Higher-order particle representation for particle-in-cell simulations

Research output: Contribution to journalArticlepeer-review


  • Dominic A.S. Brown
  • Matthew T. Bettencourt
  • Steven A. Wright
  • Satheesh Maheswaran
  • John P. Jones

Colleges, School and Institutes

External organisations

  • University of Warwick
  • Sandia National Laboratories, New Mexico
  • University of York
  • Diamond Light Source
  • AWE


In this paper we present an alternative approach to the representation of simulation particles for unstructured electrostatic and electromagnetic PIC simulations. In our modified PIC algorithm we represent particles as having a smooth shape function limited by some specified finite radius, r0. A unique feature of our approach is the representation of this shape by surrounding simulation particles with a set of virtual particles with delta shape, with fixed offsets and weights derived from Gaussian quadrature rules and the value of r0. As the virtual particles are purely computational, they provide the additional benefit of increasing the arithmetic intensity of traditionally memory bound particle kernels. The modified algorithm is implemented within Sandia National Laboratories' unstructured EMPIRE-PIC code, for electrostatic and electromagnetic simulations, using periodic boundary conditions. We show results for a representative set of benchmark problems, including electron orbit, a transverse electromagnetic wave propagating through a plasma, numerical heating, and a plasma slab expansion. Good error reduction across all of the chosen problems is achieved as the particles are made progressively smoother, with the optimal particle radius appearing to be problem-dependent.

Bibliographic note

Funding Information: This work was supported by the UK Atomic Weapons Establishment (AWE) under grant CDK0724 (AWE Technical Outreach Programme). Professor Stephen Jarvis is an AWE William Penney Fellow. Computing facilities were provided by the Scientific Computing Research Technology Platform (SCRTP) of the University of Warwick. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA-0003525 . This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government. Publisher Copyright: © 2021


Original languageEnglish
Article number110255
Number of pages19
JournalJournal of Computational Physics
Early online date8 Mar 2021
Publication statusPublished - 15 Jun 2021