Adaptive grid PIC capability for dusty plasma studies

Summary form only given. We have developed an innovative particle-in-cell (PIC) code for dusty plasma studies. The main novelty is that our code couples a grid generation/adaptation strategy to the standard PIC algorithm. This is beneficial for two reasons. First, without an adaptive grid, standard PIC codes model curved surfaces using a stair-stepping technique, which highly distorts the shapes of small (relative to the plasma Debye length) grains. This can become quite problematic in simulations of small grains, as is often the case in space and astrophysical applications, or when calculating forces on the grain surface. Our grid generation strategy conforms to objects of arbitrary shape and solves this problem. Second, we will be able to adapt our computational mesh in time as required by the physics of the simulation. These two features allow us to simulate more complicated physical structures much more accurately. Our initial 2D computational grid is generated using Winslow´s method, in which grains of arbitrary shape and size are modeled exactly as boundaries of the system. This gridding technique allows us to initially concentrate the finest meshing within the Debye sphere surrounding the grains, leaving coarser meshes where accuracy and particle statistics are less important. The time-dependent grid adaptation will be handled by the recently developed Monge-Kantorovich optimization method, allowing us to further concentrate our mesh on areas of interest as the simulation progresses. Furthermore, we have developed a semi-implicit, symplectic particle mover based on a generalization of the leapfrog method to an arbitrary curvilinear grid. By its nature, this integrator preserves phase-space volume and has been shown to conserve energy to high accuracy. Our new code is validated using the OML charging theory for spherical and cylindrical dust grains. Further tests include the charging of an electron-emitting dust grain in a uniform plasma. The final goal is t- study the forces between two emitting grains of like charge.