Implementation of the two-dimensional electrostatic particle-in-cell method

We provide a guide to implementing the particle-in-cell algorithm, which is useful for simulating diverse phenomena in plasmas. We focus on two-dimensional systems which have vector fields with three Cartesian components but depend only on two spatial coordinates. We describe the algorithm in detail...

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2020
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Universidad de Medellín
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Repositorio UDEM
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eng
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oai_identifier_str oai:repository.udem.edu.co:11407/5693
network_acronym_str REPOUDEM2
network_name_str Repositorio UDEM
repository_id_str
dc.title.none.fl_str_mv Implementation of the two-dimensional electrostatic particle-in-cell method
title Implementation of the two-dimensional electrostatic particle-in-cell method
spellingShingle Implementation of the two-dimensional electrostatic particle-in-cell method
title_short Implementation of the two-dimensional electrostatic particle-in-cell method
title_full Implementation of the two-dimensional electrostatic particle-in-cell method
title_fullStr Implementation of the two-dimensional electrostatic particle-in-cell method
title_full_unstemmed Implementation of the two-dimensional electrostatic particle-in-cell method
title_sort Implementation of the two-dimensional electrostatic particle-in-cell method
description We provide a guide to implementing the particle-in-cell algorithm, which is useful for simulating diverse phenomena in plasmas. We focus on two-dimensional systems which have vector fields with three Cartesian components but depend only on two spatial coordinates. We describe the algorithm in detail, including particle-to-grid interpolation, the fast Fourier transform, the Boris algorithm, and the use of dimensionless units. As an example, we discuss a simulation of the two-stream instability, which occurs in a plasma system composed of two counter-streaming electrons and an ion background at rest. © 2020 American Association of Physics Teachers.
publishDate 2020
dc.date.accessioned.none.fl_str_mv 2020-04-29T14:53:41Z
dc.date.available.none.fl_str_mv 2020-04-29T14:53:41Z
dc.date.none.fl_str_mv 2020
dc.type.eng.fl_str_mv Article
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dc.identifier.issn.none.fl_str_mv 29505
dc.identifier.uri.none.fl_str_mv http://hdl.handle.net/11407/5693
dc.identifier.doi.none.fl_str_mv 10.1119/10.0000375
identifier_str_mv 29505
10.1119/10.0000375
url http://hdl.handle.net/11407/5693
dc.language.iso.none.fl_str_mv eng
language eng
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dc.relation.citationvolume.none.fl_str_mv 88
dc.relation.citationissue.none.fl_str_mv 2
dc.relation.citationstartpage.none.fl_str_mv 159
dc.relation.citationendpage.none.fl_str_mv 167
dc.relation.references.none.fl_str_mv Chen, F.F., (1984) Introduction to Plasma Physics and Controlled Fusion, , Springer, New York
Havlí?ková, E., Fluid model of plasma and computational methods for solution (2006) WDS'06 Proceedings of Contributed Papers, Part III (4), pp. 180-186. , Prague, Czech Republic
Howes, G.G., Limitations of Hall MHD as a model for turbulence in weakly collisional plasmas (2009) Nonlinear Processes Geophys., 16 (2), pp. 219-232
Dendy, R.O., (1990) Plasma Dynamics, , Oxford U. P., Oxford, UK
Piel, A., (2010) Plasma Physics: An Introduction to Laboratory, Space, and Fusion Plasmas, , Springer, New York
