Regular sensitivity computation avoiding chaotic effects in particle-in-cell plasma methods

Seung Whan Chung, Stephen D. Bond, Eric C. Cyr, Jonathan B. Freund

Research output: Contribution to journalArticlepeer-review

Abstract

Particle-in-cell (PIC) simulation methods are attractive for representing species distribution functions in plasmas. However, as a model, they introduce uncertain parameters, and for quantifying their prediction uncertainty it is useful to be able to assess the sensitivity of a quantity-of-interest (QoI) to these parameters. Such sensitivity information is likewise useful for optimization. However, computing sensitivity for PIC methods is challenging due to the chaotic particle dynamics, and sensitivity techniques remain underdeveloped compared to those for Eulerian discretizations. This challenge is examined from a dual particle–continuum perspective that motivates a new sensitivity discretization. Two routes to sensitivity computation are presented and compared: a direct fully-Lagrangian particle-exact approach provides sensitivities of each particle trajectory, and a new particle-pdf discretization, which is formulated from a continuum perspective but discretized by particles to take the advantages of the same type of Lagrangian particle description leveraged by PIC methods. Since the sensitivity particles in this approach are only indirectly linked to the plasma-PIC particles, they can be positioned and weighted independently for efficiency and accuracy. The corresponding numerical algorithms are presented in mathematical detail. The advantage of the particle-pdf approach in avoiding the spurious chaotic sensitivity of the particle-exact approach is demonstrated for Debye shielding and sheath configurations. In essence, the continuum perspective makes implicit the distinctness of the particles, which circumvents the Lyapunov instability of the N-body PIC system. The cost of the particle-pdf approach is comparable to the baseline PIC simulation.

Original languageEnglish (US)
Article number108969
JournalJournal of Computational Physics
Volume400
DOIs
StatePublished - Jan 1 2020

Keywords

  • Chaos
  • Particle-in-cell methods
  • Plasma models
  • Sensitivity
  • Uncertainty quantification

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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