Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-27T15:28:34.649Z Has data issue: false hasContentIssue false
  • English
  • Français

Reduced models accounting for parallel magnetic perturbations: gyrofluid and finite Larmor radius–Landau fluid approaches

Part of: PLA The Vlasov Equation

Published online by Cambridge University Press:  01 November 2016

E. Tassi ,
P. L. Sulem  and
T. Passot
E. Tassi*
Affiliation:
Aix Marseille Univ, Univ Toulon, CNRS, CPT, 13288 Marseille, France
P. L. Sulem
Affiliation:
Université Côte d’Azur, CNRS, Observatoire de la Côte d’Azur, Laboratoire J.L. Lagrange, Boulevard de l’Observatoire, CS 34229, 06304 Nice CEDEX 4, France
T. Passot
Affiliation:
Université Côte d’Azur, CNRS, Observatoire de la Côte d’Azur, Laboratoire J.L. Lagrange, Boulevard de l’Observatoire, CS 34229, 06304 Nice CEDEX 4, France
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Reduced models are derived for a strongly magnetized collisionless plasma at scales which are large relative to the electron thermal gyroradius and in two asymptotic regimes. One corresponds to cold ions and the other to far sub-ion scales. By including the electron pressure dynamics, these models improve the Hall reduced magnetohydrodynamics (MHD) and the kinetic Alfvén wave model of Boldyrev et al. (2013 Astrophys. J., vol. 777, 2013, p. 41), respectively. We show that the two models can be obtained either within the gyrofluid formalism of Brizard (Phys. Fluids, vol. 4, 1992, pp. 1213–1228) or as suitable weakly nonlinear limits of the finite Larmor radius (FLR)–Landau fluid model of Sulem and Passot (J. Plasma Phys., vol 81, 2015, 325810103) which extends anisotropic Hall MHD by retaining low-frequency kinetic effects. It is noticeable that, at the far sub-ion scales, the simplifications originating from the gyroaveraging operators in the gyrofluid formalism and leading to subdominant ion velocity and temperature fluctuations, correspond, at the level of the FLR–Landau fluid, to cancellation between hydrodynamic contributions and ion finite Larmor radius corrections. Energy conservation properties of the models are discussed and an explicit example of a closure relation leading to a model with a Hamiltonian structure is provided.

Keywords

plasma nonlinear phenomenaspace plasma physics
Type
Research Article
Information
Journal of Plasma Physics , Volume 82 , Issue 6 , December 2016 , 705820601
Copyright
© Cambridge University Press 2016 

