## This content will become publicly available on January 1, 2021

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

## 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 here in mathematical detail. The advantage of the particle-pdf approach in avoiding the spurious chaotic sensitivity of the particle-exact approach is demonstrated for Debyemore »

- Authors:

- Univ. of Illinois at Urbana-Champaign, Urbana, IL (United States). Dept. of Mechanical Science and Engineering
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Center for Computing Research
- Univ. of Illinois at Urbana-Champaign, Urbana, IL (United States). Dept. of Mechanical Science and Engineering and Dept. of Aerospace Engineering

- Publication Date:

- Research Org.:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1570259

- Report Number(s):
- SAND2019-10797J

Journal ID: ISSN 0021-9991; 679339

- Grant/Contract Number:
- AC04-94AL85000

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of Computational Physics

- Additional Journal Information:
- Journal Volume: 400; Journal Issue: C; Journal ID: ISSN 0021-9991

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; particle-in-cell 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 particle-in-cell 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 particle-in-cell 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 particle-in-cell plasma methods". United States. doi:10.1016/j.jcp.2019.108969.
```

```
@article{osti_1570259,
```

title = {Regular sensitivity computation avoiding chaotic effects in particle-in-cell plasma methods},

author = {Chung, Seung Whan and Bond, Stephen D. and Cyr, Eric C. and Freund, Jonathan B.},

abstractNote = {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 here 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.},

doi = {10.1016/j.jcp.2019.108969},

journal = {Journal of Computational Physics},

number = C,

volume = 400,

place = {United States},

year = {2020},

month = {1}

}