# Spectral Approach to Plasma Kinetic Simulations Based on Hermite Decomposition in the Velocity Space

## Abstract

Here, spectral (transform) methods for solution of Vlasov-Maxwell system have shown significant promise as numerical methods capable of efficiently treating fluid-kinetic coupling in magnetized plasmas. We discuss SpectralPlasmaSolver (SPS), an implementation of three-dimensional, fully electromagnetic algorithm based on a decomposition of the plasma distribution function in Hermite modes in velocity space and Fourier modes in physical space. A fully-implicit time discretization is adopted for numerical stability and to ensure exact conservation laws for total mass, momentum and energy. The SPS code is parallelized using Message Passing Interface for distributed memory architectures. Application of the method to analysis of kinetic range of scales in plasma turbulence under conditions typical of the solar wind is demonstrated. With only 4 Hermite modes per velocity dimension, the algorithm yields damping rates of kinetic Alfvén waves with accuracy of 50% or better, which is sufficient to obtain a model of kinetic scales capable of reproducing many of the expected statistical properties of turbulent fluctuations. With increasing number of Hermite modes, progressively more accurate values for collisionless damping rates are obtained. Fully nonlinear simulations of decaying turbulence are presented and successfully compared with similar simulations performed using Particle-In-Cell method.

- Authors:

- Publication Date:

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

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1467122

- Alternate Identifier(s):
- OSTI ID: 1481149

- Report Number(s):
- [LA-UR-18-23813]

[Journal ID: ISSN 2296-987X; 27]

- Grant/Contract Number:
- [AC52-06NA25396]

- Resource Type:
- Published Article

- Journal Name:
- Frontiers in Astronomy and Space Sciences

- Additional Journal Information:
- [Journal Name: Frontiers in Astronomy and Space Sciences Journal Volume: 5]; Journal ID: ISSN 2296-987X

- Publisher:
- Frontiers Media SA

- Country of Publication:
- Switzerland

- Language:
- English

- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS; Heliospheric and Magnetospheric Physics; Mathematics; Magnetic Fusion Energy; plasma; kinetic; spectral; Hermite; turbulence

### Citation Formats

```
Roytershteyn, Vadim, and Delzanno, Gian Luca. Spectral Approach to Plasma Kinetic Simulations Based on Hermite Decomposition in the Velocity Space. Switzerland: N. p., 2018.
Web. doi:10.3389/fspas.2018.00027.
```

```
Roytershteyn, Vadim, & Delzanno, Gian Luca. Spectral Approach to Plasma Kinetic Simulations Based on Hermite Decomposition in the Velocity Space. Switzerland. doi:10.3389/fspas.2018.00027.
```

```
Roytershteyn, Vadim, and Delzanno, Gian Luca. Tue .
"Spectral Approach to Plasma Kinetic Simulations Based on Hermite Decomposition in the Velocity Space". Switzerland. doi:10.3389/fspas.2018.00027.
```

```
@article{osti_1467122,
```

title = {Spectral Approach to Plasma Kinetic Simulations Based on Hermite Decomposition in the Velocity Space},

author = {Roytershteyn, Vadim and Delzanno, Gian Luca},

abstractNote = {Here, spectral (transform) methods for solution of Vlasov-Maxwell system have shown significant promise as numerical methods capable of efficiently treating fluid-kinetic coupling in magnetized plasmas. We discuss SpectralPlasmaSolver (SPS), an implementation of three-dimensional, fully electromagnetic algorithm based on a decomposition of the plasma distribution function in Hermite modes in velocity space and Fourier modes in physical space. A fully-implicit time discretization is adopted for numerical stability and to ensure exact conservation laws for total mass, momentum and energy. The SPS code is parallelized using Message Passing Interface for distributed memory architectures. Application of the method to analysis of kinetic range of scales in plasma turbulence under conditions typical of the solar wind is demonstrated. With only 4 Hermite modes per velocity dimension, the algorithm yields damping rates of kinetic Alfvén waves with accuracy of 50% or better, which is sufficient to obtain a model of kinetic scales capable of reproducing many of the expected statistical properties of turbulent fluctuations. With increasing number of Hermite modes, progressively more accurate values for collisionless damping rates are obtained. Fully nonlinear simulations of decaying turbulence are presented and successfully compared with similar simulations performed using Particle-In-Cell method.},

doi = {10.3389/fspas.2018.00027},

journal = {Frontiers in Astronomy and Space Sciences},

number = ,

volume = [5],

place = {Switzerland},

year = {2018},

month = {8}

}

DOI: 10.3389/fspas.2018.00027

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