Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-25T04:25:39.540Z Has data issue: false hasContentIssue false
  • English
  • Français

Absence of recurrence in Fourier–Fourier transformed Vlasov–Poisson simulations

Published online by Cambridge University Press:  23 July 2018

Alexander J. Klimas  and
Adolfo. F. Viñas
Alexander J. Klimas*
Affiliation:
GPHI/UMBC, NASA/Goddard Space Flight Center, Greenbelt, MD 20770, USA
Adolfo. F. Viñas
Affiliation:
NASA/Goddard Space Flight Center, Greenbelt, MD 20770, USA Department of Physics, American University, Washington, DC 20016, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

It is known that the filtered, doubly Fourier transformed, Eulerian Vlasov–Poisson simulation method does not exhibit any effects of recurrence. It has not been understood why this is so. It is shown that there is only one boundary in this simulation method where user input is allowed and that the appearance or not of recurrence depends on the character of the boundary data that are imposed. Examples are given that show that the choice of boundary data that leads to recurrence-free simulations does not degrade the accuracy of Landau damping simulations.

Keywords

plasma nonlinear phenomenaplasma simulation
Type
Research Article
Information
Journal of Plasma Physics , Volume 84 , Issue 4 , August 2018 , 905840405
Copyright
© Cambridge University Press 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abbasi, H., Jenab, M. H. & Pajouh, H. H. 2011 Preventing the recurrence effect in the Vlasov simulation by randomizing phase-point velocities in phase space. Phys. Rev. E 84 (3), doi:10.1103/PhysRevE.84.036702.Google ScholarPubMed
Black, C., Germaschewski, K., Bhattacharjee, A. & Ng, C. S. 2013 Discrete kinetic eigenmode spectra of electron plasma oscillations in weakly collisional plasma: a numerical study. Phys. Plasmas 20 (1), 012125.Google Scholar
Cheng, C. Z. & Knorr, G. 1976 Integration of Vlasov equation in configuration space. J. Comput. Phys. 22 (3), 330–351.Google Scholar
Einkemmer, L. & Ostermann, A. 2014 A strategy to suppress recurrence in grid-based Vlasov solvers. Eur. Phys. J. D 68 (7), 197.Google Scholar
Eliasson, B. 2001 Outflow boundary conditions for the Fourier tranformed one-dimensional Vlasov–Poisson system. J. Sci. Comput. 61 (1), 1–28.Google Scholar
Eliasson, B. 2002 Outflow boundary conditions for the Fourier transformed two-dimensional Vlasov equation. J. Comput. Phys. 181 (1), 98–125.Google Scholar
Eliasson, B. 2003 Numerical modelling of the two-dimensional Fourier transformed Vlasov–Maxwell system. J. Comput. Phys. 190 (2), 501–522.Google Scholar
Eliasson, B. 2007 Outflow boundary conditions for the Fourier transformed three-dimensional Vlasov–Maxwell system. J. Comput. Phys. 225 (2), 1508–1532.Google Scholar
Figua, H., Bouchut, F., Feix, M. R. & Fijalkow, E. 2000 Instability of the filtering method for Vlasov’s equation. J. Comput. Phys. 159 (2), 440–447.Google Scholar
Klimas, A. J. 1987 A method for overcoming the velocity space filamentation problem in collisionless plasma model solutions. J. Comput. Phys. 68 (1), 202–226.Google Scholar
Klimas, A. J. & Fitzenreiter, R. J. 1988 On the persistence of unstable bump-on-tail electron velocity distributions in the Earth’s foreshock. J. Geophys. Res. 93 (A9), 9628–9648.Google Scholar
Klimas, A. J. & Farrell, W. M. 1994 A splitting algorithm for Vlasov simulation with filamentation filtration. J. Comput. Phys. 110 (1), 150–163.Google Scholar
Klimas, A. J., Vinas, A. F. & Araneda, J. A. 2017 Simulation study of Landau damping near the persisting to arrested transition. J. Plasma Phys. 83 (4), 905830405.Google Scholar
Krall, N. A. & Trivelpiece, A. W. 1986 Principles of Plasma Physics (ed. Harnwell, G. P.), chap. 7, pp. 349–367. San Francisco Press.Google Scholar
Landau, L. D. 1946 On the vibrations of the electronic plasma. J. Phys. (Moscow) 10, 25.Google Scholar
Lenard, A. & Bernstein, I. B. 1958 Plasma oscillations with diffusion in velocity space. Phys. Rev. 112 (5), 1456–1459.Google Scholar
Ng, C. S., Bhattacharjee, A. & Skiff, F. 1999 Kinetic eigenmodes and discrete spectrum of plasma oscillations in a weakly collisional plasma. Phys. Rev. Lett. 83 (10), 1974–1977.Google Scholar
Ng, C. S., Bhattacharjee, A. & Skiff, F. 2004 Complete spectrum of kinetic eigenmodes for plasma oscillations in a weakly collisional plasma. Phys. Rev. Lett. 92 (6), 065002.Google Scholar
Pezzi, O., Camporeale, E. & Valentini, F. 2016 Collisional effects on the numerical recurrence in Vlasov–Poisson simulations. Phys. Plasmas 23 (2), 022103.Google Scholar
Rupp, C. F., Lopez, R. A. & Araneda, J. A. 2015 Critical density for Landau damping in a two-electron-component plasma. Phys. Plasmas 22 (10), 102306.Google Scholar
Vinas, A. F. & Klimas, A. J. 2018 Flux-balance Vlasov simulation with filamentation filtration. J. Comput. Phys.; (under review).Google Scholar