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Comparison of linear modes in kinetic plasma models

Published online by Cambridge University Press:  03 April 2017

Enrico Camporeale*
Affiliation:
Center for Mathematics and Computer Science (CWI), Amsterdam, The Netherlands
David Burgess
Affiliation:
School of Physics and Astronomy, Queen Mary University of London, London, UK
*
Email address for correspondence: e.camporeale@cwi.nl

Abstract

We compare, in an extensive and systematic way, linear theory results obtained with the hybrid (ion kinetic and electron fluid), the gyrokinetic and the fully kinetic plasma models. We present a test case with parameters that are relevant for solar wind turbulence at small scales, which is a topic now recognized to need a kinetic treatment, to a certain extent. We comment on the comparison of low-frequency single modes (Alfvén/ion-cyclotron, ion-acoustic and fast modes) for a wide range of propagation angles, and on the overall spectral properties of the linear operators, for quasi-perpendicular propagation. The methodology and the results presented in this paper will be valuable when choosing which model should be used in regimes where the assumptions of each model are not trivially satisfied.

Type
Research Article
Copyright
© Cambridge University Press 2017 

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References

Boldyrev, S., Horaites, K., Xia, Q. & Perez, J. C. 2013 Toward a theory of astrophysical plasma turbulence at subproton scales. Astrophys. J. 777 (1), 41.Google Scholar
Brizard, A. J. & Hahm, T. S. 2007 Foundations of nonlinear gyrokinetic theory. Rev. Mod. Phys. 79 (2), 421.Google Scholar
Camporeale, E. 2012 Nonmodal linear theory for space plasmas. Space Sci. Rev. 172 (1–4), 397409.CrossRefGoogle Scholar
Camporeale, E. & Burgess, D. 2011 The dissipation of solar wind turbulent fluctuations at electron scales. Astrophys. J. 730 (2), 114.CrossRefGoogle Scholar
Camporeale, E., Burgess, D. & Passot, T. 2009 Transient growth in stable collisionless plasma. Phys. Plasmas 16 (3), 030703.CrossRefGoogle Scholar
Camporeale, E., Delzanno, G. L., Bergen, B. K. & Moulton, J. D. 2016 On the velocity space discretization for the Vlasov–Poisson system: comparison between implicit hermite spectral and particle-in-cell methods. Comput. Phys. Commun. 198, 4758.Google Scholar
Camporeale, E., Passot, T. & Burgess, D. 2010 Implications of a non-modal linear theory for the marginal stability state and the dissipation of fluctuations in the solar wind. Astrophys. J. 715 (1), 260.Google Scholar
Chen, G. & Chacon, L. 2014 An energy-and charge-conserving, nonlinearly implicit, electromagnetic 1d-3v Vlasov–Darwin particle-in-cell algorithm. Comput. Phys. Commun. 185 (10), 23912402.Google Scholar
Cheng, C. Z. & Johnson, J. R. 1999 A kinetic-fluid model. J. Geophys. Res. 104 (A1), 413427.Google Scholar
Degond, P., Deluzet, F. & Savelief, D. 2012 Numerical approximation of the Euler–Maxwell model in the quasineutral limit. J. Comput. Phys. 231 (4), 19171946.Google Scholar
Dendy, R. O. 1995 Plasma Physics: An Introductory Course. Cambridge University Press.Google Scholar
Franci, L., Verdini, A., Matteini, L., Landi, S. & Hellinger, P. 2015 Solar wind turbulence from mhd to sub-ion scales: high-resolution hybrid simulations. Astrophys. J. Lett. 804 (2), L39.CrossRefGoogle Scholar
Friedman, B. & Carter, T. A. 2014 Linear technique to understand non-normal turbulence applied to a magnetized plasma. Phys. Rev. Lett. 113 (2), 025003.CrossRefGoogle ScholarPubMed
Gary, S. P. 2005 Theory of Space Plasma Microinstabilities. Cambridge University Press.Google Scholar
Goswami, P., Passot, T. & Sulem, P. L. 2005 A landau fluid model for warm collisionless plasmas. Phys. Plasmas 12 (10), 102109.Google Scholar
Haynes, C. T., Burgess, D. & Camporeale, E. 2014 Reconnection and electron temperature anisotropy in sub-proton scale plasma turbulence. Astrophys. J. 783 (1), 38.CrossRefGoogle Scholar
Haynes, C. T., Burgess, D., Camporeale, E. & Sundberg, T. 2015 Electron vortex magnetic holes: a nonlinear coherent plasma structure. Phys. Plasmas 22 (1), 012309.Google Scholar
Howes, G. G., Cowley, S. C., Dorland, W., Hammett, G. W., Quataert, E. & Schekochihin, A. A. 2006 Astrophysical gyrokinetics: basic equations and linear theory. Astrophys. J. 651 (1), 590.Google Scholar
Howes, G. G., TenBarge, J. M., Dorland, W., Quataert, E., Schekochihin, A. A., Numata, R. & Tatsuno, T. 2011 Gyrokinetic simulations of solar wind turbulence from ion to electron scales. Phys. Rev. Lett. 107 (3), 035004.CrossRefGoogle ScholarPubMed
