Asymptotically preserving particle-in-cell methods for inhomogenous strongly magnetized plasmas
This work addresses the need for efficient simulation of strongly magnetized plasmas in fusion and astrophysics, where standard PIC methods suffer from severe time-step constraints.
The authors propose semi-implicit PIC methods for the Vlasov-Poisson system with strong inhomogeneous magnetic fields, achieving asymptotic preservation to the guiding-center model. Numerical experiments validate the method's accuracy and stability.
We propose a class of Particle-In-Cell (PIC) methods for the Vlasov-Poisson system with a strong and inhomogeneous external magnetic field with fixed direction, where we focus on the motion of particles in the plane orthogonal to the magnetic field (so-called poloidal directions). In this regime, the time step can be subject to stability constraints related to the smallness of Larmor radius and plasma frequency. To avoid this limitation, our approach is based on first and higher-order semi-implicit numerical schemes already validated on dissipative systems [3] and for homogeneous magnetic fields [10]. Thus, when the magnitude of the external magnetic field becomes large, this method provides a consistent PIC discretization of the guiding-center system taking into account variations of the magnetic field. We carry out some theoretical proofs and perform several numerical experiments that establish a solid validation of the method and its underlying concepts.