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Multiple-scale kinetic simulations with the energy conserving semi-implicit particle in cell method

Part of: PLA The Vlasov Equation

Published online by Cambridge University Press:  19 April 2017

Giovanni Lapenta ,
Diego Gonzalez-Herrero  and
Elisabetta Boella
Giovanni Lapenta*
Affiliation:
Department of Mathematics, KU Leuven, University of Leuven, Belgium
Diego Gonzalez-Herrero
Affiliation:
Department of Mathematics, KU Leuven, University of Leuven, Belgium
Elisabetta Boella
Affiliation:
Department of Mathematics, KU Leuven, University of Leuven, Belgium
*
†Email address for correspondence: valsusa@gmail.com
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Abstract

The recently developed energy conserving semi-implicit method (ECsim) for particle-in-cell (PIC) simulation is applied to multiple-scale problems where the electron-scale physics needs to be only partially retained and the interest is on the macroscopic or ion-scale processes. Unlike hybrid methods, the ECsim is capable of providing kinetic electron information, such as wave–electron interaction (Landau damping or cyclotron resonance) and non-Maxwellian electron velocity distributions. However, like hybrid methods, the ECsim does not need to resolve all electron scales, allowing time steps and grid spacings orders of magnitude larger than in explicit PIC schemes. The additional advantage of the ECsim is that the stability at large scale is obtained while conserving energy exactly. Three examples are presented: ion acoustic waves, electron acoustic instability and reconnection processes.

Keywords

astrophysical plasmas
Type
Research Article
Information
Journal of Plasma Physics , Volume 83 , Issue 2 , April 2017 , 705830205
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Copyright
© Cambridge University Press 2017 

