# Controlling the numerical Cerenkov instability in PIC simulations using a customized finite difference Maxwell solver and a local FFT based current correction

## Abstract

In this study we present a customized finite-difference-time-domain (FDTD) Maxwell solver for the particle-in-cell (PIC) algorithm. The solver is customized to effectively eliminate the numerical Cerenkov instability (NCI) which arises when a plasma (neutral or non-neutral) relativistically drifts on a grid when using the PIC algorithm. We control the EM dispersion curve in the direction of the plasma drift of a FDTD Maxwell solver by using a customized higher order finite difference operator for the spatial derivative along the direction of the drift (1ˆ direction). We show that this eliminates the main NCI modes with moderate |k _{1}|, while keeps additional main NCI modes well outside the range of physical interest with higher |k _{1}|. These main NCI modes can be easily filtered out along with first spatial aliasing NCI modes which are also at the edge of the fundamental Brillouin zone. The customized solver has the possible advantage of improved parallel scalability because it can be easily partitioned along 1ˆ which typically has many more cells than other directions for the problems of interest. We show that FFTs can be performed locally to current on each partition to filter out the main and first spatial aliasing NCI modes, andmore »

- Authors:

- Tsinghua Univ., Beijing (China)
- Univ. of California, Los Angeles, CA (United States)
- SLAC National Accelerator Lab., Menlo Park, CA (United States)
- Univ. de Lisboa, Lisbon (Portugal); ISCTE - Instituto Univ. de Lisboa, Lisbon (Portugal)

- Publication Date:

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

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1352201

- Alternate Identifier(s):
- OSTI ID: 1398307

- Grant/Contract Number:
- 11425521; 11535006; 11375006; ACI 1339893; 1500630; 1614949; SC0014260; SC0010064; SC0008316; AC02-76SF00515

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Computer Physics Communications

- Additional Journal Information:
- Journal Volume: 214; Journal Issue: C; Journal ID: ISSN 0010-4655

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; PIC simulation; hybrid Maxwell solver; relativistic plasma drift; numerical Cerenkov instability; Lorentz boosted frame

### Citation Formats

```
Li, Fei, Yu, Peicheng, Xu, Xinlu, Fiuza, Frederico, Decyk, Viktor K., Dalichaouch, Thamine, Davidson, Asher, Tableman, Adam, An, Weiming, Tsung, Frank S., Fonseca, Ricardo A., Lu, Wei, and Mori, Warren B.
```*Controlling the numerical Cerenkov instability in PIC simulations using a customized finite difference Maxwell solver and a local FFT based current correction*. United States: N. p., 2017.
Web. doi:10.1016/j.cpc.2017.01.001.

```
Li, Fei, Yu, Peicheng, Xu, Xinlu, Fiuza, Frederico, Decyk, Viktor K., Dalichaouch, Thamine, Davidson, Asher, Tableman, Adam, An, Weiming, Tsung, Frank S., Fonseca, Ricardo A., Lu, Wei, & Mori, Warren B.
```*Controlling the numerical Cerenkov instability in PIC simulations using a customized finite difference Maxwell solver and a local FFT based current correction*. United States. doi:10.1016/j.cpc.2017.01.001.

```
Li, Fei, Yu, Peicheng, Xu, Xinlu, Fiuza, Frederico, Decyk, Viktor K., Dalichaouch, Thamine, Davidson, Asher, Tableman, Adam, An, Weiming, Tsung, Frank S., Fonseca, Ricardo A., Lu, Wei, and Mori, Warren B. Thu .
"Controlling the numerical Cerenkov instability in PIC simulations using a customized finite difference Maxwell solver and a local FFT based current correction". United States.
doi:10.1016/j.cpc.2017.01.001. https://www.osti.gov/servlets/purl/1352201.
```

```
@article{osti_1352201,
```

title = {Controlling the numerical Cerenkov instability in PIC simulations using a customized finite difference Maxwell solver and a local FFT based current correction},

author = {Li, Fei and Yu, Peicheng and Xu, Xinlu and Fiuza, Frederico and Decyk, Viktor K. and Dalichaouch, Thamine and Davidson, Asher and Tableman, Adam and An, Weiming and Tsung, Frank S. and Fonseca, Ricardo A. and Lu, Wei and Mori, Warren B.},

abstractNote = {In this study we present a customized finite-difference-time-domain (FDTD) Maxwell solver for the particle-in-cell (PIC) algorithm. The solver is customized to effectively eliminate the numerical Cerenkov instability (NCI) which arises when a plasma (neutral or non-neutral) relativistically drifts on a grid when using the PIC algorithm. We control the EM dispersion curve in the direction of the plasma drift of a FDTD Maxwell solver by using a customized higher order finite difference operator for the spatial derivative along the direction of the drift (1ˆ direction). We show that this eliminates the main NCI modes with moderate |k1|, while keeps additional main NCI modes well outside the range of physical interest with higher |k1|. These main NCI modes can be easily filtered out along with first spatial aliasing NCI modes which are also at the edge of the fundamental Brillouin zone. The customized solver has the possible advantage of improved parallel scalability because it can be easily partitioned along 1ˆ which typically has many more cells than other directions for the problems of interest. We show that FFTs can be performed locally to current on each partition to filter out the main and first spatial aliasing NCI modes, and to correct the current so that it satisfies the continuity equation for the customized spatial derivative. This ensures that Gauss’ Law is satisfied. Lastly, we present simulation examples of one relativistically drifting plasma, of two colliding relativistically drifting plasmas, and of nonlinear laser wakefield acceleration (LWFA) in a Lorentz boosted frame that show no evidence of the NCI can be observed when using this customized Maxwell solver together with its NCI elimination scheme.},

doi = {10.1016/j.cpc.2017.01.001},

journal = {Computer Physics Communications},

number = C,

volume = 214,

place = {United States},

year = {Thu Jan 12 00:00:00 EST 2017},

month = {Thu Jan 12 00:00:00 EST 2017}

}

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