Verboncoeur, J.P., Particle simulation of plasmas: Review and advances (2005) Plasma Phys. Controlled Fusion, 47, pp. A231-A260
Birdsall, C.K., Langdon, A.B., (2004) Plasma Physics Via Computer Simulation, , Taylor & Francis, Oxfordshire, UK
Pritchett, P.L., Particle-in-cell simulation of plasmas - A tutorial (2003) Space Plasma Simulation, 615, pp. 1-24. , edited by C. T. Büchner, Jörg Scholer, and Manfred Dum, Lecture Notes in Physics (Springer, New York)
Benedetti, C., Sgattoni, A., Turchetti, G., Londrillo, P., ALaDyn: A high-accuracy PIC code for the Maxwell-Vlasov equations (2008) IEEE Trans. Plasma Sci., 36 (4), pp. 1790-1798
Martins, S.F., Fonseca, R.A., Vieira, J., Silva, L.O., Lu, W., Mori, W.B., Modeling laser Wakefield accelerator experiments with ultrafast particle-in-cell simulations in boosted frames (2010) Phys. Plasmas, 17
Klimo, O., Weber, S., Tikhonchuk, V.T., Limpouch, J., Particle-in-cell simulations of laser-plasma interaction for the shock ignition scenario (2010) Plasma Phys. Controlled Fusion, 52 (5)
Derouillat, J., Beck, A., Pérez, F., Vinci, T., Chiaramello, M., Grassi, A., Flé, M., Grech, M., SMILEI: A collaborative, open-source, multi-purpose particle-in-cell code for plasma simulation (2018) Comput. Phys. Commun., 222, pp. 351-373
https://github.com/UCLA-Plasma-Simulation-Group, UCLA Plasma Simulation Group
Ellis, I.N., Strozzi, D.J., Winjum, B.J., Tsung, F.S., Grismayer, T., Mori, W.B., Fahlen, J.E., Williams, E.A., Convective Raman amplification of light pulses causing kinetic inflation in inertial fusion plasmas (2012) Phys. Plasmas, 19
Yan, R., Ren, C., Li, J., Maximov, A.V., Mori, W.B., Sheng, Z.-M., Tsung, F.S., Generating energetic electrons through staged acceleration in the two-plasmon-decay instability in inertial confinement fusion (2012) Phys. Rev. Lett., 108
Mozer, F.S., Pritchett, P.L., Magnetic field reconnection: A first-principles perspective (2010) Phys. Today, 63 (6), pp. 34-39
Pritchett, P.L., Coroniti, F.V., A kinetic ballooning/interchange instability in the magnetotail (2010) J. Geophys. Res.: Space Phys., 15, pp. 1-11. , https://doi.org/10.1029/2009JA014752
Vieira, J., Martins, J.L., Pathak, V.B., Fonseca, R.A., Mori, W.B., Silva, L.O., Magnetically assisted self-injection and radiation generation for plasma-based acceleration (2012) Plasma Phys. Controlled Fusion, 54
Vieira, J., Fonseca, R.A., Mori, W.B., Silva, L.O., Ion motion in self-modulated plasma Wakefield accelerators (2012) Phys. Rev. Lett., 109
Kimura, W.D., Milchberg, H.M., Muggli, P., Li, X., Mori, W.B., Hollow plasma channel for positron plasma Wakefield acceleration (2011) Phys. Rev. Spec. Top. - Accel. Beams, 14
Verleye, B., Henri, P., Wuyts, R., Lapenta, G., Meerbergen, K., Implementation of a 2D electrostatic particle-in-cell algorithm in unified parallel C with dynamic load-balancing (2013) Comput. Fluids, 80 (1), pp. 10-16
Wolf, E.M., Causley, M., Christlieb, A., Bettencourt, M., A particle-in-cell method for the simulation of plasmas based on an unconditionally stable field solver (2016) J. Comput. Phys., 326, pp. 342-372
Tajima, T., Clark, A., Craddock, G.G., Gilden, D.L., Leung, W.K., Li, Y.M., Robertson, J.A., Saltzman, B.J., Particle simulation of plasmas and stellar systems (1985) Am. J. Phys., 53, pp. 365-370
https://github.com/dfrodriguezp/PiCM-cpp, PiCM-cpp
Miyake, T., Omura, Y., Matsumoto, H., Kojima, H., Two-dimensional computer simulations of electrostatic solitary waves observed by Geotail spacecraft (1998) J. Geophys. Res., 103, pp. 11841-11850. , https://doi.org/10.1029/98JA00760
