MATURATION

The simulation under real conditions of partially magnetized low temperature plasmas by Lagrangian approaches, though using powerful Particle-In-Cell (PIC) techniques supplemented with efficient high-performance computing methods, requires considerable computing resources for large plasma densities. This is explained by two main limitations. First, stability conditions that constrain the numerical parameters to resolve the small space and time scales. These numerical parameters are the mesh size of the grid used to compute the electric field and the time step between two consecutive computations. Second, PIC methods rely on a sampling of the distribution function by numerical particles whose motion is time integrated in the self-consistent electric field. The PIC algorithm remains close to physics and offers an incomparable efficiency with regard to Eulerian methods, discretizing the distribution function onto a mesh. It is widely and successfully operated for the discretization of kinetic plasma models for more than 40 years. Nonetheless, to spare the computational resources, the number of numerical particles is limited compared to that of the physical particles. Inherent to this “coarse” sampling, PIC algorithms produce numerical approximations prone to statistical fluctuations that vanish slowly with the mean number of particles per cell. The mesh accessible on typical high performance computing machines may 10^9 cells, which brings the mesh size close to the scale of the physics, but the mean number of numerical particles in each cell shall be limited, to mitigate the memory footprint as well as the computational time. A breakthrough is therefore necessary to reduce the computational resources by orders of magnitude and make possible the use of explicit PIC method for large scale and/or densities for 3D computations. This is the issue addressed within the MATURATION project aiming at introducing a new class of PIC algorithms with an unprecedented computational efficiency, by analyzing and improving, parallelizing and optimizing as well as benchmarking, in the demanding context of partially magnetized low temperature plasmass through 2D large scale and 3D computations, a method recently proposed in the literature, based on a combination of sparse grid techniques and PIC algorithm.