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Hamiltonian magnetic reconnection with parallel electron heat flux dynamics

Part of: Complex Plasma Phenomena

Published online by Cambridge University Press:  13 July 2015

D. Grasso  and
E. Tassi
D. Grasso*
Affiliation:
Istituto dei Sistemi Complessi – CNR, Via dei Taurini 19, 00185, Roma, Italy Dipartimento Energia, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Torino, Italy
E. Tassi
Affiliation:
Aix-Marseille Université, Université de Toulon, CNRS, CPT, UMR 7332, 13288 Marseille, France
*
†Email address for correspondence: [email protected]
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Abstract

We analyse, both analytically and numerically, a two-dimensional six-field fluid model for collisionless magnetic reconnection, accounting for temperature and heat flux fluctuations along the direction of the magnetic guide field. We show that the model possesses a Hamiltonian structure with a non-canonical Poisson bracket. This bracket is characterized by the presence of six infinite families of Casimirs, associated with Lagrangian invariants. This reveals that the model can be reformulated as a system of advection equations, thus generalizing previous results obtained for Hamiltonian isothermal fluid models for reconnection. Numerical simulations indicate that the presence of heat flux and temperature fluctuations yields slightly larger growth rates and similar saturated island amplitudes, with respect to the isothermal models. For values of the sonic Larmor radius much smaller than the electron skin depth, heat flux fluctuations tend to be suppressed and temperature fluctuations follow density fluctuations. Increasing the sonic Larmor radius results in an increasing fraction of magnetic energy converted into heat flux, at the expense of temperature fluctuations. In particular, heat flux fluctuations tend to become relevant along the magnetic island separatrices. The qualitative structures associated with the electron field variables are also reinterpreted in terms of the rotation of the Lagrangian invariants of the system.

Type
Research Article
Information
Journal of Plasma Physics , Volume 81 , Issue 5 , October 2015 , 495810501
Copyright
© Cambridge University Press 2015 

