PM2D: A parallel GPU-based code for the kinetic simulation of laser plasma instabilities at large scales

Abstract

Laser plasma instabilities (LPIs) have significant influences on the laser energy deposition efficiency and therefore are important processes in inertial confined fusion (ICF). Numerical simulations play important roles in revealing the complex physics of LPIs. Since LPIs are typically a three wave coupling process, the precise simulations of LPIs with kinetic effects require to resolve the laser period (around one femtosecond) and laser wavelength (less than one micron). In the typical ICF experiments, however, LPIs are involved in a spatial scale of several millimeters and a temporal scale of several nanoseconds. Therefore, the precise kinetic simulations of LPIs in such scales require huge computational resources and are hard to be carried out by present kinetic codes like particle-in-cell (PIC) codes. In this paper, a full wave fluid model of LPIs is constructed and numerically solved by the particle-mesh method, where the plasma is described by macro particles that can move across the mesh grids freely. Based upon this model, a two-dimensional (2D) GPU code named PM2D is developed. The PM2D code can simulate the kinetic effects of LPIs self-consistently as normal PIC codes. Moreover, as the physical model adopted in the PM2D code is specifically constructed for LPIs, the required macro particles per grid in the simulations can be largely reduced and thus overall simulation cost is considerably reduced comparing with PIC codes. More importantly, the numerical noise in the PM2D code is much lower, which makes it more robust than PIC codes in the simulation of LPIs for the long-time scale above 10 picoseconds. After the distributed computing is realized, our PM2D code is able to run on GPU clusters with a total mesh grids up to several billions, which meets the requirements for the simulations of LPIs at ICF experimental scale with reasonable cost.

Program summary

Program Title: PM2D

CPC Library link to program files: https://doi.org/10.17632/xscj6vnkkw.1

Licensing provisions: GNU General Public License v3.0.

Programming language: C++, CUDA.

Nature of problem: Although the large scale simulations of laser plasma instabilities (LPIs) is of great significance for the inertial confinement fusion (ICF), there is still no suitable code to simulate these problems. PM2D code based on a GPU platform provides an effective method to simulate these large scale problems in ICF.

Solution method: A fluid model for LPIs is established firstly, which contains wave equations that describe the laser propagating process, electron and ion fluid equations that describe the plasma motions, and a Poisson's equation that describes the electrostatic field induced by charge separation. The wave equation is solved on a rectangular region using absorption boundary conditions on all of four boundaries. The absorption boundary condition on the left boundary is further extended to allow the incidence of driven lasers and absorption of scattering lasers simultaneously. The fluid equations in the physical model are solved by the particle-mesh method, in which the macro particles are driven to move by fluid forces. Since macro particles can move freely within the fixed fluid grids, the PM2D code can capture the kinetic effects self-consistently. The Poisson's equation for the electrostatic field is solved by a Fourier decomposition method in the y direction, which helps to decrease the simulation cost greatly. The PM2D code is developed on a GPU platform base on CUDA toolkit, which largely increase the computational speed.