# Hybrid iterative approach for simulation of radio-frequency fields in plasma

## Abstract

In this work, a novel iterative approach for solving discretized linear wave equations in a frequency domain, which combines time evolution with iterative relaxation schemes, is presented. In this hybrid approach, each iteration cycle consists of evolution of electromagnetic (EM) fields in time over a specified number of field periods followed by several iterative relaxations. Provided that there is sufficient dissipation, both the time evolution and the iterative relaxations contribute to the convergence of the EM fields to the solution of the formulated full wave boundary value problem. Time evolution rapidly distributes EM fields, propagating with group velocity, over the simulation domain, while the iterative relaxations smooth the fields, reducing the numerical errors such that iteration cycles converge to a steady state solution, approximating the solution of the formulated problem. This approach is intended for large scale simulations which are beyond the capabilities of direct solvers presently used for solving wave equations in the frequency domain. Lastly, the technique is demonstrated for solving wave equations on a regular grid using a cold plasma dielectric model with collisions for 2D modeling of EM fields in tokamak in an electron cyclotron frequency range.

- Authors:

- FAR-TECH, Inc., San Diego, CA (United States)

- Publication Date:

- Research Org.:
- FAR-TECH, Inc., San Diego, CA (United States); Univ. of California, Oakland, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1540222

- Alternate Identifier(s):
- OSTI ID: 1463936

- Grant/Contract Number:
- SC0011863; AC02-05CH11231

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 25; Journal Issue: 8; Journal ID: ISSN 1070-664X

- Publisher:
- American Institute of Physics (AIP)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY

### Citation Formats

```
Svidzinski, V. A., Kim, J. S., Zhao, L., Galkin, S. A., and Spencer, J. A. Hybrid iterative approach for simulation of radio-frequency fields in plasma. United States: N. p., 2018.
Web. doi:10.1063/1.5037110.
```

```
Svidzinski, V. A., Kim, J. S., Zhao, L., Galkin, S. A., & Spencer, J. A. Hybrid iterative approach for simulation of radio-frequency fields in plasma. United States. doi:10.1063/1.5037110.
```

```
Svidzinski, V. A., Kim, J. S., Zhao, L., Galkin, S. A., and Spencer, J. A. Fri .
"Hybrid iterative approach for simulation of radio-frequency fields in plasma". United States. doi:10.1063/1.5037110. https://www.osti.gov/servlets/purl/1540222.
```

```
@article{osti_1540222,
```

title = {Hybrid iterative approach for simulation of radio-frequency fields in plasma},

author = {Svidzinski, V. A. and Kim, J. S. and Zhao, L. and Galkin, S. A. and Spencer, J. A.},

abstractNote = {In this work, a novel iterative approach for solving discretized linear wave equations in a frequency domain, which combines time evolution with iterative relaxation schemes, is presented. In this hybrid approach, each iteration cycle consists of evolution of electromagnetic (EM) fields in time over a specified number of field periods followed by several iterative relaxations. Provided that there is sufficient dissipation, both the time evolution and the iterative relaxations contribute to the convergence of the EM fields to the solution of the formulated full wave boundary value problem. Time evolution rapidly distributes EM fields, propagating with group velocity, over the simulation domain, while the iterative relaxations smooth the fields, reducing the numerical errors such that iteration cycles converge to a steady state solution, approximating the solution of the formulated problem. This approach is intended for large scale simulations which are beyond the capabilities of direct solvers presently used for solving wave equations in the frequency domain. Lastly, the technique is demonstrated for solving wave equations on a regular grid using a cold plasma dielectric model with collisions for 2D modeling of EM fields in tokamak in an electron cyclotron frequency range.},

doi = {10.1063/1.5037110},

journal = {Physics of Plasmas},

number = 8,

volume = 25,

place = {United States},

year = {2018},

month = {8}

}

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