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On the value of the reconnection rate

  • L. Comisso (a1) and A. Bhattacharjee (a1)

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.

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Email address for correspondence: lcomisso@princeton.edu

References

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Andrés, N., Dmitruk, P. & Gómez, D. 2016 Influence of the Hall effect and electron inertia in collisionless magnetic reconnection. Phys. Plasmas 23, 022903.
Aydemir, A. Y. 1992 Nonlinear studies of $m=1$ modes in high-temperature plasmas. Phys. Fluids B 4, 3469.
Bessho, N. & Bhattacharjee, A. 2005 Collisionless reconnection in an electron–positron plasma. Phys. Rev. Lett. 95, 245001.
Bhattacharjee, A., Germaschewski, K. & Ng, C.-S. 2005 Current singularities: drivers of impulsive reconnection. Phys. Plasmas 12, 042305.
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.
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, 37153719.
Biskamp, D. 1986 Magnetic reconnection via current sheets. Phys. Fluids 29, 1520.
Biskamp, D., Schwarz, E. & Drake, J. F. 1995 Ion-controlled collisionless magnetic reconnection. Phys. Rev. Lett. 75, 3850.
Borgogno, D., Grasso, D., Porcelli, F., Califano, F., Pegoraro, F. & Farina, D. 2005 Aspects of three-dimensional magnetic reconnection. Phys. Plasmas 12, 032309.
Cassak, P. A., Shay, M. A. & Drake, J. F. 2009 Scaling of Sweet–Parker reconnection with secondary islands. Phys. Plasmas 16, 120702.
Chacón, L., Simakov, A. N., Lukin, V. S. & Zocco, A. 2008 Fast reconnection in nonrelativistic 2D electron-positron plasmas. Phys. Rev. Lett. 101, 025003.
Christie, A. 1936 The A.B.C. Murders. Collins Crime Club.
Comisso, L. & Asenjo, F. A. 2014 Thermal-inertial effects on magnetic reconnection in relativistic pair plasmas. Phys. Rev. Lett. 113, 045001.
Comisso, L. & Grasso, D. 2016 Visco-resistive plasmoid instability. Phys. Plasmas 23, 032111.
Comisso, L., Grasso, D. & Waelbroeck, F. L. 2015 Extended theory of the Taylor problem in the plasmoid-unstable regime. Phys. Plasmas 22, 042109.
Comisso, L., Grasso, D., Waelbroeck, F. L. & Borgogno, D. 2013 Gyro-induced acceleration of magnetic reconnection. Phys. Plasmas 20, 092118.
Comisso, L., Lingam, M., Huang, Y.-M. & Bhattacharjee, A. 2016 General theory of the plasmoid instability. Phys. Plasmas 23, 100702.
Daughton, W. & Karimabadi, H. 2007 Collisionless magnetic reconnection in large-scale electron-positron plasmas. Phys. Plasmas 14, 072303.
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.
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.
Daughton, W., Scudder, J. & Karimabadi, H. 2006 Fully kinetic simulations of undriven magnetic reconnection with open boundary conditions. Phys. Plasmas 13, 072101.
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.
Fitzpatrick, R. 2004 Scaling of forced magnetic reconnection in the Hall-magnetohydrodynamic Taylor problem. Plasmas 11, 937.
Grasso, D., Pegoraro, F., Porcelli, F. & Califano, F. 1999 Hamiltonian magnetic reconnection. Plasma Phys. Control. Fusion 41, 1497.
Greene, J. M. 1998 Geometrical properties of three-dimensional reconnecting magnetic fields with nulls. J. Geophys. Res. 93, 85838590.
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.
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.
Huang, Y.-M. & Bhattacharjee, A. 2010 Scaling laws of resistive magnetohydrodynamic reconnection in the high-Lundquist-number, plasmoid-unstable regime. Phys. Plasmas 17, 062104.
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.
Ji, H. & Daughton, W. 2011 Phase diagram for magnetic reconnection in heliophysical, astrophysical, and laboratory plasmas. Phys. Plasmas 18, 111207.