Hunana, P., Goldstein, M. L., Passot, T., Sulem, P. L., Laveder, D. & Zank, G. P. 2013 Polarization and compressibility of oblique kinetic Alfvén waves. Astrophys. J. 766 (2), 93.Google Scholar
Kiyani, K. H., Chapman, S. C., Sahraoui, F., Hnat, B., Fauvarque, O. & Khotyaintsev, Y. V. 2013 Enhanced magnetic compressibility and isotropic scale invariance at sub-ion larmor scales in solar wind turbulence. Astrophys. J. 763, 10.Google Scholar
Lion, S., Alexandrova, O. & Zaslavsky, A. 2016 Coherent events and spectral shape at ion kinetic scales in the fast solar wind turbulence. Astrophys. J. 824, 47.Google Scholar
Matthews, A. P. 1994 Current advance method and cyclic leapfrog for 2d multispecies hybrid plasma simulations. J. Comput. Phys. 112 (1), 102116.Google Scholar
Narita, Y., Glassmeier, K.-H., Sahraoui, F. & Goldstein, M. L. 2010 Wave-vector dependence of magnetic-turbulence spectra in the solar wind. Phys. Rev. Lett. 104 (17), 171101.Google Scholar
Osman, K. T. & Horbury, T. S. 2009 Quantitative estimates of the slab and 2-D power in solar wind turbulence using multispacecraft data. J. Geophys. Res. 114, A06103.Google Scholar
Park, W., Belova, E. V., Fu, G. Y., Tang, X. Z., Strauss, H. R. & Sugiyama, L. E. 1999 Plasma simulation studies using multilevel physics models. Phys. Plasmas 6 (5), 17961803.Google Scholar
Podesta, J. J. 2010 Transient growth in stable linearized Vlasov–Maxwell plasmas. Phys. Plasmas 17 (12), 122101.Google Scholar
Podesta, J. J. 2012 The need to consider ion bernstein waves as a dissipation channel of solar wind turbulence. J. Geophys. Res. 117 (A7).Google Scholar
Ratushnaya, V. & Samtaney, R. 2014 Non-modal stability analysis and transient growth in a magnetized Vlasov plasma. Europhys. Lett. 108 (5), 55001.Google Scholar
Sahraoui, F., Belmont, G. & Goldstein, M. L. 2012 New insight into short-wavelength solar wind fluctuations from Vlasov theory. Astrophys. J. 748 (2), 100.Google Scholar
Sahraoui, F., Goldstein, M. L., Belmont, G., Canu, P. & Rezeau, L. 2010 Three dimensional anisotropic k spectra of turbulence at subproton scales in the solar wind. Phys. Rev. Lett. 105 (13), 131101.Google Scholar
Sahraoui, F., Goldstein, M. L., Robert, P. & Khotyaintsev, Y. V. 2009 Evidence of a cascade and dissipation of solar-wind turbulence at the electron gyroscale. Phys. Rev. Lett. 102 (23), 231102.Google Scholar
Salem, C. S., Howes, G. G., Sundkvist, D., Bale, S. D., Chaston, C. C., Chen, C. H. K. & Mozer, F. S. 2012 Identification of kinetic Alfvén wave turbulence in the solar wind. Astrophys. J. Lett. 745 (1), L9.Google Scholar
Schekochihin, A. A., Cowley, S. C., Dorland, W., Hammett, G. W., Howes, G. G., Quataert, E. & Tatsuno, T. 2009 Astrophysical gyrokinetics: kinetic and fluid turbulent cascades in magnetized weakly collisional plasmas. Astrophys. J. Suppl. 182 (1), 310.CrossRefGoogle Scholar
Servidio, S., Valentini, F., Califano, F. & Veltri, P. 2012 Local kinetic effects in two-dimensional plasma turbulence. Phys. Rev. Lett. 108 (4), 045001.Google Scholar
Stix, T. H. 1962 The Theory of Plasma Waves, vol. 1. McGraw-Hill.Google Scholar
Swanson, D. G. 2012 Plasma Waves. Elsevier.Google Scholar
TenBarge, J. M., Howes, G. G. & Dorland, W. 2013 Collisionless damping at electron scales in solar wind turbulence. Astrophys. J. 774 (2), 139.CrossRefGoogle Scholar
Trefethen, L. N. & Embree, M. 2005 Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators. Princeton University Press.Google Scholar
Tronci, C. & Camporeale, E. 2015 Neutral Vlasov kinetic theory of magnetized plasmas. Phys. Plasmas 22 (2), 020704.CrossRefGoogle Scholar
Tronci, C., Tassi, E., Camporeale, E. & Morrison, P. J. 2014 Hybrid Vlasov-mhd models: Hamiltonian versus non-Hamiltonian. Plasma Phys. Control. Fusion 56 (9), 095008.CrossRefGoogle Scholar
Valentini, F., Califano, F. & Veltri, P. 2010 Two-dimensional kinetic turbulence in the solar wind. Phys. Rev. Lett. 104 (20), 205002.CrossRefGoogle ScholarPubMed
Valentini, F., Trávníček, P., Califano, F., Hellinger, P. & Mangeney, A. 2007 A hybrid-Vlasov model based on the current advance method for the simulation of collisionless magnetized plasma. J. Comput. Phys. 225 (1), 753770.CrossRefGoogle Scholar
Vásconez, C. L., Valentini, F., Camporeale, E. & Veltri, P. 2014 Vlasov simulations of kinetic Alfvén waves at proton kinetic scales. Phys. Plasmas 21 (11), 112107.Google Scholar
Waltz, R. E., Staebler, G. M., Dorland, W., Hammett, G. W., Kotschenreuther, M. & Konings, J. A. 1997 A gyro-landau-fluid transport model. Phys. Plasmas 4 (7), 24822496.CrossRefGoogle Scholar
Zhao, J. S., Voitenko, Y., Yu, M. Y., Lu, J. Y. & Wu, D. J. 2014 Properties of short-wavelength oblique Alfvén and slow waves. Astrophys. J. 793 (2), 107.Google Scholar