## A fully implicit, conservative, non-linear, electromagnetic hybrid particle-ion/fluid-electron algorithm

## Abstract

The quasi-neutral hybrid model with kinetic ions and fluid electrons is a promising approach for bridging the inherent multi-scale nature of many problems in space and laboratory plasmas. A novel, implicit, particle-in-cell based scheme for the hybrid model is derived for fully 3D electromagnetic problems with multiple ion species, which features global mass, momentum and energy conservation. The scheme includes sub-cycling and orbit-averaging for the ions, with cell-centered finite differences and implicit midpoint time advance. To reduce discrete particle noise, the scheme allows arbitrary-order shape functions for the particle-mesh interpolations and the application of conservative binomial smoothing. The algorithm is verified for a number of test problems to demonstrate the correctness of the implementation, the unique conservation properties, and the favorable stability properties of the new scheme. In particular, there is no indication of unstable growth of the finite-grid instability for a population of cold ions drifting through a uniform spatial mesh, in a set-up where several commonly used non-conservative schemes are highly unstable.

- 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:
- 1477697

- Report Number(s):
- LA-UR-18-21708

Journal ID: ISSN 0021-9991

- Grant/Contract Number:
- AC52-06NA25396

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of Computational Physics

- Additional Journal Information:
- Journal Volume: 376; Journal ID: ISSN 0021-9991

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; hybrid; plasma; particle-in-cell; implicit; conservative; finite grid instability

### Citation Formats

```
Stanier, A., Chacón, L., and Chen, G. A fully implicit, conservative, non-linear, electromagnetic hybrid particle-ion/fluid-electron algorithm. United States: N. p., 2018.
Web. doi:10.1016/j.jcp.2018.09.038.
```

```
Stanier, A., Chacón, L., & Chen, G. A fully implicit, conservative, non-linear, electromagnetic hybrid particle-ion/fluid-electron algorithm. United States. doi:10.1016/j.jcp.2018.09.038.
```

```
Stanier, A., Chacón, L., and Chen, G. Thu .
"A fully implicit, conservative, non-linear, electromagnetic hybrid particle-ion/fluid-electron algorithm". United States. doi:10.1016/j.jcp.2018.09.038. https://www.osti.gov/servlets/purl/1477697.
```

```
@article{osti_1477697,
```

title = {A fully implicit, conservative, non-linear, electromagnetic hybrid particle-ion/fluid-electron algorithm},

author = {Stanier, A. and Chacón, L. and Chen, G.},

abstractNote = {The quasi-neutral hybrid model with kinetic ions and fluid electrons is a promising approach for bridging the inherent multi-scale nature of many problems in space and laboratory plasmas. A novel, implicit, particle-in-cell based scheme for the hybrid model is derived for fully 3D electromagnetic problems with multiple ion species, which features global mass, momentum and energy conservation. The scheme includes sub-cycling and orbit-averaging for the ions, with cell-centered finite differences and implicit midpoint time advance. To reduce discrete particle noise, the scheme allows arbitrary-order shape functions for the particle-mesh interpolations and the application of conservative binomial smoothing. The algorithm is verified for a number of test problems to demonstrate the correctness of the implementation, the unique conservation properties, and the favorable stability properties of the new scheme. In particular, there is no indication of unstable growth of the finite-grid instability for a population of cold ions drifting through a uniform spatial mesh, in a set-up where several commonly used non-conservative schemes are highly unstable.},

doi = {10.1016/j.jcp.2018.09.038},

journal = {Journal of Computational Physics},

number = ,

volume = 376,

place = {United States},

year = {2018},

month = {9}

}