Olson, J., Miloch, W.J., Ratynskaia, S., Yaroshenko, V., Potential structure around the Cassini spacecraft near the orbit of Enceladus (2010) Phys. Plasmas, 17
Blandón, J., Grisales, J., Riascos, H., Electrostatic plasma simulation by particle-in-cell method using ANACONDA package (2017) J. Phys.: Conf. Ser., 850. , in
Dehnen, W., Read, J.I., N-body simulations of gravitational dynamics (2011) Eur. Phys. J. Plus, 126, p. 55
Aggarwal, S., Two-stream instability in plasmas with arbitrary (1979) Astrophys. Space Sci., 66, pp. 341-348
Umeda, T., Omura, Y., Miyake, T., Matsumoto, H., Ashour-Abdalla, M., Nonlinear evolution of the electron two-stream instability: Two-dimensional particle simulations (2006) J. Geophys. Res.: Space Phys., 111 (10), pp. 1-9. , https://doi.org/10.1029/2006JA011762
Forslund, D.W., Fundamentals of plasma simulation (1985) Space Sci. Rev., 42 (1-2), pp. 3-16
Weisstein, E.W., Discrete Fourier Transform, , http://mathworld.wolfram.com/DiscreteFourierTransform.html
Boris, J.P., (1970) Acceleration Calculation from A Scalar Potential, , Report No. MATT-769 (Plasma Physics Laboratory, Princeton University)
Qin, H., Zhang, S., Xiao, J., Liu, J., Sun, Y., Tang, W.M., Why is Boris algorithm so good? (2013) Phys. Plasmas, 20 (8)
Boozer, A.D., Simulating a one-dimensional plasma (2010) Am. J. Phys., 78 (6), pp. 580-584
Hutchinson, I.H., Electron holes in phase space: What they are and why they matter (2017) Phys. Plasmas, 24
Ghorbanalilu, M., Abdollahzadeh, E., Rahbari, S.H., Particle-in-cell simulation of two stream instability in the non-extensive statistics (2014) Laser Part. Beams, 32 (3), pp. 399-407
Wu, M., Lu, Q., Zhu, J., Du, A., Wang, S., The magnetic structures of electron phase-space holes formed in the electron two-stream instability (2012) Astrophys. Space Sci., 338 (1), pp. 81-85
Mingyu, W., Quanming, L., Jie, Z., Peiran, W., Shui, W., Wu, M., Lu, Q., Wang, S., Electromagnetic particle-in-cell simulations of electron holes formed during the electron two-stream instability (2013) Plasma Sci. Technol., 15 (1), pp. 17-24
https://github.com/dfrodriguezp/PiCM-cpp/wiki, PiCM-cpWiki
Engel, A.V., Cozens, J.R., Flame plasmas (1965) Advances in Electronics and Electron Physics, 20, pp. 99-146. , edited by L. L. Marton (Academic Press, Massachusetts)
Sturrock, P.A., Excitation of plasma oscillations (1960) Phys. Rev., 117, pp. 1426-1429
Hasegawa, A., Theory of longitudinal plasma instabilities (1968) Phys. Rev., 169, pp. 204-214
Kumar, A., Shukla, C., Das, A., Kaw, P., Energy principle for excitations in plasmas with counterstreaming electron flows (2018) AIP Adv., 8
Anderson, D., Fedele, R., Lisak, M., A tutorial presentation of the two stream instability and Landau damping (2001) Am. J. Phys., 69 (12), pp. 1262-1266
Boyd, T.J.M., Sanderson, J.J., (2003) The Physics of Plasmas, , Cambridge U. P., Cambridge, UK
Tomori, A., Plasma dispersion relation and instabilities in electron velocity distribution function (2014) WDS'14 Proceedings of Contributed Papers-Physics, pp. 298-303. , Prague, Czech Republic
Matsumoto, H., Omura, Y., Particle simulation of electromagnetic waves and its application to space plasmas (1985) Computer Simulation of Space Plasmas (A86-21759 08-75), pp. 3-41. , edited by H. Matsumoto and T. Sato (Reidel Publishing, Dordrecht, Netherlands)
Omura, Y., Matsumoto, H., Miyake, T., Kojima, H., Electron beam instabilities as generation mechanism of electrostatic solitary waves in the magnetotail (1996) J. Geophys. Res.: Space Phys., 101 (A2), pp. 2685-2697. , https://doi.org/10.1029/95JA03145
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_16ec
rights_invalid_str_mv http://purl.org/coar/access_right/c_16ec