Kleva, R. G., Drake, J. F. & Waelbroeck, F. L. 1995 Fast reconnection in high temperature plasmas. Phys. Plasmas 2, 23.
Kulsrud, R. M. 2001 Magnetic reconnection: Sweet–Parker versus Petschek. Earth Planets Space 53, 417422.
Kulsrud, R. M. 2005 Plasma Physics for Astrophysics. Princeton University Press.
Kulsrud, R. M. 2011 Intuitive approach to magnetic reconnection. Phys. Plasmas 18, 111201.
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.
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.
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.
Loureiro, N. F., Schekochihin, A. A. & Cowley, S. C. 2007 Instability of current sheets and formation of plasmoid chains. Phys. Plasmas 14, 100703.
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, 16731676.
Mandt, M. E., Denton, R. E. & Drake, J. F. 1994 Transition to whistler mediated magnetic reconnection. Geophys. Res. Lett. 21, 7376.
Matthaeus, W. H. & Lamkin, S. L. 1986 Turbulent magnetic reconnection. Phys. Fluids 29, 2513.
Ottaviani, M. & Porcelli, F. 1993 Nonlinear collisionless magnetic reconnection. Phys. Rev. Lett. 21, 082114.
Park, W., Monticello, D. A. & White, R. B. 1984 Reconnection rates of magnetic fields including the effects of viscosity. Phys. Fluids 27, 137.
Parker, E. N. 1957 Sweet’s mechanism for merging magnetic fields in conducting fluids. J. Geophys. Res. 62, 509520.
Petschek, H. E. 1964 Magnetic Field Annihilation (ed. Hess, W. N.), AAS/NASA Symposium on the Physics of Solar Flares, p. 425. NASA.
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.
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.
Priest, E. & Forbes, T. 1986 New models for fast steady state magnetic reconnection. J. Geophys. Res. 9, 55795588.
Priest, E. & Forbes, T. 2000 Magnetic Reconnection: MHD Theory and Applications. Cambridge University Press.
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.
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.
Shay, M. A. & Drake, J. F. 1998 The role of electron dissipation on the rate of collisionless magnetic reconnection. Geophys. Res. Lett. 25, 37593762.
Shay, M., Drake, J., Rogers, B. & Denton, R. 1999 The scaling of collisionless, magnetic reconnection for large systems. Geophys. Res. Lett. 26, 21632166.
Shay, M., Drake, J., Swisdak, M. & Rogers, B. 2004 The scaling of embedded collisionless reconnection. Phys. Plasmas 11, 2199.
Shibata, K. & Tanuma, S. 2001 Plasmoid-induced-reconnection and fractal reconnection. Earth, Planets Space 53, 473482.
Stanier, A., Simakov, A. N., Chacón, L. & Daughton, W. 2015 Fluid versus kinetic magnetic reconnection with strong guide fields. Phys. Plasmas 22, 101203.
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.
Tajima, T. & Shibata, K. 1997 Plasma Astrophysics, Frontiers in Physics. Addison-Wesley.
Uzdensky, D. A., Loureiro, N. F. & Schekochihin, A. A. 2010 Fast magnetic reconnection in the plasmoid-dominated regime. Phys. Rev. Lett. 105, 235002.
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.
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.
Wilmot-Smith, A. L. & Hornig, G. 2011 A time-dependent model for magnetic reconnection in the presence of a separator. Astrophys. J. 740, 89.
Yamada, M., Kulsrud, R. & Ji, H. 2010 Magnetic reconnection. Rev. Mod. Phys. 82, 603.
Zenitani, S. & Hesse, M. 2008 Self-regulation of the reconnecting current layer in relativistic pair plasma reconnection. Astrophys. J. 684, 1477.
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On the value of the reconnection rate

  • L. Comisso (a1) and A. Bhattacharjee (a1)

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