An Axisymmetric 2D3V Semi-Lagrangian Vlasov Model for Kinetic Simulation of Plasma Beam Expansion in Divergent Magnetic Field

We report on the development and implementation of an axisymmetric 2D3V (r, z, v_r, v_θ, v_z) semi-Lagrangian Vlasov model within our large-scale parallel code, Vlasolver. The model advects the electron and ion velocity distribution functions (VDFs) along characteristics using a conservative, positivity-preserving, third-order PFC reconstruction method. This approach eliminates the statistical noise inherent to the Particle-in-Cell (PIC) method and ensures low numerical diffusion, while enforcing the axisymmetric geometry and its associated geometric source terms.



As a first application, we model a plasma beam expanding in a divergent magnetic field, a process central to magnetic nozzles. In contrast to fluid simulations that rely on simplified thermodynamic closures, our model provides direct, noise-free access to the full electron VDF. This enables a first-principle investigation of non-equilibrium thermodynamics by resolving key kinetic features such as temperature anisotropy, parallel heat flux, and the evolution of high-energy VDF tails. This work establishes a high-fidelity kinetic framework for advancing the predictive modeling of magnetic nozzles.