Objectives

Low Temperature Plasmas (LTPs) are ionized gases composed of electrons with energies in the range of 10 eV, ions initially at rest, but potentially accelerated to hundreds of eV and, neutral atoms or molecules usually at the room temperature. When both, the neutral gas pressure and the electron energy are in a convenient range of values, the ionization mean free path is sufficiently small to ignite and self-sustain a plasma discharge. This process is operated to extract highly energetic ion beams from plasmas, these beams being used in numerous application fields (e.g. ion sources for Tokamak plasma heating, electric propulsion, …). The energy of the ions within the beam is limited by collisions of ions against neutrals therefore such devices shall operate at low neutral gas pressure to preserve a good yield. To increase the gas ionization an external (magnetostatic) magnetic field is routinely applied to confine the electrons in the ionization chamber, increasing their mean life time and therefore the probability to collide with neutrals. In the literature, the term of partially magnetized LTPs is often referred, since the ions, due to their large mass compared to the electrons, remain unmagnetized. The presence of a magnetic field with a significant strength introduces a formidable complexity in a system that already exhibits a multiscale nature, due to the magnetization of the electrons, the low electron-to-ion mass ratio, the small scales attached to the Debye length or plasma period characteristic of any plasma evolution. This highlights the challenges faced by numerical methods to reproduce the evolution of partially magnetized LTPs, the evolution of such plasmas being severely anisotropic with structures very likely to develop. Most importantly, numerous complex mechanisms triggering instabilities are genuinely three dimensional. These phenomena may develop on fine scales compared to that of the device, furthermore they cannot be tackled with simple, and numerically efficient, Eulerian-fluid approaches. In this context, the use of kinetic plasma descriptions, accounting for distribution functions evolving in a six dimensional phase-space (plus time) is mandatory, hence the need of efficient numerical methods.

The simulation under real conditions of partially magnetized LTPs 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 fields. 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 attain 109 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 LTPs 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.