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On the value of the reconnection rate

Part of: Solved and Unsolved problems in Plasma Physics Focus on Plasma Astrophysics

Published online by Cambridge University Press:  04 November 2016

L. Comisso Open the ORCID record for L. Comisso [Opens in a new window]  and
A. Bhattacharjee
L. Comisso*
Affiliation:
Department of Astrophysical Sciences and Princeton Plasma Physics Laboratory, Princeton University, Princeton, NJ 08544, USA
A. Bhattacharjee
Affiliation:
Department of Astrophysical Sciences and Princeton Plasma Physics Laboratory, Princeton University, Princeton, NJ 08544, USA
*
†Email address for correspondence: lcomisso@princeton.edu
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Abstract

Numerical simulations have consistently shown that the reconnection rate in certain collisionless regimes can be fast, of the order of $0.1v_{A}B_{u}$ , where $v_{A}$ and $B_{u}$ are the Alfvén speed and the reconnecting magnetic field upstream of the ion diffusion region. This particular value has been reported in myriad numerical simulations under disparate conditions. However, despite decades of research, the reasons underpinning this specific value remain mysterious. Here, we present an overview of this problem and discuss the conditions under which the ‘0.1 value’ is attained. Furthermore, we explain why this problem should be interpreted in terms of the ion diffusion region length.

Keywords

astrophysical plasmasplasma nonlinear phenomenaspace plasma physics

Information

Type
Research Article
Information
Journal of Plasma Physics , Volume 82 , Issue 6 , December 2016 , 595820601
Copyright
© Cambridge University Press 2016 

