## This content will become publicly available on April 18, 2020

## Energy-conserving perfect-conductor boundary conditions for an implicit, curvilinear Darwin particle-in-cell algorithm

## Abstract

We propose here a conservative prescription for perfect-conductor boundary conditions for a Darwin particle-in-cell (PIC) model on curvilinear meshes and arbitrarily shaped boundaries. The Darwin model is a subset of Maxwell's equation in which the electromagnetic mode (light wave) has been analytically removed. This renders the Darwin formulation elliptic, instead of hyperbolic. Historically, Darwin-PIC practitioners have had difficulty implementing a well-posed set of boundary conditions for realistic applications. In this study, we demonstrate the well-posedness and effectiveness of a simple boundary-condition prescription for perfect conductors of specified potential and of arbitrary shape in multiple dimensions, using a recently developed conservative, implicit Darwin-PIC algorithm. The boundary conditions conserve the electromagnetic energy, and preserve the Coulomb gauge of the vector potential, $\mathrm{\nabla}\xb7\mathbf{A}=0$ exactly. We demonstrate that global energy is exactly conserved in curvilinear, simply-connected domains in the specific case of particles reflecting off perfect conductors.

- Authors:

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

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21); USDOE National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1511229

- Report Number(s):
- LA-UR-18-21246

Journal ID: ISSN 0021-9991

- Grant/Contract Number:
- 89233218CNA000001

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of Computational Physics

- Additional Journal Information:
- Journal Volume: 391; Journal ID: ISSN 0021-9991

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATION; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; particle in cell; curvilinear meshes; implicit timestepping; nonlinear solvers; energy conservation

### Citation Formats

```
Chacón, L., and Chen, G.. Energy-conserving perfect-conductor boundary conditions for an implicit, curvilinear Darwin particle-in-cell algorithm. United States: N. p., 2019.
Web. doi:10.1016/j.jcp.2019.04.032.
```

```
Chacón, L., & Chen, G.. Energy-conserving perfect-conductor boundary conditions for an implicit, curvilinear Darwin particle-in-cell algorithm. United States. doi:10.1016/j.jcp.2019.04.032.
```

```
Chacón, L., and Chen, G.. Thu .
"Energy-conserving perfect-conductor boundary conditions for an implicit, curvilinear Darwin particle-in-cell algorithm". United States. doi:10.1016/j.jcp.2019.04.032.
```

```
@article{osti_1511229,
```

title = {Energy-conserving perfect-conductor boundary conditions for an implicit, curvilinear Darwin particle-in-cell algorithm},

author = {Chacón, L. and Chen, G.},

abstractNote = {We propose here a conservative prescription for perfect-conductor boundary conditions for a Darwin particle-in-cell (PIC) model on curvilinear meshes and arbitrarily shaped boundaries. The Darwin model is a subset of Maxwell's equation in which the electromagnetic mode (light wave) has been analytically removed. This renders the Darwin formulation elliptic, instead of hyperbolic. Historically, Darwin-PIC practitioners have had difficulty implementing a well-posed set of boundary conditions for realistic applications. In this study, we demonstrate the well-posedness and effectiveness of a simple boundary-condition prescription for perfect conductors of specified potential and of arbitrary shape in multiple dimensions, using a recently developed conservative, implicit Darwin-PIC algorithm. The boundary conditions conserve the electromagnetic energy, and preserve the Coulomb gauge of the vector potential, ∇·A=0 exactly. We demonstrate that global energy is exactly conserved in curvilinear, simply-connected domains in the specific case of particles reflecting off perfect conductors.},

doi = {10.1016/j.jcp.2019.04.032},

journal = {Journal of Computational Physics},

number = ,

volume = 391,

place = {United States},

year = {2019},

month = {4}

}