Numerical instability due to relativistic plasma drift in EM-PIC simulations

Detalhes bibliográficos
Autor(a) principal: Xu, X.
Data de Publicação: 2013
Outros Autores: Yu, P., Martins, S. F., Tsung, F. S., Decyk, V. K., Vieira, J., Fonseca, R. A., Lu, W., Silva, L. O., Mori, W. B.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://dx.doi.org/10.1016/j.cpc.2013.07.003
https://ciencia.iscte-iul.pt/public/pub/id/13328
http://hdl.handle.net/10071/7307
Resumo: The numerical instability observed in electromagnetic particle-in-cell (EM-PIC) simulations with a plasma drifting with relativistic velocities is studied using both theory and computer simulations. We derive the numerical dispersion relation for a cold plasma drifting with a relativistic velocity, and find an instability attributed to the intersection between beam resonances and the electromagnetic modes in the drifting plasma. The intersection can occur in the fundamental Brillouin zones when EM waves with phase velocities less than the speed of light exist, and from aliasing beam resonances and aliasing EM modes. The unstable modes are neither purely transverse nor longitudinal. The characteristic patterns of the instability in Fourier space for various simulation setups and Maxwell equation solvers are explored by solving the corresponding numerical dispersion relations. Furthermore, based upon these characteristic patterns, we derive an asymptotic expression for the instability growth rate. The asymptotic expression greatly speeds up the calculation of the instability growth rate and makes the parameter scans for minimal growth rate feasible even for full three dimensions. The results are compared against simulation results, and good agreements are found. These results can be used as a guide to develop possible approaches to mitigate the instability. We examine the use of a spectral solver and show that such a solver when combined with a low pass filter with a cutoff value of vertical bar(k) over right arrow vertical bar essentially eliminates the instability while not modifying modes of physical interest. The use of a spectral solver also provides minimal errors to electromagnetic modes in the lowest Brillouin zones.
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spelling Numerical instability due to relativistic plasma drift in EM-PIC simulationsParticle in cellPlasma simulationRelativistic plasma driftNumerical dispersion relationNumerical instabilityNumerical Cherenkov radiationThe numerical instability observed in electromagnetic particle-in-cell (EM-PIC) simulations with a plasma drifting with relativistic velocities is studied using both theory and computer simulations. We derive the numerical dispersion relation for a cold plasma drifting with a relativistic velocity, and find an instability attributed to the intersection between beam resonances and the electromagnetic modes in the drifting plasma. The intersection can occur in the fundamental Brillouin zones when EM waves with phase velocities less than the speed of light exist, and from aliasing beam resonances and aliasing EM modes. The unstable modes are neither purely transverse nor longitudinal. The characteristic patterns of the instability in Fourier space for various simulation setups and Maxwell equation solvers are explored by solving the corresponding numerical dispersion relations. Furthermore, based upon these characteristic patterns, we derive an asymptotic expression for the instability growth rate. The asymptotic expression greatly speeds up the calculation of the instability growth rate and makes the parameter scans for minimal growth rate feasible even for full three dimensions. The results are compared against simulation results, and good agreements are found. These results can be used as a guide to develop possible approaches to mitigate the instability. We examine the use of a spectral solver and show that such a solver when combined with a low pass filter with a cutoff value of vertical bar(k) over right arrow vertical bar essentially eliminates the instability while not modifying modes of physical interest. The use of a spectral solver also provides minimal errors to electromagnetic modes in the lowest Brillouin zones.Elsevier2014-05-21T14:01:22Z2013-11-01T00:00:00Z2013-112014-05-21T13:59:27Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://dx.doi.org/10.1016/j.cpc.2013.07.003https://ciencia.iscte-iul.pt/public/pub/id/13328http://hdl.handle.net/10071/7307eng0010-4655Xu, X.Yu, P.Martins, S. F.Tsung, F. S.Decyk, V. K.Vieira, J.Fonseca, R. A.Lu, W.Silva, L. O.Mori, W. B.info:eu-repo/semantics/embargoedAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-07-07T03:18:26Zoai:repositorio.iscte-iul.pt:10071/7307Portal AgregadorONGhttps://www.rcaap.pt/oai/openairemluisa.alvim@gmail.comopendoar:71602024-07-07T03:18:26Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Numerical instability due to relativistic plasma drift in EM-PIC simulations
title Numerical instability due to relativistic plasma drift in EM-PIC simulations
spellingShingle Numerical instability due to relativistic plasma drift in EM-PIC simulations
Xu, X.