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References

Andrés, N., Dmitruk, P. & Gómez, D. 2016 Influence of the Hall effect and electron inertia in collisionless magnetic reconnection. Phys. Plasmas 23, 022903.Google Scholar
Aydemir, A. Y. 1992 Nonlinear studies of $m=1$ modes in high-temperature plasmas. Phys. Fluids B 4, 3469.CrossRefGoogle Scholar
Bessho, N. & Bhattacharjee, A. 2005 Collisionless reconnection in an electron–positron plasma. Phys. Rev. Lett. 95, 245001.Google Scholar
Bhattacharjee, A., Germaschewski, K. & Ng, C.-S. 2005 Current singularities: drivers of impulsive reconnection. Phys. Plasmas 12, 042305.CrossRefGoogle Scholar
Bhattacharjee, A., Huang, Y.-M., Yang, H. & Rogers, B. 2009 Fast reconnection in high-Lundquist-number plasmas due to the plasmoid instability. Phys. Plasmas 16, 112102.CrossRefGoogle Scholar
Birn, J., Drake, J. F., Shay, M. A., Rogers, B. N., Denton, R. E., Hesse, M., Kuznetsova, M., Ma, Z. W., Bhattacharjee, A., Otto, A. et al. 2001 Geospace environmental modeling (GEM) magnetic reconnection challenge. J. Geophys. Res. 106, 3715–3719.Google Scholar
Biskamp, D. 1986 Magnetic reconnection via current sheets. Phys. Fluids 29, 1520.CrossRefGoogle Scholar
Biskamp, D., Schwarz, E. & Drake, J. F. 1995 Ion-controlled collisionless magnetic reconnection. Phys. Rev. Lett. 75, 3850.Google Scholar
Borgogno, D., Grasso, D., Porcelli, F., Califano, F., Pegoraro, F. & Farina, D. 2005 Aspects of three-dimensional magnetic reconnection. Phys. Plasmas 12, 032309.Google Scholar
Cassak, P. A., Shay, M. A. & Drake, J. F. 2009 Scaling of Sweet–Parker reconnection with secondary islands. Phys. Plasmas 16, 120702.Google Scholar
Chacón, L., Simakov, A. N., Lukin, V. S. & Zocco, A. 2008 Fast reconnection in nonrelativistic 2D electron-positron plasmas. Phys. Rev. Lett. 101, 025003.Google Scholar
Christie, A. 1936 The A.B.C. Murders. Collins Crime Club.Google Scholar
Comisso, L. & Asenjo, F. A. 2014 Thermal-inertial effects on magnetic reconnection in relativistic pair plasmas. Phys. Rev. Lett. 113, 045001.Google Scholar
Comisso, L. & Grasso, D. 2016 Visco-resistive plasmoid instability. Phys. Plasmas 23, 032111.Google Scholar
Comisso, L., Grasso, D. & Waelbroeck, F. L. 2015 Extended theory of the Taylor problem in the plasmoid-unstable regime. Phys. Plasmas 22, 042109.Google Scholar
Comisso, L., Grasso, D., Waelbroeck, F. L. & Borgogno, D. 2013 Gyro-induced acceleration of magnetic reconnection. Phys. Plasmas 20, 092118.Google Scholar
Comisso, L., Lingam, M., Huang, Y.-M. & Bhattacharjee, A. 2016 General theory of the plasmoid instability. Phys. Plasmas 23, 100702.Google Scholar
Daughton, W. & Karimabadi, H. 2007 Collisionless magnetic reconnection in large-scale electron-positron plasmas. Phys. Plasmas 14, 072303.Google Scholar
Daughton, W., Nakamura, T. K. M., Karimabadi, H., Roytershteyn, V. & Loring, B. 2014 Computing the reconnection rate in turbulent kinetic layers by using electron mixing to identify topology. Phys. Plasmas 21, 052307.Google Scholar
Daughton, W., Roytershteyn, V., Albright, B. J., Karimabadi, H., Yin, L. & Bowers, K. J. 2009 Transition from collisional to kinetic regimes in large-scale reconnection layers. Phys. Rev. Lett. 103, 065004.CrossRefGoogle ScholarPubMed
Daughton, W., Scudder, J. & Karimabadi, H. 2006 Fully kinetic simulations of undriven magnetic reconnection with open boundary conditions. Phys. Plasmas 13, 072101.Google Scholar
Dorelli, J. C. & Bhattacharjee, A. 2008 Defining and identifying three-dimensional magnetic reconnection in resistive magnetohydrodynamic simulations of Earth’s magnetosphere. Phys. Plasmas 15, 056504.Google Scholar
Fitzpatrick, R. 2004 Scaling of forced magnetic reconnection in the Hall-magnetohydrodynamic Taylor problem. Plasmas 11, 937.CrossRefGoogle Scholar
Grasso, D., Pegoraro, F., Porcelli, F. & Califano, F. 1999 Hamiltonian magnetic reconnection. Plasma Phys. Control. Fusion 41, 1497.Google Scholar
Greene, J. M. 1998 Geometrical properties of three-dimensional reconnecting magnetic fields with nulls. J. Geophys. Res. 93, 8583–8590.Google Scholar
Guo, F., Liu, Y.-H., Daughton, W. & Li, H. 2015 Particle acceleration and plasma dynamics during magnetic reconnection in the magnetically dominated regime. Astrophys. J. 806, 167.Google Scholar
Hesse, M., Forbes, T. & Birn, J. 2005 On the relation between reconnected magnetic flux and parallel electric fields in the solar corona. Astrophys. J. 631, 1227.Google Scholar
Huang, Y.-M. & Bhattacharjee, A. 2010 Scaling laws of resistive magnetohydrodynamic reconnection in the high-Lundquist-number, plasmoid-unstable regime. Phys. Plasmas 17, 062104.Google Scholar
Huang, Y.-M., Bhattacharjee, A. & Boozer, A. H. 2014 Rapid change of field line connectivity and reconnection in stochastic magnetic fields. Astrophys. J. 793, 106.Google Scholar
Ji, H. & Daughton, W. 2011 Phase diagram for magnetic reconnection in heliophysical, astrophysical, and laboratory plasmas. Phys. Plasmas 18, 111207.Google Scholar
Kleva, R. G., Drake, J. F. & Waelbroeck, F. L. 1995 Fast reconnection in high temperature plasmas. Phys. Plasmas 2, 23.Google Scholar
