Laser Plasma Simulation Environment
Coercing the laws of physics into mere suggestions.
The laser-plasma simulation environment (LPSE) is a computer code designed to solve problems in the area of high-energy-density physics (HEDP). This guide describes the setup and operation of the LPSE system. Its architecture makes it appropriate for problems requiring grids up to of the order of (109) cells, and where multiple laser beams must interact with a 3-D plasma. Simpler, 1 and 2-D simulations can also be performed using far-less computational resources. The system is “easily” extensible, since new physics and virtual instrumentation modules can be added as user-written C++ classes.
In it’s present form, LPSE is capable of solving two kinds problems that are of interest to the plasma physics community. The first uses a spectral algorithm to simulate two-plasmon decay (TPD) between Langmuir and ion-acoustic waves driven by an imposed light field. Self-consistent Landau-damping coefficients can be included in this calculation. The second method uses finite differences to solve for an evolving light field and coupled Langmuir and ion-acoustic waves. This approach allows for complicated interactions between the three fields, leading to effects such as stimulated Brillouin scattering (SBS) and stimulated Raman scattering (SRS). There is also limited support for combining TPD, SBS, and SRS within a single finite-differenced simulation.
The underlying philosophy of LPSE is to enable the simulation of laser–plasma interactions (LPI) in relatively large volumes of space with acceptable computation effort. The level of physical detail is intended to lie between more fundamental particle-in-cell (PIC) codes, such as OSIRIS; and full-scale radiation–hydrodynamics codes such as HYDRA . Unlike other LPI simulation programs, LPSE makes few assumptions about beam direction, plasma density, or flow velocities. Its major limitation, as opposed to PIC codes, is that its underlying equations are linearized. This tends to restrict solutions to regimes with light intensities less than of the order of (1016) W/cm2.
LPSE can be expected to run with just about any version of Unix, including Linux, on any reasonably modern PC or RISC workstation. Some form of graphics hardware support is recommended for efficiently visualizing the results. In practice, very large 3-D problems are best solved on a distributed-memory supercomputer comprised of at least 100 CPU cores with a total of at least 100 GB of physical memory. It is easy to generate tens to hundreds of GB of output data per simulation, so having access to a significant amount of disk space is also recommended.
Perspective users should be aware that LPSE is a complex system targeted toward professional scientists and graduate students. Significant effort (e.g., weeks to months) is required to learn the underlying physics well enough to generate publishable results.
Example: Cross-Beam Energy Transfer
If two or more beams intersect within a plasma at SBS resonance conditions, the scattered light can migrate from one beam to the other. In the context of inertial confinement fusion, this can divert light energy away from the fuel pellet and out of the region of interest. The underlying mechanism is SBS. While a strong light pulse implodes a fuel pellet, as shown on the left figure below, the outer layer of CH plasma explodes radially outward. Its density tends to decrease exponentially from the shell, and its velocity increases linearly outward. In the region of of the order of (Mach 1) speed, SBS can develop. Crossing beams, either from backscattered light or from other primary lasers can seed the process through Doppler shifting of the light’s frequency. The result is that the primary (inward) beam is diverted away from its target as shown in the the right image of the 2-D “spherical” simulation below. This effect is called CBET (cross-beam energy transfer).
Two-dimensional LPSE simulation of a small-scale preformed plasma profile, illustrating the geometry for cross-beam energy transfer. Snapshots of the electric-field intensity are shown, normalized to its maximum value, for two overlapping laser beams (0 and 1). (a) and (b) correspond to a time 1 ps after injection of the beams from the boundary, while (c) is at 10 ps when CBET has fully developed. (a) and (c) show the entire simulated region, while (b) is an enlargement of the region indicated by the white box in (a). The red circle gives the location of the critical density. The blue and white lines are ray trajectories for beams 0 and 1 respectively, giving the local direction of propagation of each beam. The interference pattern seen in (b) leads to a density perturbation that can transfer energy from beam 0 to 1. The green arrow in (c) indicates the direction of energy transfer near the point, giving rise to a shadow downstream.
The following figure illustrates both the electric-field strength and ion-acoustic wave pattern for a full 3-D simulation of CBET.
Three-dimensional CBET: Subscale 3-D CBET simulation showing isosurfaces of E02 in blue, and isosurfaces of Nelf in red. The 45° interference pattern (i.e., the virtual grating) formed by the ion-acoustic waves is clearly evident.
Two simple light beams cross within a plasma that is flowing from right to left. The flow speed is near Mach 1 in the middle of the box. The outer isosurfaces show the intensity of the light’s electric field strength. The inner surfaces show the interference pattern that develops because of SBS resonance. One can see energy being diverted from the near–far beam into the left–right beam.