dc.publisher.none.fl_str_mv American Association of Physics Teachers
dc.publisher.program.none.fl_str_mv Facultad de Ciencias Básicas
dc.publisher.faculty.none.fl_str_mv Facultad de Ciencias Básicas
publisher.none.fl_str_mv American Association of Physics Teachers
dc.source.none.fl_str_mv American Journal of Physics
institution Universidad de Medellín
repository.name.fl_str_mv Repositorio Institucional Universidad de Medellin
repository.mail.fl_str_mv repositorio@udem.edu.co
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spelling 20202020-04-29T14:53:41Z2020-04-29T14:53:41Z29505http://hdl.handle.net/11407/569310.1119/10.0000375We provide a guide to implementing the particle-in-cell algorithm, which is useful for simulating diverse phenomena in plasmas. We focus on two-dimensional systems which have vector fields with three Cartesian components but depend only on two spatial coordinates. We describe the algorithm in detail, including particle-to-grid interpolation, the fast Fourier transform, the Boris algorithm, and the use of dimensionless units. As an example, we discuss a simulation of the two-stream instability, which occurs in a plasma system composed of two counter-streaming electrons and an ion background at rest. © 2020 American Association of Physics Teachers.engAmerican Association of Physics TeachersFacultad de Ciencias BásicasFacultad de Ciencias Básicashttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85078927777&doi=10.1119%2f10.0000375&partnerID=40&md5=cfb460ddaed58ff53e092245f1cddbe3882159167Chen, F.F., (1984) Introduction to Plasma Physics and Controlled Fusion, , Springer, New YorkHavlí?ková, E., Fluid model of plasma and computational methods for solution (2006) WDS'06 Proceedings of Contributed Papers, Part III (4), pp. 180-186. , Prague, Czech RepublicHowes, G.G., Limitations of Hall MHD as a model for turbulence in weakly collisional plasmas (2009) Nonlinear Processes Geophys., 16 (2), pp. 219-232Dendy, R.O., (1990) Plasma Dynamics, , Oxford U. P., Oxford, UKPiel, A., (2010) Plasma Physics: An Introduction to Laboratory, Space, and Fusion Plasmas, , Springer, New YorkVerboncoeur, J.P., Particle simulation of plasmas: Review and advances (2005) Plasma Phys. Controlled Fusion, 47, pp. A231-A260Birdsall, C.K., Langdon, A.B., (2004) Plasma Physics Via Computer Simulation, , Taylor & Francis, Oxfordshire, UKPritchett, P.L., Particle-in-cell simulation of plasmas - A tutorial (2003) Space Plasma Simulation, 615, pp. 1-24. , edited by C. T. Büchner, Jörg Scholer, and Manfred Dum, Lecture Notes in Physics (Springer, New York)Benedetti, C., Sgattoni, A., Turchetti, G., Londrillo, P., ALaDyn: A high-accuracy PIC code for the Maxwell-Vlasov equations (2008) IEEE Trans. Plasma Sci., 36 (4), pp. 1790-1798Martins, S.F., Fonseca, R.A., Vieira, J., Silva, L.O., Lu, W., Mori, W.B., Modeling laser Wakefield accelerator experiments with ultrafast particle-in-cell simulations in boosted frames (2010) Phys. Plasmas, 17Klimo, O., Weber, S., Tikhonchuk, V.T., Limpouch, J., Particle-in-cell simulations of laser-plasma interaction for the shock ignition scenario (2010) Plasma Phys. Controlled Fusion, 52 (5)Derouillat, J., Beck, A., Pérez, F., Vinci, T., Chiaramello, M., Grassi, A., Flé, M., Grech, M., SMILEI: A collaborative, open-source, multi-purpose particle-in-cell code for plasma simulation (2018) Comput. Phys. Commun., 222, pp. 351-373https://github.com/UCLA-Plasma-Simulation-Group, UCLA Plasma Simulation GroupEllis, I.N., Strozzi, D.J., Winjum, B.J., Tsung, F.S., Grismayer, T., Mori, W.B., Fahlen, J.E., Williams, E.A., Convective Raman amplification of light pulses causing kinetic inflation in inertial fusion plasmas (2012) Phys. Plasmas, 19Yan, R., Ren, C., Li, J., Maximov, A.V., Mori, W.B., Sheng, Z.