# Kinetic Simulation of Collisional Magnetized Plasmas with Semi-implicit Time Integration

## Abstract

Plasmas with varying collisionalities occur in many applications, such as tokamak edge regions, where the flows are characterized by significant variations in density and temperature. While a kinetic model is necessary for weakly-collisional high-temperature plasmas, high collisionality in colder regions render the equations numerically stiff due to disparate time scales. In this study, we propose an implicit–explicit algorithm for such cases, where the collisional term is integrated implicitly in time, while the advective term is integrated explicitly in time, thus allowing time step sizes that are comparable to the advective time scales. This partitioning results in a more efficient algorithm than those using explicit time integrators, where the time step sizes are constrained by the stiff collisional time scales. Finally, we implement semi-implicit additive Runge–Kutta methods in COGENT, a high-order finite-volume gyrokinetic code and test the accuracy, convergence, and computational cost of these semi-implicit methods for test cases with highly-collisional plasmas.

- Authors:

- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Physics Division

- Publication Date:

- Research Org.:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)

- OSTI Identifier:
- 1458696

- Report Number(s):
- LLNL-JRNL-735522

Journal ID: ISSN 0885-7474; 887762

- Grant/Contract Number:
- AC52-07NA27344

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Journal of Scientific Computing

- Additional Journal Information:
- Journal Name: Journal of Scientific Computing; Journal ID: ISSN 0885-7474

- Publisher:
- Springer

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; IMEX time integration; plasma physics; gyrokinetic simulations; Vlasov–Fokker–Planck equations

### Citation Formats

```
Ghosh, Debojyoti, Dorf, Mikhail A., Dorr, Milo R., and Hittinger, Jeffrey A. F..
```*Kinetic Simulation of Collisional Magnetized Plasmas with Semi-implicit Time Integration*. United States: N. p., 2018.
Web. doi:10.1007/s10915-018-0726-6.

```
Ghosh, Debojyoti, Dorf, Mikhail A., Dorr, Milo R., & Hittinger, Jeffrey A. F..
```*Kinetic Simulation of Collisional Magnetized Plasmas with Semi-implicit Time Integration*. United States. doi:10.1007/s10915-018-0726-6.

```
Ghosh, Debojyoti, Dorf, Mikhail A., Dorr, Milo R., and Hittinger, Jeffrey A. F.. Sat .
"Kinetic Simulation of Collisional Magnetized Plasmas with Semi-implicit Time Integration". United States.
doi:10.1007/s10915-018-0726-6.
```

```
@article{osti_1458696,
```

title = {Kinetic Simulation of Collisional Magnetized Plasmas with Semi-implicit Time Integration},

author = {Ghosh, Debojyoti and Dorf, Mikhail A. and Dorr, Milo R. and Hittinger, Jeffrey A. F.},

abstractNote = {Plasmas with varying collisionalities occur in many applications, such as tokamak edge regions, where the flows are characterized by significant variations in density and temperature. While a kinetic model is necessary for weakly-collisional high-temperature plasmas, high collisionality in colder regions render the equations numerically stiff due to disparate time scales. In this study, we propose an implicit–explicit algorithm for such cases, where the collisional term is integrated implicitly in time, while the advective term is integrated explicitly in time, thus allowing time step sizes that are comparable to the advective time scales. This partitioning results in a more efficient algorithm than those using explicit time integrators, where the time step sizes are constrained by the stiff collisional time scales. Finally, we implement semi-implicit additive Runge–Kutta methods in COGENT, a high-order finite-volume gyrokinetic code and test the accuracy, convergence, and computational cost of these semi-implicit methods for test cases with highly-collisional plasmas.},

doi = {10.1007/s10915-018-0726-6},

journal = {Journal of Scientific Computing},

number = ,

volume = ,

place = {United States},

year = {Sat May 12 00:00:00 EDT 2018},

month = {Sat May 12 00:00:00 EDT 2018}

}