Particle in cell
Plasma simulation
Relativistic plasma drift
Numerical dispersion relation
Numerical instability
Numerical Cherenkov radiation
title_short Numerical instability due to relativistic plasma drift in EM-PIC simulations
title_full Numerical instability due to relativistic plasma drift in EM-PIC simulations
title_fullStr Numerical instability due to relativistic plasma drift in EM-PIC simulations
title_full_unstemmed Numerical instability due to relativistic plasma drift in EM-PIC simulations
title_sort Numerical instability due to relativistic plasma drift in EM-PIC simulations
author Xu, X.
author_facet Xu, X.
Yu, P.
Martins, S. F.
Tsung, F. S.
Decyk, V. K.
Vieira, J.
Fonseca, R. A.
Lu, W.
Silva, L. O.
Mori, W. B.
author_role author
author2 Yu, P.
Martins, S. F.
Tsung, F. S.
Decyk, V. K.
Vieira, J.
Fonseca, R. A.
Lu, W.
Silva, L. O.
Mori, W. B.
author2_role author
author
author
author
author
author
author
author
author
dc.contributor.author.fl_str_mv Xu, X.
Yu, P.
Martins, S. F.
Tsung, F. S.
Decyk, V. K.
Vieira, J.
Fonseca, R. A.
Lu, W.
Silva, L. O.
Mori, W. B.
dc.subject.por.fl_str_mv Particle in cell
Plasma simulation
Relativistic plasma drift
Numerical dispersion relation
Numerical instability
Numerical Cherenkov radiation
topic Particle in cell
Plasma simulation
Relativistic plasma drift
Numerical dispersion relation
Numerical instability
Numerical Cherenkov radiation
description The numerical instability observed in electromagnetic particle-in-cell (EM-PIC) simulations with a plasma drifting with relativistic velocities is studied using both theory and computer simulations. We derive the numerical dispersion relation for a cold plasma drifting with a relativistic velocity, and find an instability attributed to the intersection between beam resonances and the electromagnetic modes in the drifting plasma. The intersection can occur in the fundamental Brillouin zones when EM waves with phase velocities less than the speed of light exist, and from aliasing beam resonances and aliasing EM modes. The unstable modes are neither purely transverse nor longitudinal. The characteristic patterns of the instability in Fourier space for various simulation setups and Maxwell equation solvers are explored by solving the corresponding numerical dispersion relations. Furthermore, based upon these characteristic patterns, we derive an asymptotic expression for the instability growth rate. The asymptotic expression greatly speeds up the calculation of the instability growth rate and makes the parameter scans for minimal growth rate feasible even for full three dimensions. The results are compared against simulation results, and good agreements are found. These results can be used as a guide to develop possible approaches to mitigate the instability. We examine the use of a spectral solver and show that such a solver when combined with a low pass filter with a cutoff value of vertical bar(k) over right arrow vertical bar essentially eliminates the instability while not modifying modes of physical interest. The use of a spectral solver also provides minimal errors to electromagnetic modes in the lowest Brillouin zones.
publishDate 2013
dc.date.none.fl_str_mv 2013-11-01T00:00:00Z
2013-11
2014-05-21T14:01:22Z
2014-05-21T13:59:27Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://dx.doi.org/10.1016/j.cpc.2013.07.003
https://ciencia.iscte-iul.pt/public/pub/id/13328
http://hdl.handle.net/10071/7307
url http://dx.doi.org/10.1016/j.cpc.2013.07.003
https://ciencia.iscte-iul.pt/public/pub/id/13328
http://hdl.handle.net/10071/7307
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0010-4655
dc.rights.driver.fl_str_mv info:eu-repo/semantics/embargoedAccess
eu_rights_str_mv embargoedAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
repository.mail.fl_str_mv mluisa.alvim@gmail.com
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