191 / 2023-04-15 16:57:54

Plasma kinetics: Discrete Boltzmann modelling and Richtmyer-Meshkov instability

plasma kinetic,magnetohydrodynamic,Richtmyer-Meshkov instability

惯性约束聚变物理学 > 内爆和不稳定性

Plasma exists widely in natural and industrial fields such as initial confinement fusion (ICF). Compared with neutral fluids, the spatial and temporal scales are more abundant and complex in plasma system, which brings great challenge to the relevant theoretical, experimental and numerical research. Therefore, the establishing of accurate and reliable physical models for predicating and capturing those multi-scale structures is of great importance for understanding the fundamental and underlying physical mechanisms of plasma systems.

At present, three kinds of physical models are mainly adopted for plasma system. The first kinds are various magnetohydrodynamic fluids equations based on continuum hypothesis, which are most mature and widely used. The second kinds are molecular dynamics based on Newton's second law. The third kinds are various kinetic methods based on non-equilibrium statical physics which bridge macroscopic and microscopic models. From microscopic to macroscopic, the step by step transformation of the model causes the decline of the description ability, but extend the spatio-temporal scope of numerical simulation.

In general, the small structures, fast changing modes and abundant interfaces such as material interface and shock wave, will usually cause plasma system in strong thermodynamic non-equilibrium state (TNE) state, which may undermine the validity of macroscopic models. Besides, researchers have pointed out that the kinetic effects caused by particle collisions may have the potential to impact the ICF, which deserved more attention.

In this work, a discrete Boltzmann model (DBM) for plasma kinetics is proposed. The DBM contains two physical functions. The first is to capture the main features aiming to investigate and the second is to present schemes for checking thermodynamic non-equilibrium state and describing TNE effects. For the first function, mathematically, the model is composed of a discrete Boltzmann equation coupled by a magnetic induction equation. Physically, the model is equivalent to a hydrodynamic model plus a coarse-grained model for the most relevant TNE behaviors including the entropy production rate. The first function is verified by recovering hydrodynamic non-equilibrium (HNE) behaviors of a number of typical benchmark problems. Extracting and analyzing the most relevant TNE effects in Orszag-Tang problem are practical applications of the second function. As a further application, the Richtmyer-Meshkov instability with interface inverse and re-shock process is numerically studied. It is found that, in the case without magnetic field, the non-organized momentum flux shows the most pronounced effects near shock front, while the non-organized energy flux shows the most pronounced behaviors near perturbed interface. The influence of magnetic field on TNE effects shows stages: before the interface inverse, the TNE strength is enhanced by reducing the interface inverse speed; while after the interface inverse, the TNE strength is significantly reduced. Both the global averaged TNE strength and entropy production rate contributed by non-organized energy flux can be used as physical criteria to identify whether or not the magnetic field is sufficient to prevent the interface inverse.