BORPIC++: A Body-of-Revolution Particle-in-Cell Algorithm with Radial Perfectly Matched Layers and Dual Polarizations

Plasma turbulence, arising from nonlinear interactions in charged plasma, occurs in various environments such as astrophysical and ionospheric plasmas. Extreme space weather events pose risks to space assets, especially regarding radiation belt flux enhancements affecting satellites. “Radiation belt remediation” schemes, including heavy ion beam injection, aim to scatter energetic electrons. 3D particle-in-cell (PIC) simulations model these interactions, but their computational demands are significant. To address this, we propose an innovative axisymmetric full PIC unstructured mesh simulation model, particularly beneficial for plasmas with cylindrical symmetry, enabling higher resolution and longer simulations. A novel irregular-mesh-based electromagnetic particle-in-cell algorithm has been developed for fully kinetic plasma simulations involving in the body-of-revolution geometries. Leveraging the cylindrical symmetry, we utilize a field rescaling and a coordinate mapping based on transformation optics to convert the original 3D Maxwell's equations in a cylindrical coordinate system into the equivalent 2D one in the meridian plane. We exploit the discrete exterior calculus for the consistent discretization of various Maxwell dynamical variables on irregular meshes. As a result, exact charge conservation is attained on a discrete mesh from first principles. We model dual polarizations accounting for all possible motions of charged particles. A cylindrical perfectly matched layer is implemented in the radial direction to enable the simulation of open space problems while avoiding spurious interactions between reflected waves and charged particles can be avoided. As a numerical application of the BORPIC++ algorithm, we simulate the the ion beam deflection caused by a magnetic dipole positioned on an insulating plate. This simulation corresponds to small-scale laboratory experiments mimicking lunar magnetic anomalies caused by interactions with the solar wind. Specifically, we investigate the induced surface potentials behavior on the plate while taking account secondary electron emission effects.