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Simulation study of Landau damping near the persisting to arrested transition

  • Alexander J. Klimas (a1), Adolfo F. Viñas (a2) and Jaime A. Araneda (a3)
Abstract

A one-dimensional electrostatic filtered Vlasov–Poisson simulation study is discussed. The transition from persisting to arrested Landau damping that is produced by increasing the strength of a sinusoidal perturbation on a background Vlasov–Poisson equilibrium is explored. Emphasis is placed on observed features of the electron phase-space distribution when the perturbation strength is near the transition value. A single ubiquitous waveform is found perturbing the space-averaged phase-space distribution at almost any time in all of the simulations; the sole exception is the saturation stage that can occur at the end of the arrested damping scenario. This waveform contains relatively strong, very narrow structures in velocity bracketing $\pm v_{\text{res}}$ – the velocities at which electrons must move to traverse the dominant field mode wavelength in one of its oscillation periods – and propagating with $\pm v_{\text{res}}$ respectively. Local streams of electrons are found in these structures crossing the resonant velocities from low speed to high speed during Landau damping and from high speed to low speed during Landau growth. At the arrest time, when the field strength is briefly constant, these streams vanish. It is conjectured that the expected transfer of energy between electrons and field during Landau growth or damping has been visualized for the first time. No evidence is found in the phase-space distribution to support recent well-established discoveries of a second-order phase transition in the electric field evolution. While trapping is known to play a role for larger perturbation strengths, it is shown that trapping plays no role at any time in any of the simulations near the transition perturbation strength.

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Copyright
Corresponding author
Email address for correspondence: alex.klimas@nasa.gov
References
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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.
Brodin G. 1997a Nonlinear Landau damping. Phys. Rev. Lett. 78 (7), 1263.
Brodin G. 1997b A new approach to linear Landau damping. Am. J. Phys. 65 (1), 66.
Brunetti M., Califano F. & Pegoraro F. 2000 Asymptotic evolution of nonlinear Landau damping. Phys. Rev. E 62 (3), 4109.
Califano F., Galeotti L. & Mangeney A. 2006 The Vlasov–Poisson model and the validity of a numerical approach. Phys. Plasmas 13 (8), 082102.
Case K. M. 1959 Plasma oscillations. Ann. Phys. 7 (3), 349.
Cheng C. Z. & Knorr G. 1976 Integration of Vlasov equation in configuration space. J. Comput. Phys. 22 (3), 330.
Dawson J. 1961 On Landau damping. Phys. Fluids 4 (7), 869.
De Marco R., Carbone V. & Veltri P. 2006 A modified fermi model for wave-particle interactions in plasmas. Phys. Rev. Lett. 96 (12), 125003.
Demeio L. & Zweifel P. F. 1990 Numerical simulations of perturbed Vlasov equilibria. Phys. Fluids B 2 (6), 1252.
Einkemmer L. & Ostermann A. 2014 A strategy to suppress recurrence in grid-based Vlasov solvers. Eur. Phys. J. D 68 (7), 197.
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.
Fitzenreiter R. J., Klimas A. J. & Scudder J. D. 1984 Detection of bump-on-tail reduced electron velocity distributions at the electron foreshock boundary. Geophys. Res. Lett. 11 (5), 496.
Fitzenreiter R. J., Scudder J. D. & Klimas A. J. 1990 3-Dimensional analytical model for the spatial variation of the foreshock electron distribution function – systematics and comparisons with ISEE observations. J. Geophys. Res. 95 (A4), 4155.
Fitzenreiter R. J., Vinas A. F., Klimas A. J., Lepping R. P., Kaiser M. L. & Onsager T. G. 1996 Wind observations of the electron foreshock. Geophys. Res. Lett. 23 (10), 1235.
Galeotti L. & Califano F. 2005 Asymptotic evolution of weakly collisional Vlasov–Poisson plasmas. Phys. Rev. Lett. 95 (1), 015002.
Isichenko M. B. 1997 Nonlinear Landau damping in collisionless plasma and inviscid fluid. Phys. Rev. Lett. 78 (12), 2369.
Ivanov A. V. & Cairns I. H. 2006 Nontrapping arrest of Langmuir wave damping near the threshold amplitude. Phys. Rev. Lett. 96 (17), 175001.
Ivanov A. V., Cairns I. H. & Robinson P. A. 2004 Wave damping as a critical phenomenon. Phys. Plasmas 11 (10), 4649.
Ivanov A. V., Vladimirov S. V. & Robinson P. A. 2005 Criticality in a Vlasov–Poisson system: a fermioniclike universality class. Phys. Rev. E 71 (5), 056406.
Klimas A. J. 1983a A numerical method based on the Fourier-Fourier transform approach for modeling 1-D electron plasma evolution. J. Comput. Phys. 50 (2), 270.
Klimas A. J. 1983b A mechanism for plasma waves at the harmonics of the plasma frequency in the electron foreshock boundary. J. Geophys. Res. 88 (NA11), 9081.
Klimas A. J. 1987 A method for overcoming the velocity space filamentation problem in collisionless plasma model solutions. J. Comput. Phys. 68 (1), 202.
Klimas A. J. 1990 Trapping saturation of the bump-on-tail instability and electrostatic harmonic excitation in Earth’s foreshock. J. Geophys. Res. 95 (A9), 14905.
Klimas A. J. & Farrell W. M. 1994 A splitting algorithm for Vlasov simulation with filamentation filtration. J. Comput. Phys. 110 (1), 150.
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.
Krall N. A. & Trivelpiece A. W. 1986 Principles of Plasma Physics (ed. Harnwell G. P.), chap. 7, p. 349. San Francisco Press.
Lancellotti C. & Dorning J. J. 1998a Critical initial states in collisionless plasmas. Phys. Rev. Lett. 81 (23), 5137.
Lancellotti C. & Dorning J. J. 1998b Nonlinear Landau damping in a collisionless plasma. Phys. Rev. Lett. 80 (23), 5236.
Landau L. D. 1946 On the vibrations of the electronic plasma. J. Phys. (Moscow) 10, 25.
Lenard A. & Bernstein I. B. 1958 Plasma oscillations with diffusion in velocity space. Phys. Rev. 112 (5), 1456.
Lesur M., Diamond P. H. & Kosuga Y. 2014 Phase-space jets drive transport and anomalous resistivity. Phys. Plasmas 21 (11), 112307.
Manfredi G. 1997 Long-time behavior of nonlinear Landau damping. Phys. Rev. Lett. 79 (15), 2815.
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.
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.
O’Neil T. 1965 Collisionless damping of nonlinear plasma oscillations. Phys. Fluids 8 (12), 2255.
Pezzi O., Camporeale E. & Valentini F. 2016 Collisional effects on the numerical recurrence in Vlasov–Poisson simulations. Phys. Plasmas 23 (2), 022103.
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.
Valentini F., Carbone V., Veltri P. & Mangeney A. 2005 Self-consistent Lagrangian study of nonlinear Landau damping. Phys. Rev. E 71 (1), 017402.
Van Kampen N. G. 1955 On the theory of stationary waves in plasmas. Physica 21 (12), 949.
Xu H. & Sheng Z. M. 2012 Critical initial amplitude of Langmuir wave damping. Plasma Sci. Technol. 14 (3), 181.
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