Title: Finite spatial-grid effects in energy-conserving particle-in-cell algorithms

Abstract

Finite-grid (or aliasing) instabilities are pervasive in particle-in-cell (PIC) plasma simulation algorithms, and force the modeler to resolve the smallest (Debye) length scale in the problem regardless of dynamical relevance. These instabilities originate in the aliasing of interpolation errors between mesh quantities and particles (which live in the space–time continuum). Recently, strictly energy-conserving PIC (EC-PIC) algorithms have been developed that promise enhanced robustness against aliasing instabilities. In this study, we confirm by analysis that EC-PIC is stable against aliasing instabilities for stationary plasmas. For drifting plasmas, we demonstrate by analysis and numerical experiments that, while EC-PIC algorithms are not free from these instabilities in principle, they feature a benign stability threshold for finite-temperature plasmas that make them usable in practice for a large class of problems (featuring ambipolarity and realistic ion-electron mass ratios) without the need to consider the size of the Debye length. We also demonstrate that this threshold is absent for the popular momentum-conserving PIC algorithms, which are therefore unstable for both drifting and stationary plasmas beyond a threshold in cell size compared to Debye length. Finite-grid (or aliasing) instabilities are pervasive in particle-in-cell (PIC) plasma simulation algorithms, and force the modeler to resolve the smallest (Debye) lengthmore » scale in the problem regardless of dynamical relevance. These instabilities originate in the aliasing of interpolation errors between mesh quantities and particles (which live in the space–time continuum). Recently, strictly energy-conserving PIC (EC-PIC) algorithms have been developed that promise enhanced robustness against aliasing instabilities. In this study, we confirm by analysis that EC-PIC is stable against aliasing instabilities for stationary plasmas. For drifting plasmas, we demonstrate by analysis and numerical experiments that, while EC-PIC algorithms are not free from these instabilities in principle, they feature a benign stability threshold for finite-temperature plasmas that make them usable in practice for a large class of problems (featuring ambipolarity and realistic ion-electron mass ratios) without the need to consider the size of the Debye length. Finally, we also demonstrate that this threshold is absent for the popular momentum-conserving PIC algorithms, which are therefore unstable for both drifting and stationary plasmas beyond a threshold in cell size compared to Debye length.« less

Authors:

Barnes, D. C.  ^[1];

• Search DOE PAGES for author "Barnes, D. C."
• Search DOE PAGES for ORCID "0000-0002-0111-1621"

Chacón, L.  ^[2]

• Search DOE PAGES for author "Chacón, L."
• Search DOE PAGES for ORCID "0000-0002-4566-8763"

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+ Show Author Affiliations

1. Coronado Consulting, Lamy, NM (United States)
2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Publication Date:

Tue Sep 01 00:00:00 EDT 2020

Research Org.:

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Sponsoring Org.:

USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE National Nuclear Security Administration (NNSA)

OSTI Identifier:

1659174

Alternate Identifier(s):

OSTI ID: 1810894

Report Number(s):

LA-UR-18-31023
Journal ID: ISSN 0010-4655

Grant/Contract Number:  

89233218CNA000001; AC52-06NA25396

Resource Type:

Accepted Manuscript

Journal Name:

Computer Physics Communications

Additional Journal Information:

Journal Volume: 258; Journal ID: ISSN 0010-4655

Publisher:

Elsevier

Country of Publication:

United States

Language:

English

Subject:

97 MATHEMATICS AND COMPUTING; Mathematics; Magnetic Fusion Energy; PIC; energy-conserving; spatial-grid effects; stability regime; filtering; shape functions