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 finitedifferencetimedomain (FDTD) Maxwell solver for the particleincell (PIC) algorithm. The solver is customized to effectively eliminate the numerical Cerenkov instability (NCI) which arises when a plasma (neutral or nonneutral) 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; AC0276SF00515
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Computer Physics Communications
 Additional Journal Information:
 Journal Volume: 214; Journal Issue: C; Journal ID: ISSN 00104655
 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 finitedifferencetimedomain (FDTD) Maxwell solver for the particleincell (PIC) algorithm. The solver is customized to effectively eliminate the numerical Cerenkov instability (NCI) which arises when a plasma (neutral or nonneutral) 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},
issn = {00104655},
number = C,
volume = 214,
place = {United States},
year = {2017},
month = {1}
}
Web of Science