An explicit multiscale pseudo orbit-averaging time integration algorithm
This incremental work addresses computational efficiency for plasma physics simulations, specifically in magnetic mirror configurations.
The authors tackled the problem of efficiently solving differential equations with high-frequency modes by developing an explicit multiscale algorithm that separates fast and slow dynamics, achieving a 30,000× speedup in reduced kinetic models of plasmas in magnetic mirrors.
We present an explicit multiscale algorithm for solving differential equations for problems with high-frequency modes that can be averaged over by separating and scaling the fast and slow dynamics within a single equation. We introduce a phased time integrator for cases where the boundaries of dynamical scales are known: one phase solves the unmodified equation, while the other freezes part of phase-space and slows down the evolution of the fast dynamics. This algorithm is applied to reduced kinetic models of plasmas in magnetic mirrors, which feature a distinct boundary between a region dominated by rapid particle transit and a region characterized by slow collisions. Two representative model problems are presented that decompose the dynamics of the magnetic mirror into a simpler, computationally inexpensive form. The model problems demonstrate a speedup by a factor of order $Ï/ ν_c$, where $Ï$ is the fast oscillation frequency and $ν_c$ is the slow damping rate. This is a 30,000$\times$ speedup for a case of practical interest.