-M., Tsung, F.S., Generating energetic electrons through staged acceleration in the two-plasmon-decay instability in inertial confinement fusion (2012) Phys. Rev. Lett., 108Mozer, F.S., Pritchett, P.L., Magnetic field reconnection: A first-principles perspective (2010) Phys. Today, 63 (6), pp. 34-39Pritchett, P.L., Coroniti, F.V., A kinetic ballooning/interchange instability in the magnetotail (2010) J. Geophys. Res.: Space Phys., 15, pp. 1-11. , https://doi.org/10.1029/2009JA014752Vieira, J., Martins, J.L., Pathak, V.B., Fonseca, R.A., Mori, W.B., Silva, L.O., Magnetically assisted self-injection and radiation generation for plasma-based acceleration (2012) Plasma Phys. Controlled Fusion, 54Vieira, J., Fonseca, R.A., Mori, W.B., Silva, L.O., Ion motion in self-modulated plasma Wakefield accelerators (2012) Phys. Rev. Lett., 109Kimura, W.D., Milchberg, H.M., Muggli, P., Li, X., Mori, W.B., Hollow plasma channel for positron plasma Wakefield acceleration (2011) Phys. Rev. Spec. Top. - Accel. Beams, 14Verleye, B., Henri, P., Wuyts, R., Lapenta, G., Meerbergen, K., Implementation of a 2D electrostatic particle-in-cell algorithm in unified parallel C with dynamic load-balancing (2013) Comput. Fluids, 80 (1), pp. 10-16Wolf, E.M., Causley, M., Christlieb, A., Bettencourt, M., A particle-in-cell method for the simulation of plasmas based on an unconditionally stable field solver (2016) J. Comput. Phys., 326, pp. 342-372Tajima, T., Clark, A., Craddock, G.G., Gilden, D.L., Leung, W.K., Li, Y.M., Robertson, J.A., Saltzman, B.J., Particle simulation of plasmas and stellar systems (1985) Am. J. Phys., 53, pp. 365-370https://github.com/dfrodriguezp/PiCM-cpp, PiCM-cppMiyake, T., Omura, Y., Matsumoto, H., Kojima, H., Two-dimensional computer simulations of electrostatic solitary waves observed by Geotail spacecraft (1998) J. Geophys. Res., 103, pp. 11841-11850. , https://doi.org/10.1029/98JA00760Olson, J., Miloch, W.J., Ratynskaia, S., Yaroshenko, V., Potential structure around the Cassini spacecraft near the orbit of Enceladus (2010) Phys. Plasmas, 17Blandón, J., Grisales, J., Riascos, H., Electrostatic plasma simulation by particle-in-cell method using ANACONDA package (2017) J. Phys.: Conf. Ser., 850. , inDehnen, W., Read, J.I., N-body simulations of gravitational dynamics (2011) Eur. Phys. J. Plus, 126, p. 55Aggarwal, S., Two-stream instability in plasmas with arbitrary (1979) Astrophys. Space Sci., 66, pp. 341-348Umeda, T., Omura, Y., Miyake, T., Matsumoto, H., Ashour-Abdalla, M., Nonlinear evolution of the electron two-stream instability: Two-dimensional particle simulations (2006) J. Geophys. Res.: Space Phys., 111 (10), pp. 1-9. , https://doi.org/10.1029/2006JA011762Forslund, D.W., Fundamentals of plasma simulation (1985) Space Sci. Rev., 42 (1-2), pp. 3-16Weisstein, E.W., Discrete Fourier Transform, , http://mathworld.wolfram.com/DiscreteFourierTransform.htmlBoris, J.P., (1970) Acceleration Calculation from A Scalar Potential, , Report No. MATT-769 (Plasma Physics Laboratory, Princeton University)Qin, H., Zhang, S., Xiao, J., Liu, J., Sun, Y., Tang, W.M., Why is Boris algorithm so good? (2013) Phys. Plasmas, 20 (8)Boozer, A.D., Simulating a one-dimensional plasma (2010) Am. J. Phys., 78 (6), pp. 580-584Hutchinson, I.H., Electron holes in phase space: What they are and why they matter (2017) Phys. Plasmas, 24Ghorbanalilu, M., Abdollahzadeh, E., Rahbari, S.H., Particle-in-cell simulation of two stream instability