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Title: On numerical errors to the fields surrounding a relativistically moving particle in PIC codes

Abstract

The particle-in-cell (PIC) method is widely used to model the self-consistent interaction between discrete particles and electromagnetic fields. It has been successfully applied to problems across plasma physics including plasma based acceleration, inertial confinement fusion, magnetically confined fusion, space physics, astrophysics, high energy density plasmas. In many cases the physics involves how relativistic particles (those with high relativistic γ factors) are generated and interact with plasmas. However, when relativistic particles stream across the grid, both in “vacuum” and in plasma, many numerical issues may arise which can lead to unphysical results. We present a detailed analysis of how discretized Maxwell solvers used in PIC codes can lead to numerical errors to the fields that surround particles that move at relativistic speeds across the grid. Expressions for the axial electric field as integrals in k space are presented that reveal two types of errors. The first arises from errors to the numerator of the integrand and leads to unphysical fields that are antisymmetric about the particle. Furthermore, the second arises from errors to the denominator of the integrand and lead to Cherenkov like radiation in “vacuum”. These fields are not anti-symmetric, extend behind the particle, and cause the particle to acceleratemore » or decelerate depending on the solver and parameters. The unphysical fields are studied in detail for two representative solvers - the Yee solver and the FFT based solver. Although the Cherenkov fields are absent, the space charge fields are still present in the fundamental Brillouin zone for the FFT based solvers. In addition, the Cherenkov fields are present in higher order zones for the FFT based solvers. Comparison between the analytical solutions and PIC simulation results are presented. A solution for eliminating these unphysical fields by modifying the k operator in the axial direction is also presented. Using a customized finite difference solver, this solution was successfully implemented into OSIRIS [1]. Results from the customized solver are also presented. Additionally, this solution will be useful for a beam of particles that all move in one direction with a small angular divergence.« less

Authors:
 [1];  [2]; ORCiD logo [2];  [2];  [3];  [2];  [2];  [4];  [5];  [2]
+ Show Author Affiliations
  1. Univ. of California, Los Angeles, CA (United States); SLAC National Accelerator Lab., Menlo Park, CA (United States)
  2. Univ. of California, Los Angeles, CA (United States)
  3. Beijing Normal Univ. (China)
  4. Inst. of Superior Tecnico (IST), Lisbon (Portugal). Inst. de Plasma e Fusao Nuclear; Inst. Univ. de Lisboa (ISCTE), Lisbon (Portugal)
  5. SLAC National Accelerator Lab., Menlo Park, CA (United States)
Publication Date:
Research Org.:
SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)
Sponsoring Org.:
National Science Foundation (NSF); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR). Scientific Discovery through Advanced Computing (SciDAC); Ciência e Tecnologia (FCT)
OSTI Identifier:
1637496
Alternate Identifier(s):
OSTI ID: 1615407
Grant/Contract Number:  
AC02-76SF00515; SC0010064; 644405; 1734315; ACI-1339893; PTDC/FIS-PLA/2940/2014
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 413; Journal Issue: C; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Relativistic drifting particles; numerical Cherenkov radiation; numerical space charge like field; particle-in-cell method

Citation Formats

Xu, Xinlu, Li, Fei, Tsung, Frank S., Dalichaouch, Thamine N., An, Weiming, Wen, Han, Decyk, Viktor K., Fonseca, Ricardo A., Hogan, Mark J., and Mori, Warren B. On numerical errors to the fields surrounding a relativistically moving particle in PIC codes. United States: N. p., 2020. Web. doi:10.1016/j.jcp.2020.109451.
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Xu, Xinlu, Li, Fei, Tsung, Frank S., Dalichaouch, Thamine N., An, Weiming, Wen, Han, Decyk, Viktor K., Fonseca, Ricardo A., Hogan, Mark J., & Mori, Warren B. On numerical errors to the fields surrounding a relativistically moving particle in PIC codes. United States. https://doi.org/10.1016/j.jcp.2020.109451
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Xu, Xinlu, Li, Fei, Tsung, Frank S., Dalichaouch, Thamine N., An, Weiming, Wen, Han, Decyk, Viktor K., Fonseca, Ricardo A., Hogan, Mark J., and Mori, Warren B. Fri . "On numerical errors to the fields surrounding a relativistically moving particle in PIC codes". United States. https://doi.org/10.1016/j.jcp.2020.109451. https://www.osti.gov/servlets/purl/1637496.
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@article{osti_1637496,
title = {On numerical errors to the fields surrounding a relativistically moving particle in PIC codes},
author = {Xu, Xinlu and Li, Fei and Tsung, Frank S. and Dalichaouch, Thamine N. and An, Weiming and Wen, Han and Decyk, Viktor K. and Fonseca, Ricardo A. and Hogan, Mark J. and Mori, Warren B.},
abstractNote = {The particle-in-cell (PIC) method is widely used to model the self-consistent interaction between discrete particles and electromagnetic fields. It has been successfully applied to problems across plasma physics including plasma based acceleration, inertial confinement fusion, magnetically confined fusion, space physics, astrophysics, high energy density plasmas. In many cases the physics involves how relativistic particles (those with high relativistic γ factors) are generated and interact with plasmas. However, when relativistic particles stream across the grid, both in “vacuum” and in plasma, many numerical issues may arise which can lead to unphysical results. We present a detailed analysis of how discretized Maxwell solvers used in PIC codes can lead to numerical errors to the fields that surround particles that move at relativistic speeds across the grid. Expressions for the axial electric field as integrals in k space are presented that reveal two types of errors. The first arises from errors to the numerator of the integrand and leads to unphysical fields that are antisymmetric about the particle. Furthermore, the second arises from errors to the denominator of the integrand and lead to Cherenkov like radiation in “vacuum”. These fields are not anti-symmetric, extend behind the particle, and cause the particle to accelerate or decelerate depending on the solver and parameters. The unphysical fields are studied in detail for two representative solvers - the Yee solver and the FFT based solver. Although the Cherenkov fields are absent, the space charge fields are still present in the fundamental Brillouin zone for the FFT based solvers. In addition, the Cherenkov fields are present in higher order zones for the FFT based solvers. Comparison between the analytical solutions and PIC simulation results are presented. A solution for eliminating these unphysical fields by modifying the k operator in the axial direction is also presented. Using a customized finite difference solver, this solution was successfully implemented into OSIRIS [1]. Results from the customized solver are also presented. Additionally, this solution will be useful for a beam of particles that all move in one direction with a small angular divergence.},
doi = {10.1016/j.jcp.2020.109451},
journal = {Journal of Computational Physics},
number = C,
volume = 413,
place = {United States},
year = {Fri Apr 03 00:00:00 EDT 2020},
month = {Fri Apr 03 00:00:00 EDT 2020}
}
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https://doi.org/10.1016/j.jcp.2020.109451
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