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

  • Giovanni Lapenta (a1), Diego Gonzalez-Herrero (a1) and Elisabetta Boella (a1)

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.

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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
Birdsall, C. K. & Langdon, A. B. 2004 Plasma Physics via Computer Simulation. Taylor & Francis.
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, 37153720.
Birn, J. & Priest, E. R. 2007 Reconnection of Magnetic Fields: Magnetohydrodynamics and Collisionless Theory and Observations. Cambridge University Press.
Biskamp, D. 2000 Magnetic Reconnection in Plasmas. Cambridge University Press.
Brackbill, J. U. & Cohen, B. I.(Eds) 1985 Multiple Time Scales. Academic.
Brackbill, J. U. & Forslund, D. W. 1982 An implicit method for electromagnetic plasma simulation in two dimension. J. Comput. Phys. 46, 271308.
Burgess, D., Sulsky, D. & Brackbill, J. U. 1992 Mass matrix formulation of the flip particle-in-cell method. J. Comput. Phys. 103, 115.
Chen, G., Chacón, L. & Barnes, D. C. 2011 An energy- and charge-conserving, implicit, electrostatic particle-in-cell algorithm. J. Comput. Phys. 230, 70187036.
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, 151168.
De Boor, C. 1978 A Practical Guide to Splines. Springer.
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.
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.
Drake, J. F., Shay, M. A., Thongthai, W. & Swisdak, M. 2005 Production of energetic electrons during magnetic reconnection. Phys. Rev. Lett. 94, 095001.
Fried, B. D. & Conte, S. P. 1961 The Plasma Dispersion Function. Academic.
Gary, S. P. 2005 Theory of Space Plasma Microinstabilities. Cambridge University Press.
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.
Hewett, D. W. & Langdon, A. B. 1987 Electromagnetic direct implicit plasma simulation. J. Comput. Phys. 72, 121155.
Hockney, R. W. & Eastwood, J. W. 1988 Computer Simulation Using Particles. Taylor & Francis.
Langdon, A. B., Cohen, B. I. & Friedman, A. 1983 Direct implicit large time-step particle simulation of plasmas. J. Comput. Phys. 51, 107138.
Lapenta, G. 2012 Particle simulations of space weather. J. Comput. Phys. 231, 795821.
Lapenta, G.2016 Exactly energy conserving implicit moment particle in cell formulation. arXiv:1602.06326.
Lapenta, G., Brackbill, J. U. & Ricci, P. 2006 Kinetic approach to microscopic–macroscopic coupling in space and laboratory plasmas. Phys. Plasmas 13, 055904.
Lapenta, G. & Markidis, S. 2011 Particle acceleration and energy conservation in particle in cell simulations. Phys. Plasmas 18, 072101.
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.
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.
Lapenta, G., Markidis, S., Divin, A., Newman, D. & Goldman, M. 2014 Separatrices: the crux of reconnection. J. Plasma Phys. 81, 139.
Markidis, S. & Lapenta, G. 2011 The energy conserving particle-in-cell method. J. Comput. Phys. 230, 70377052.
Markidis, S., Lapenta, G. & Rizwan-uddin 2010 Multi-scale simulations of plasma with iPIC3D. Maths Comput. Simul. 80, 15091519.
Moses, R. W., Finn, J. M. & Ling, K. M. 1993 Plasma heating by collisionless magnetic reconnection: analysis and computation. J. Geophys. Res. 98, 40134040.
Sulsky, D. & Brackbill, J. U. 1991 A numerical method for suspension flow. J. Comput. Phys. 96, 339368.
Vu, H. X. & Brackbill, J. U. 1992 Celest1d: an implicit, fully-kinetic model for low-frequency, electromagnetic plasma simulation. Comput. Phys. Commun. 69, 253276.
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Journal of Plasma Physics
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