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References

Biskamp, D. 2000 Magnetic Reconnection in Plasmas. Cambridge University Press.Google Scholar
Cafaro, E., Grasso, D., Pegoraro, F., Porcelli, F. & Saluzzi, A. 1998 Invariants and geometric structures in nonlinear Hamiltonian reconnection. Phys. Rev. Lett. 80, 4430–4433.Google Scholar
Comisso, L., Grasso, D., Tassi, E. & Waelbroeck, F. L. 2012 Numerical investigation of a compressible gyrofluid model for collisionless magnetic reconnection. Phys. Plasmas 19, 042103.Google Scholar
Coppi, B. 1964 Inertial instabilities in plasmas. Phys. Lett. 11, 226–228.CrossRefGoogle Scholar
de Blank, H. J. 2001 Kinetic model of electrons in drift-Alfvén current vortices. Phys. Plasmas 8, 3927–3935.Google Scholar
Del Sarto, D., Califano, F. & Pegoraro, F. 2006 Electron parallel compressibility in the nonlinear development of two-dimensional collisionless magnetohydrodynamic reconnection. Mod. Phys. Lett. B 20, 931–961.Google Scholar
Fitzpatrick, R. & Porcelli, F. 2004 Collisionless magnetic reconnection with arbitrary guide field. Phys. Plasmas 11, 4713–4718; and 2007 Phys. Plasmas 14, 049902 (Erratum).CrossRefGoogle Scholar
Furth, H. P., Killen, J. & Rosenbluth, M. N. 1963 Finite resistivity instabilities of a sheet pinch. Phys. Fluids 6, 459–484.Google Scholar
Grasso, D., Borgogno, D., Pegoraro, F. & Tassi, E. 2009 Coupling between reconnection and Kelvin–Helmholtz instabilities in collisionless plasmas. Nonlinear Process. Geophys. 16, 241–249.CrossRefGoogle Scholar
Grasso, D., Califano, F., Pegoraro, F. & Porcelli, F. 2000 Ion Larmor radius effects in collisionless reconnection. Plasma Phys. Rep. 26, 548–555.Google Scholar
Grasso, D., Califano, F., Pegoraro, F. & Porcelli, F. 2001 Phase mixing and island saturation in Hamiltonian reconnection. Phys. Rev. Lett. 86, 5051–5054.Google Scholar
Grasso, D., Tassi, E. & Waelbroeck, F. L. 2010 Nonlinear gyrofluid simulations of collisionless reconnection. Phys. Plasmas 17, 082312.CrossRefGoogle Scholar
Hammett, G. W., Beer, M. A., Dorland, W., Cowley, S. C. & Smith, S. A. 1993 Developments in the gyrofluid approach to tokamak turbulence simulations. Plasma Phys. Control. Fusion 35, 973–985.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
Hesse, M., Kuznetsova, M. & Birn, J. 2004 The role of electron heat flux in guide-field magnetic reconnection. Phys. Plasmas 11, 5387–5397.Google Scholar
Holm, D. D., Marsden, J. E., Ratiu, T. S. & Weinstein, A. 1985 Nonlinear stability of fluid and plasma equilibria. Phys. Rep. 123, 1–116.Google Scholar
Kuvshinov, B. N., Pegoraro, F. & Schep, T. J. 1994 Hamiltonian formulation of low-frequency, nonlinear plasma dynamics. Phys. Lett. A 191, 296–300.Google Scholar
Liseikina, T. V., Pegoraro, F. & Echkina, E. Yu. 2004 Foliation and mixing of the electron drift-kinetic distribution function in nonlinear two-dimensional magnetic reconnection. Phys. Plasmas 11, 3535–3545.CrossRefGoogle Scholar
Loureiro, N. F., Schekochihin, A. A. & Zocco, A. 2013 Fast collisionless reconnection and electron heating in strongly magnetized plasmas. Phys. Rev. Lett. 111, 025002.Google Scholar
Morrison, P. J. 1998 Hamiltonian description of the ideal fluid. Rev. Mod. Phys. 70, 467–521.Google Scholar
Pegoraro, F., Liseikina, T. & Echkina, E. Yu. 2005a Mixing of the electron distribution function in nonlinear 2D magnetic reconnection. Transport Theory Statist. Phys. 34, 243–259.CrossRefGoogle Scholar
Pegoraro, F., Liseikina, T. & Echkina, E. Yu. 2005b Nonlinear drift-kinetic evolution of the electron distribution function in two-dimensional magnetic reconnection. Phys. Scr. T 116, 88–92.Google Scholar
Porcelli, F. 1991 Collisionless $m=1$ tearing mode. Phys. Rev. Lett. 66, 425–428.CrossRefGoogle ScholarPubMed
Priest, E. R. & Forbes, T. G. 2000 Magnetic Reconnection: MHD Theory and Applications. Cambridge University Press.CrossRefGoogle Scholar
Schep, T. J., Pegoraro, F. & Kuvshinov, B. N. 1994 Generalized two fluid theory of magnetic structures. Phys. Plasmas 1, 2843–2852.CrossRefGoogle Scholar
Scott, B. 2010 Derivation via free energy conservation constraints of gyrofluid equations with finite-gyroradius electromagnetic nonlinearities. Phys. Plasmas 17, 102306.CrossRefGoogle Scholar
Snyder, P. B. & Hammett, G. W. 2001 A Landau fluid model for electromagnetic plasma microturbulence. Phys. Plasmas 8, 3199–3216.Google Scholar
Tassi, E. 2014a Hamiltonian derivation of a gyrofluid model for collisionless magnetic reconnection. J. Phys.: Conf. Ser. 561, 012018.Google Scholar
Tassi, E. 2014b Hamiltonian closures for two-moment fluid models derived from drift-kinetic equations. J. Phys. A: Math. Theor. 47, 195501.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.Google Scholar
Tassi, E., Morrison, P. J., Waelbroeck, F. L. & Grasso, D. 2008 Hamiltonian formulation and analysis of a collisionless fluid reconnection model. Plasma Phys. Control. Fusion 50, 085014.Google Scholar
Thiffeault, J.-L. & Morrison, P. J. 2000 Classification and Casimir invariants of Lie–Poisson brackets. Physica D 136, 205–244.CrossRefGoogle Scholar
Waelbroeck, F. L., Hazeltine, R. D. & Morrison, P. J. 2009 A Hamiltonian electromagnetic gyrofluid model. Phys. Plasmas 16, 032109.CrossRefGoogle Scholar
Waelbroeck, F. L., Morrison, P. J. & Horton, W. 2004 Hamiltonian formulation and coherent structures in electrostatic turbulence. Plasma Phys. Control. Fusion 46, 1331–1350.Google Scholar
Waelbroeck, F. L. & Tassi, E. 2012 A compressible Hamiltonian electromagnetic gyrofluid model. Commun. Nonlinear Sci. Numer. Simul. 17, 2171–2178.Google Scholar
Yamada, M., Kulsrud, R. & Ji, H. 2010 Magnetic reconnection. Rev. Mod. Phys. 82, 603–664.Google Scholar
Zocco, A. & Schekochihin, A. A. 2011 Reduced fluid-kinetic equations for low-frequency dynamics, magnetic reconnection, and electron heating in low-beta plasmas. Phys. Plasmas 18, 102309.CrossRefGoogle Scholar