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

Boldyrev, S., Horaites, K., Xia, Q. & Perez, J. C. 2013 Toward a theory of astrophysical plasma turbulence at subproton scales. Astrophys. J. 777, 41.CrossRefGoogle Scholar
Brizard, A. 1989 Nonlinear gyrokinetic Maxwell-Vlasov equations using magnetic co-ordinates. J. Plasma Phys. 41, 541–559.CrossRefGoogle Scholar
Brizard, A. 1992 Nonlinear gyrofluid description of turbulent magnetized plasmas. Phys. Fluids 4, 1213–1228.CrossRefGoogle Scholar
Dorland, W. & Hammett, G. W. 1993 Gyrofluid turbulence models with kinetic effects. Phys. Fluids B 5, 812–835.CrossRefGoogle Scholar
Fitzpatrick, R. & Porcelli, F. 2004 Collisionless magnetic reconnection with arbitrary guide field. Phys. Plasmas 11, 4713–4718.CrossRefGoogle Scholar
Fitzpatrick, R. & Porcelli, F. 2007 Collisionless magnetic reconnection with arbitrary guide field. Phys. Plasmas 14, 049902; (erratum).Google Scholar
Hammett, G. W. & Perkins, F. W. 1990 Fluid moment models for Landau damping with application to the ion-temperature gradient instability. Phys. Rev. Lett. 64, 3019–3022.Google Scholar
Hazeltine, R. D., Hsu, C. T. & Morrison, P. J. 1987 Hamiltonian four-field model for nonlinear tokamak dynamics. Phys. Fluids 30, 3204–3211.CrossRefGoogle Scholar
Hazeltine, R. D., Kotschenreuther, K. & Morrison, P. J. 1985 A four-field model for tokamak plasma dynamics. Phys. Fluids 28, 2466–2477.Google Scholar
Hedrick, C. L. & Leboeuf, J. N. 1992 Landau fluid equations for electromagnetic and electrostatic fluctuations. Phys. Plasmas B4, 3915–3934.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, 590–614.Google Scholar
Hsu, C. T., Hazeltine, R. D. & Morrison, P. J. 1986 A generalized reduced fluid model with finite ion-gyroradius effects. Phys. Fluids 29, 1480–1487.CrossRefGoogle Scholar
Kiyani, K. H., Chapman, S. C., Sahraoui, F., Hnat, B., Fauvarque, O. & Khotyaintsev, Yu. V. 2013 Enhanced magnetic compressibility and isotropic scale invariance at sub-ion Larmor scales in solar wind turbulence. Astrophys. J. 663, 10.CrossRefGoogle Scholar
Kuznetsov, E., Passot, T. & Sulem, P. L. 2012 On the mirror instability in the presence of electron temperature anisotropy. J. Plasma Phys. 19, 092116.Google Scholar
Morrison, P. J. 1998 Hamiltonian description of the ideal fluid. Rev. Mod. Phys. 70, 467–521.Google Scholar
Passot, T. & Sulem, P. L. 2007 Collisionless magnetohydrodynamics with gyrokinetic effects. Phys. Plasmas 14, 082502.Google Scholar
Passot, T. & Sulem, P. L. 2015 A model for the non-universal power-law of the solar wind sub-ion scale magnetic spectrum. Astrophys. J. Lett. 812, L37.Google Scholar
Rönnmark, K.1982 Waves in homogeneous, anisotropic multicomponent plasmas (WHAMP). Tech. Rep. 179. Kiruna Geophysical Institute.Google Scholar
Schekochihin, A. A., Cowley, S. C., Rincon, F. & Rosin, M. S. 2010 Magnetofuid dynamics of magnetized cosmic plasma: firehose and gyrothermal instabilities. Mon. Not. R. Astron. Soc. 405, 291–300.Google Scholar
Schekochihin, A. A., Cowley, S. C., W. Dorland, G. W. Hammett, Howes, G. G., Quataert, E. & Tatsuno, T. 2009 Astrophysical gyrokinetics: kinetic and fluid turbulent cascades in magnetized weakly collisional plasmas. Astrophys. J. Supp. 182, 310.CrossRefGoogle Scholar
Scott, B. D. 2010 Derivation via free energy conservation constraints of gyrofluid equations with finite-gyroradius electromagnetic nonlinearities. Phys. Plasmas 17, 102306.Google Scholar
Snyder, P. B. & Hammett, G. W. 2001 A Landau fluid model for electromagnetic plasma microturbulence. Phys. Plasmas 8, 3199–3216.Google Scholar
Sulem, P. L & Passot, T. 2015 Landau fluid closures with nonlinear large-scale finite Larmor radius corrections for collisionless plasmas. J. Plasma Phys. 81, 325810103.Google Scholar
Sulem, P. L., Passot, T., Laveder, D. & Borgogno, D. 2016 Influence of the nonlinearity parameter on the solar-wind sub-ion magnetic energy spectrum: FLR-Landau fluid simulations. Astrophys. J. 818, 66.Google Scholar
Tassi, E., Morrison, P. J., Grasso, D. & Pegoraro, F. 2010 Hamiltonian four-field model for magnetic reconnection: nonlinear dynamics and extension to three dimensions with externally applied fields. Nucl. Fusion 50, 034007.CrossRefGoogle Scholar
Thiffeault, J. L. & Morrison, P. J. 2000 Classification and Casimir invariants of Lie–Poisson brackets. Physica D 136, 205–244.Google Scholar
Waelbroeck, F. L. & Tassi, E. 2012 A compressible Hamiltonian electromagnetic gyrofluid model. Commun. Nonlinear Sci. Numer. Simul. 17, 2171.CrossRefGoogle Scholar