Explicit relaxation Particle-in-Cell methods for Vlasov-Poisson equations with a strong magnetic field
This work provides energy-conserving explicit PIC methods for plasma simulations with strong magnetic fields, addressing a key challenge in computational plasma physics.
The authors developed explicit relaxation Particle-in-Cell (ER-PIC) methods for Vlasov-Poisson equations with strong magnetic fields, achieving exact energy conservation. Numerical experiments across multiple regimes confirmed accuracy and energy conservation, with second-order error bounds for Strang-type and uniform first-order accuracy for Lie-Trotter schemes.
In this work, we present a novel family of explicit relaxation Particle-in-Cell (ER-PIC) methods for the Vlasov-Poisson equation with a strong magnetic field. These schemes achieve exact energy conservation by combining a splitting framework with the dynamic updating of a relaxation parameter at each time step. Using an averaging technique, we rigorously establish second-order error bounds for the Strang-type ER-PIC method and uniform first order accuracy in position for the Lie-Trotter ER-PIC scheme. Numerical experiments across the fluid, finite Larmor radius, and diffusion regimes confirm the accuracy and energy conservation of our methods.