Abstract Details
Abstracts
Author: William Barham
Requested Type: Poster
Submitted: 2026-03-12 15:53:51
Co-authors: J. W. Burby
Contact Info:
Los Alamos National Laboratory
307 Ridgecrest Ave, Unit C
White Rock, NM 87547
USA
Abstract Text:
Symplectic particle-in-cell (PIC) algorithms, obtained from structure-preserving spatial and temporal discretizations respecting the Hamiltonian or variational structure of the Vlasov equation, are often assumed to preserve phase-space structure in long kinetic plasma simulations, but this can fail in practice. We introduce a computable symplecticity diagnostic based on the first Poincaré integral invariant (i.e. loop integrals of the Liouville 1-form) which can be evaluated with spectral accuracy from sampled phase-space trajectories. Applying the diagnostic to symplectic electrostatic PIC methods reveals a surprising implementation constraint: linear charge deposition/interpolation (commonly used in production PIC) yields a discrete time-advance map that is not symplectic, even when using a symplectic time-stepping method. We show that quadratic or higher shape functions are necessary to obtain a truly symplectic, structure-preserving PIC integrator. The diagnostic offers a robust verification tool for long-time kinetic modeling of fusion-relevant plasmas.
Characterization: 4.0
Comments: