### A time-implicit numerical method and benchmarks for the relativistic Vlasov–Ampere equations

Here, we present a time-implicit numerical method to solve the relativistic Vlasov–Ampere system of equations on a two dimensional phase space grid. The time-splitting algorithm we use allows the generalization of the work presented here to higher dimensions keeping the linear aspect of the resulting discrete set of equations. The implicit method is benchmarked against linear theory results for the relativistic Landau damping for which analytical expressions using the Maxwell-Juttner distribution function are derived. We note that, independently from the shape of the distribution function, the relativistic treatment features collective behaviors that do not exist in the non relativistic case. The numerical study of the relativistic two-stream instability completes the set of benchmarking tests.

- Publication Date:

- Grant/Contract Number:
- SC0008382; FG02-08ER55000; PHY-1104683

- Type:
- Accepted Manuscript

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 23; Journal Issue: 1; Journal ID: ISSN 1070-664X

- Publisher:
- American Institute of Physics (AIP)

- Research Org:
- Univ. of Nebraska-Lincoln, Lincoln, NE (United States)

- Sponsoring Org:
- USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC-24); National Science Foundation (NSF)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; relativistic Vlasov; implicit; Eulerian; electric fields; numerical solutions; Maxwell equations; particle distribution functions; cumulative distribution functions

- OSTI Identifier:
- 1334790

- Alternate Identifier(s):
- OSTI ID: 1234172

```
Carrie, Michael, and Shadwick, B. A..
```*A time-implicit numerical method and benchmarks for the relativistic Vlasov–Ampere equations*. United States: N. p.,
Web. doi:10.1063/1.4938035.

```
Carrie, Michael, & Shadwick, B. A..
```*A time-implicit numerical method and benchmarks for the relativistic Vlasov–Ampere equations*. United States. doi:10.1063/1.4938035.

```
Carrie, Michael, and Shadwick, B. A.. 2016.
"A time-implicit numerical method and benchmarks for the relativistic Vlasov–Ampere equations". United States.
doi:10.1063/1.4938035. https://www.osti.gov/servlets/purl/1334790.
```

```
@article{osti_1334790,
```

title = {A time-implicit numerical method and benchmarks for the relativistic Vlasov–Ampere equations},

author = {Carrie, Michael and Shadwick, B. A.},

abstractNote = {Here, we present a time-implicit numerical method to solve the relativistic Vlasov–Ampere system of equations on a two dimensional phase space grid. The time-splitting algorithm we use allows the generalization of the work presented here to higher dimensions keeping the linear aspect of the resulting discrete set of equations. The implicit method is benchmarked against linear theory results for the relativistic Landau damping for which analytical expressions using the Maxwell-Juttner distribution function are derived. We note that, independently from the shape of the distribution function, the relativistic treatment features collective behaviors that do not exist in the non relativistic case. The numerical study of the relativistic two-stream instability completes the set of benchmarking tests.},

doi = {10.1063/1.4938035},

journal = {Physics of Plasmas},

number = 1,

volume = 23,

place = {United States},

year = {2016},

month = {1}

}