Kulsrud, R. M. 2001 Magnetic reconnection: Sweet–Parker versus Petschek. Earth Planets Space 53, 417–422.Google Scholar
Kulsrud, R. M. 2005 Plasma Physics for Astrophysics. Princeton University Press.Google Scholar
Kulsrud, R. M. 2011 Intuitive approach to magnetic reconnection. Phys. Plasmas 18, 111201.Google Scholar
Lau, Y.-T. & Finn, J. M. 1990 Three-dimensional kinematic reconnection in the presence of field nulls and closed field lines. Astrophys. J. 350, 672.Google Scholar
Liu, Y.-H., Daughton, W., Karimabadi, H., Li, H. & Gary, S. P. 2014 Do dispersive waves play a role in collisionless magnetic reconnection? Phys. Plasmas 21, 022113.Google Scholar
Liu, Y.-H., Guo, F., Daughton, W., Li, H. & Hesse, M. 2015 Scaling of magnetic reconnection in relativistic collisionless pair plasmas. Phys. Rev. Lett. 114, 095002.Google Scholar
Loureiro, N. F., Schekochihin, A. A. & Cowley, S. C. 2007 Instability of current sheets and formation of plasmoid chains. Phys. Plasmas 14, 100703.CrossRefGoogle Scholar
Ma, Z. W. & Bhattacharjee, A. 1996 Fast impulsive reconnection and current sheet intensification due to electron pressure gradients in semi-collisional plasmas. Geophys. Res. Lett. 23, 1673–1676.Google Scholar
Mandt, M. E., Denton, R. E. & Drake, J. F. 1994 Transition to whistler mediated magnetic reconnection. Geophys. Res. Lett. 21, 73–76.Google Scholar
Matthaeus, W. H. & Lamkin, S. L. 1986 Turbulent magnetic reconnection. Phys. Fluids 29, 2513.Google Scholar
Ottaviani, M. & Porcelli, F. 1993 Nonlinear collisionless magnetic reconnection. Phys. Rev. Lett. 21, 082114.Google Scholar
Park, W., Monticello, D. A. & White, R. B. 1984 Reconnection rates of magnetic fields including the effects of viscosity. Phys. Fluids 27, 137.Google Scholar
Parker, E. N. 1957 Sweet’s mechanism for merging magnetic fields in conducting fluids. J. Geophys. Res. 62, 509–520.Google Scholar
Petschek, H. E. 1964 Magnetic Field Annihilation (ed. Hess, W. N.), AAS/NASA Symposium on the Physics of Solar Flares, p. 425. NASA.Google Scholar
Porcelli, F., Borgogno, D., Califano, F., Grasso, D., Ottaviani, M. & Pegoraro, F. 2002 Recent advances in collisionless magnetic reconnection. Plasma Phys. Control. Fusion 44, 389.Google Scholar
Priest, E. 1985 Current sheets in solar flares. In Unstable Current Systems and Plasma Instabilities in Astrophysics, IAU 107 (ed. Kundu, M. R. & Holman, G. D.), p. 233. Reidel.Google Scholar
Priest, E. & Forbes, T. 1986 New models for fast steady state magnetic reconnection. J. Geophys. Res. 9, 5579–5588.Google Scholar
Priest, E. & Forbes, T. 2000 Magnetic Reconnection: MHD Theory and Applications. Cambridge University Press.Google Scholar
Rogers, B. N., Denton, R. E., Drake, J. F. & Shay, M. A. 2001 Role of dispersive waves in collisionless magnetic reconnection. Phys. Rev. Lett. 87, 195004.CrossRefGoogle ScholarPubMed
Servidio, S., Matthaeus, W. H., Shay, M. A., Cassak, P. A. & Dmitruk, P. 2009 Magnetic reconnection in two-dimensional magnetohydrodynamic turbulence. Phys. Rev. Lett. 102, 115003.Google Scholar
Shay, M. A. & Drake, J. F. 1998 The role of electron dissipation on the rate of collisionless magnetic reconnection. Geophys. Res. Lett. 25, 3759–3762.Google Scholar
Shay, M., Drake, J., Rogers, B. & Denton, R. 1999 The scaling of collisionless, magnetic reconnection for large systems. Geophys. Res. Lett. 26, 2163–2166.Google Scholar
Shay, M., Drake, J., Swisdak, M. & Rogers, B. 2004 The scaling of embedded collisionless reconnection. Phys. Plasmas 11, 2199.Google Scholar
Shibata, K. & Tanuma, S. 2001 Plasmoid-induced-reconnection and fractal reconnection. Earth, Planets Space 53, 473–482.CrossRefGoogle Scholar
Stanier, A., Simakov, A. N., Chacón, L. & Daughton, W. 2015 Fluid versus kinetic magnetic reconnection with strong guide fields. Phys. Plasmas 22, 101203.Google Scholar
Sweet, P. A. 1958 The neutral point theory of solar flares. In Electromagnetic Phenomena in Cosmical Physics (ed. Lehnert, B.), p. 123. Cambridge University Press.Google Scholar
Tajima, T. & Shibata, K. 1997 Plasma Astrophysics, Frontiers in Physics. Addison-Wesley.Google Scholar
Uzdensky, D. A., Loureiro, N. F. & Schekochihin, A. A. 2010 Fast magnetic reconnection in the plasmoid-dominated regime. Phys. Rev. Lett. 105, 235002.Google Scholar
Wang, X. & Bhattacharjee, A. 1993 Nonlinear dynamics of the $m=1$ instability and fast sawtooth collapse in high-temperature plasmas. Phys. Rev. Lett. 70, 1627.Google Scholar
Wendel, D. E., Olson, D. K., Hesse, M., Aunai, N., Kuznetsova, M., Karimabadi, H., Daughton, W. & Adrian, M. L. 2013 The relation between reconnected flux, the parallel electric field, and the reconnection rate in a three-dimensional kinetic simulation of magnetic reconnection. Phys. Plasmas 20, 122105.CrossRefGoogle Scholar
Wilmot-Smith, A. L. & Hornig, G. 2011 A time-dependent model for magnetic reconnection in the presence of a separator. Astrophys. J. 740, 89.Google Scholar
Yamada, M., Kulsrud, R. & Ji, H. 2010 Magnetic reconnection. Rev. Mod. Phys. 82, 603.Google Scholar
Zenitani, S. & Hesse, M. 2008 Self-regulation of the reconnecting current layer in relativistic pair plasma reconnection. Astrophys. J. 684, 1477.Google Scholar