A Structure-Preserving Decorated Particle Method for the Vlasov-Poisson System

TL;DR

This paper introduces a practical, structure-preserving decorated particle method for the Vlasov-Poisson system, demonstrating that fewer particles can achieve accuracy comparable to standard PIC algorithms.

Contribution

It presents a new implementation of the Scovel-Weinstein decorated particle framework, showing its computational advantages over traditional PIC methods.

Findings

Decorated particles require fewer particles for similar accuracy.

The method preserves the Hamiltonian structure of the continuum model.

Numerical experiments validate the efficiency and accuracy of the approach.

Abstract

We revisit the Scovel-Weinstein framework (Scovel & Weinstein, CPAM 1994) for reducing the Vlasov-Poisson system while preserving its Hamiltonian structure. Standard particle-in-cell (PIC) algorithms approximate the distribution function by macro-particles with position and velocity. In contrast, Scovel-Weinstein decorated particles involve additional shape degrees of freedom, while maintaining a finite-dimensional reduction with Hamiltonian structure inherited from the continuum model. Although the original work established this structure three decades ago, its computational potential has remained largely unexplored. We present a practical implementation of the Scovel-Weinstein model and compare it with a standard PIC algorithm. Numerical experiments demonstrate that macro-particles in standard PIC can be replaced by far fewer decorated particles while retaining comparable accuracy. This decorated particle approach offers a new structure-preserving paradigm for kinetic plasma simulation.