in the non-extensive statistics (2014) Laser Part. Beams, 32 (3), pp. 399-407Wu, M., Lu, Q., Zhu, J., Du, A., Wang, S., The magnetic structures of electron phase-space holes formed in the electron two-stream instability (2012) Astrophys. Space Sci., 338 (1), pp. 81-85Mingyu, W., Quanming, L., Jie, Z., Peiran, W., Shui, W., Wu, M., Lu, Q., Wang, S., Electromagnetic particle-in-cell simulations of electron holes formed during the electron two-stream instability (2013) Plasma Sci. Technol., 15 (1), pp. 17-24https://github.com/dfrodriguezp/PiCM-cpp/wiki, PiCM-cpWikiEngel, A.V., Cozens, J.R., Flame plasmas (1965) Advances in Electronics and Electron Physics, 20, pp. 99-146. , edited by L. L. Marton (Academic Press, Massachusetts)Sturrock, P.A., Excitation of plasma oscillations (1960) Phys. Rev., 117, pp. 1426-1429Hasegawa, A., Theory of longitudinal plasma instabilities (1968) Phys. Rev., 169, pp. 204-214Kumar, A., Shukla, C., Das, A., Kaw, P., Energy principle for excitations in plasmas with counterstreaming electron flows (2018) AIP Adv., 8Anderson, D., Fedele, R., Lisak, M., A tutorial presentation of the two stream instability and Landau damping (2001) Am. J. Phys., 69 (12), pp. 1262-1266Boyd, T.J.M., Sanderson, J.J., (2003) The Physics of Plasmas, , Cambridge U. P., Cambridge, UKTomori, A., Plasma dispersion relation and instabilities in electron velocity distribution function (2014) WDS'14 Proceedings of Contributed Papers-Physics, pp. 298-303. , Prague, Czech RepublicMatsumoto, H., Omura, Y., Particle simulation of electromagnetic waves and its application to space plasmas (1985) Computer Simulation of Space Plasmas (A86-21759 08-75), pp. 3-41. , edited by H. Matsumoto and T. Sato (Reidel Publishing, Dordrecht, Netherlands)Omura, Y., Matsumoto, H., Miyake, T., Kojima, H., Electron beam instabilities as generation mechanism of electrostatic solitary waves in the magnetotail (1996) J. Geophys. Res.: Space Phys., 101 (A2), pp. 2685-2697. , https://doi.org/10.1029/95JA03145American Journal of PhysicsImplementation of the two-dimensional electrostatic particle-in-cell methodArticleinfo:eu-repo/semantics/articlehttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Rodríguez-Patiño, D.F., PCM Computational Applications, Departamento de Física y Química, Universidad Nacional de Colombia, Manizales, 170003, Colombia, Basic Sciences Faculty, Universidad de Medellín, Medellín, 050026, Colombia; Ramírez, S., PCM Computational Applications, Departamento de Física y Química, Universidad Nacional de Colombia, Manizales, 170003, Colombia, Basic Sciences Faculty, Universidad de Medellín, Medellín, 050026, Colombia; Salcedo-Gallo, J.S., PCM Computational Applications, Departamento de Física y Química, Universidad Nacional de Colombia, Manizales, 170003, Colombia, Basic Sciences Faculty, Universidad de Medellín, Medellín, 050026, Colombia; Hoyos, J.H., PCM Computational Applications, Departamento de Física y Química, Universidad Nacional de Colombia, Manizales, 170003, Colombia, Basic Sciences Faculty, Universidad de Medellín, Medellín, 050026, Colombia; Restrepo-Parra, E., PCM Computational Applications, Departamento de Física y Química, Universidad Nacional de Colombia, Manizales, 170003, Colombia, Basic Sciences Faculty, Universidad de Medellín, Medellín, 050026, Colombiahttp://purl.org/coar/access_right/c_16ecRodríguez-Patiño D.F.Ramírez S.Salcedo-Gallo J.S.Hoyos J.H.Restrepo-Parra E.11407/5693oai:repository.udem.edu.co:11407/56932020-05-27 17:51:46.109Repositorio Institucional Universidad de Medellinrepositorio@udem.edu.co

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