitive to transverse flows. In the simulations, the late-time SBS reflectivity is 25%, which compares favorably to the 10%–20% range measured in actual experiments. The simulations in this paper are the first PIC simulations of ICF experiments in which both the temporal and spatial scales of the experiments are captured in their entireties.