Regular sensitivity computation avoiding chaotic effects in particleincell plasma methods
Abstract
Particleincell (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 quantityofinterest (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 fullyLagrangian particleexact approach provides sensitivities of each particle trajectory, and a new particlepdf 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 plasmaPIC particles, they can be positioned and weighted independently for efficiency and accuracy. The corresponding numerical algorithms are presented here in mathematical detail. The advantage of the particlepdf approach in avoiding the spurious chaotic sensitivity of the particleexact approach is demonstrated for Debyemore »
 Authors:

 Univ. of Illinois at UrbanaChampaign, Urbana, IL (United States). Dept. of Mechanical Science and Engineering
 Sandia National Lab. (SNLNM), Albuquerque, NM (United States). Center for Computing Research
 Univ. of Illinois at UrbanaChampaign, Urbana, IL (United States). Dept. of Mechanical Science and Engineering and Dept. of Aerospace Engineering
 Publication Date:
 Research Org.:
 Sandia National Lab. (SNLNM), Albuquerque, NM (United States)
 Sponsoring Org.:
 USDOE National Nuclear Security Administration (NNSA)
 OSTI Identifier:
 1570259
 Alternate Identifier(s):
 OSTI ID: 1703198
 Report Number(s):
 SAND201910797J
Journal ID: ISSN 00219991; 679339; TRN: US2001260
 Grant/Contract Number:
 AC0494AL85000; NA0002374; NA0003525
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Computational Physics
 Additional Journal Information:
 Journal Volume: 400; Journal Issue: C; Journal ID: ISSN 00219991
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; particleincell methods; sensitivity; chaos; uncertainty quanitification; plasma models
Citation Formats
Chung, Seung Whan, Bond, Stephen D., Cyr, Eric C., and Freund, Jonathan B. Regular sensitivity computation avoiding chaotic effects in particleincell plasma methods. United States: N. p., 2020.
Web. doi:10.1016/j.jcp.2019.108969.
Chung, Seung Whan, Bond, Stephen D., Cyr, Eric C., & Freund, Jonathan B. Regular sensitivity computation avoiding chaotic effects in particleincell plasma methods. United States. doi:10.1016/j.jcp.2019.108969.
Chung, Seung Whan, Bond, Stephen D., Cyr, Eric C., and Freund, Jonathan B. Wed .
"Regular sensitivity computation avoiding chaotic effects in particleincell plasma methods". United States. doi:10.1016/j.jcp.2019.108969. https://www.osti.gov/servlets/purl/1570259.
@article{osti_1570259,
title = {Regular sensitivity computation avoiding chaotic effects in particleincell plasma methods},
author = {Chung, Seung Whan and Bond, Stephen D. and Cyr, Eric C. and Freund, Jonathan B.},
abstractNote = {Particleincell (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 quantityofinterest (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 fullyLagrangian particleexact approach provides sensitivities of each particle trajectory, and a new particlepdf 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 plasmaPIC particles, they can be positioned and weighted independently for efficiency and accuracy. The corresponding numerical algorithms are presented here in mathematical detail. The advantage of the particlepdf approach in avoiding the spurious chaotic sensitivity of the particleexact 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 Nbody PIC system. The cost of the particlepdf approach is comparable to the baseline PIC simulation.},
doi = {10.1016/j.jcp.2019.108969},
journal = {Journal of Computational Physics},
number = C,
volume = 400,
place = {United States},
year = {2020},
month = {1}
}