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References

Balay, S., Abhyankar, S., Adams, M. F., Brown, J., Brune, P., Buschelman, K., Dalcin, L., Eijkhout, V., Gropp, W. D., Kaushik, D. et al. 2016 PETSc Web page http://www.mcs.anl.gov/petsc.Google Scholar
Birdsall, C. K. & Langdon, A. B. 2004 Plasma Physics via Computer Simulation. Taylor & Francis.Google Scholar
Birn, J., Drake, J. F., Shay, M. A., Rogers, B. N., Denton, R. E., Hesse, M., Kuznetsova, M., Ma, Z. W., Bhattacharjee, A., Otto, A. et al. 2001 Geospace environmental modeling (GEM) magnetic reconnection challenge. J. Geophys. Res. 106, 3715–3720.Google Scholar
Birn, J. & Priest, E. R. 2007 Reconnection of Magnetic Fields: Magnetohydrodynamics and Collisionless Theory and Observations. Cambridge University Press.Google Scholar
Biskamp, D. 2000 Magnetic Reconnection in Plasmas. Cambridge University Press.Google Scholar
Brackbill, J. U. & Cohen, B. I.(Eds) 1985 Multiple Time Scales. Academic.Google Scholar
Brackbill, J. U. & Forslund, D. W. 1982 An implicit method for electromagnetic plasma simulation in two dimension. J. Comput. Phys. 46, 271–308.Google Scholar
Burgess, D., Sulsky, D. & Brackbill, J. U. 1992 Mass matrix formulation of the flip particle-in-cell method. J. Comput. Phys. 103, 1–15.Google Scholar
Chen, G., Chacón, L. & Barnes, D. C. 2011 An energy- and charge-conserving, implicit, electrostatic particle-in-cell algorithm. J. Comput. Phys. 230, 7018–7036.CrossRefGoogle Scholar
Cohen, B. I., Langdon, A. B., Hewett, D. W. & Procassini, R. J. 1989 Performance and optimization of direct implicit particle simulation. J. Comput. Phys. 81, 151–168.Google Scholar
De Boor, C. 1978 A Practical Guide to Splines. Springer.Google Scholar
Divin, A., Lapenta, G., Markidis, S., Newman, D. L. & Goldman, M. V. 2012 Numerical simulations of separatrix instabilities in collisionless magnetic reconnection. Phys. Plasmas 19, 042110.Google Scholar
Divin, A., Markidis, S., Lapenta, G., Semenov, V. S., Erkaev, N. V. & Biernat, H. K. 2010 Model of electron pressure anisotropy in the electron diffusion region of collisionless magnetic reconnection. Phys. Plasmas 17, 122102.CrossRefGoogle Scholar
Drake, J. F., Shay, M. A., Thongthai, W. & Swisdak, M. 2005 Production of energetic electrons during magnetic reconnection. Phys. Rev. Lett. 94, 095001.Google Scholar
Fried, B. D. & Conte, S. P. 1961 The Plasma Dispersion Function. Academic.Google Scholar
Gary, S. P. 2005 Theory of Space Plasma Microinstabilities. Cambridge University Press.Google Scholar
Goldman, M. V., Lapenta, G., Newman, D. L., Markidis, S. & Che, H. 2011 Jet deflection by very weak guide fields during magnetic reconnection. Phys. Rev. Lett. 107, 135001.Google Scholar
Hewett, D. W. & Langdon, A. B. 1987 Electromagnetic direct implicit plasma simulation. J. Comput. Phys. 72, 121–155.Google Scholar
Hockney, R. W. & Eastwood, J. W. 1988 Computer Simulation Using Particles. Taylor & Francis.Google Scholar
Langdon, A. B., Cohen, B. I. & Friedman, A. 1983 Direct implicit large time-step particle simulation of plasmas. J. Comput. Phys. 51, 107–138.CrossRefGoogle Scholar
Lapenta, G. 2012 Particle simulations of space weather. J. Comput. Phys. 231, 795–821.Google Scholar
Lapenta, G.2016 Exactly energy conserving implicit moment particle in cell formulation. arXiv:1602.06326.CrossRefGoogle Scholar
Lapenta, G., Brackbill, J. U. & Ricci, P. 2006 Kinetic approach to microscopic–macroscopic coupling in space and laboratory plasmas. Phys. Plasmas 13, 055904.Google Scholar
Lapenta, G. & Markidis, S. 2011 Particle acceleration and energy conservation in particle in cell simulations. Phys. Plasmas 18, 072101.Google Scholar
Lapenta, G., Markidis, S., Divin, A., Goldman, M. & Newman, D. 2010 Scales of guide field reconnection at the hydrogen mass ratio. Phys. Plasmas 17, 082106.Google Scholar
Lapenta, G., Markidis, S., Divin, A., Goldman, M. V. & Newman, D. L. 2011 Bipolar electric field signatures of reconnection separatrices for a hydrogen plasma at realistic guide fields. Geophys. Res. Lett. 38, L17104.Google Scholar
Lapenta, G., Markidis, S., Divin, A., Newman, D. & Goldman, M. 2014 Separatrices: the crux of reconnection. J. Plasma Phys. 81, 1–39.Google Scholar
Markidis, S. & Lapenta, G. 2011 The energy conserving particle-in-cell method. J. Comput. Phys. 230, 7037–7052.Google Scholar
Markidis, S., Lapenta, G. & Rizwan-uddin 2010 Multi-scale simulations of plasma with iPIC3D. Maths Comput. Simul. 80, 1509–1519.Google Scholar
Moses, R. W., Finn, J. M. & Ling, K. M. 1993 Plasma heating by collisionless magnetic reconnection: analysis and computation. J. Geophys. Res. 98, 4013–4040.Google Scholar
Sulsky, D. & Brackbill, J. U. 1991 A numerical method for suspension flow. J. Comput. Phys. 96, 339–368.Google Scholar
Vu, H. X. & Brackbill, J. U. 1992 Celest1d: an implicit, fully-kinetic model for low-frequency, electromagnetic plasma simulation. Comput. Phys. Commun. 69, 253–276.Google Scholar