Numerical instability due to relativistic plasma drift in EM-PIC simulations
Autor(a) principal: | |
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Data de Publicação: | 2013 |
Outros Autores: | , , , , , , , , |
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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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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1817546438633062400 |