# A new method for analyzing and visualizing plasma simulations using a phase-space tessellation

## Abstract

We apply a novel phase-space interpolation technique referred to as the simplex-in-cell (SIC) method to analyze two- and three-dimensional particle-in-cell (PIC) simulations of electromagnetic plasmas. SIC relies on a discretization of the initial phase-space distribution function into simplices, which allows an approximation to the full, continuously defined distribution function to be constructed at any later time in the simulation. This allows densities, currents, and even full momentum distribution functions to be measured at any point in the simulation domain without averaging over control volumes. The SIC approach applies to any PIC simulation for which a tessellation of the initial particle distribution can be constructed. In this study, we use outputs from standard PIC simulations of the Weibel instability and compare physical quantities such as charge and current densities calculated in postprocessing using SIC and standard particle deposits. Using 2D simulations with 1–65 536 particles-per-cell, we find that SIC eliminates discrete particle noise and in some cases can reach a given noise level using ~1000 times fewer simulation particles than with standard particle deposition schemes. In regions of low density, such as between current filaments, SIC is able to capture small amplitude features even with fewer particles than gridpoints due tomore »

- Authors:

- Stanford Univ., CA (United States). Dept. of Physics, and Kavli Inst. for Particle Astrophysics and Cosmology; SLAC National Accelerator Lab., Menlo Park, CA (United States). High Energy Density Science Division
- SLAC National Accelerator Lab., Menlo Park, CA (United States). High Energy Density Science Division
- Stanford Univ., CA (United States). Dept. of Physics, and Kavli Inst. for Particle Astrophysics and Cosmology; SLAC National Accelerator Lab., Menlo Park, CA (United States)

- Publication Date:

- Research Org.:
- SLAC National Accelerator Lab., Menlo Park, CA (United States)

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

- OSTI Identifier:
- 1468691

- Alternate Identifier(s):
- OSTI ID: 1459754

- Grant/Contract Number:
- AC11339893; AC02-76SF00515; 100237

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 25; Journal Issue: 7; 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

```
Totorica, Samuel R., Fiuza, Frederico, and Abel, Tom. A new method for analyzing and visualizing plasma simulations using a phase-space tessellation. United States: N. p., 2018.
Web. doi:10.1063/1.5037348.
```

```
Totorica, Samuel R., Fiuza, Frederico, & Abel, Tom. A new method for analyzing and visualizing plasma simulations using a phase-space tessellation. United States. doi:10.1063/1.5037348.
```

```
Totorica, Samuel R., Fiuza, Frederico, and Abel, Tom. Wed .
"A new method for analyzing and visualizing plasma simulations using a phase-space tessellation". United States. doi:10.1063/1.5037348. https://www.osti.gov/servlets/purl/1468691.
```

```
@article{osti_1468691,
```

title = {A new method for analyzing and visualizing plasma simulations using a phase-space tessellation},

author = {Totorica, Samuel R. and Fiuza, Frederico and Abel, Tom},

abstractNote = {We apply a novel phase-space interpolation technique referred to as the simplex-in-cell (SIC) method to analyze two- and three-dimensional particle-in-cell (PIC) simulations of electromagnetic plasmas. SIC relies on a discretization of the initial phase-space distribution function into simplices, which allows an approximation to the full, continuously defined distribution function to be constructed at any later time in the simulation. This allows densities, currents, and even full momentum distribution functions to be measured at any point in the simulation domain without averaging over control volumes. The SIC approach applies to any PIC simulation for which a tessellation of the initial particle distribution can be constructed. In this study, we use outputs from standard PIC simulations of the Weibel instability and compare physical quantities such as charge and current densities calculated in postprocessing using SIC and standard particle deposits. Using 2D simulations with 1–65 536 particles-per-cell, we find that SIC eliminates discrete particle noise and in some cases can reach a given noise level using ~1000 times fewer simulation particles than with standard particle deposition schemes. In regions of low density, such as between current filaments, SIC is able to capture small amplitude features even with fewer particles than gridpoints due to the deformable nature of the SIC volume elements. Here, by calculating momentum distributions, we show how SIC can capture low density tails in the spectrum using far fewer particles than are necessary for standard particle deposits. We calculate the charge density on spatial grids of increasing resolution to demonstrate the ability of SIC to reveal fine-scale details that are not accessible with standard particle deposits. Finally, we show how SIC can be extended to 3D and give an example of its use to calculate the charge density from 3D PIC simulations of the Weibel instability. These results motivate the future implementation of SIC directly in the simulation force calculation for a novel low-noise electromagnetic plasma simulation method.},

doi = {10.1063/1.5037348},

journal = {Physics of Plasmas},

number = 7,

volume = 25,

place = {United States},

year = {2018},

month = {7}

}

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