Skip to main content Accessibility help

Three-dimensional magnetic reconnection and its application to solar flares

  • Miho Janvier (a1)


Solar flares are powerful radiations occurring in the Sun’s atmosphere. They are powered by magnetic reconnection, a phenomenon that can convert magnetic energy into other forms of energy such as heat and kinetic energy, and which is believed to be ubiquitous in the universe. With the ever increasing spatial and temporal resolutions of solar observations, as well as numerical simulations benefiting from increasing computer power, we can now probe into the nature and the characteristics of magnetic reconnection in three dimensions to better understand the phenomenon’s consequences during eruptive flares in our star’s atmosphere. We review in the following the efforts made on different fronts to approach the problem of magnetic reconnection. In particular, we will see how understanding the magnetic topology in three dimensions helps in locating the most probable regions for reconnection to occur, how the current layer evolves in three dimensions and how reconnection leads to the formation of flux ropes, plasmoids and flaring loops.

  • View HTML
    • Send article to Kindle

      To send this article to your Kindle, first ensure is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the or variations. ‘’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Three-dimensional magnetic reconnection and its application to solar flares
      Available formats

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Three-dimensional magnetic reconnection and its application to solar flares
      Available formats

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Three-dimensional magnetic reconnection and its application to solar flares
      Available formats


Corresponding author

Email address for correspondence:


Hide All
Al-Hachami, A. K. & Pontin, D. I. 2010 Magnetic reconnection at 3d null points: effect of magnetic field asymmetry. Astron. Astrophys. 512, A84.
Amari, T., Luciani, J. F., Aly, J. J., Mikić, Z. & Linker, J. 2003a Coronal mass ejection: initiation, magnetic helicity, and flux ropes. I. Boundary motion-driven evolution. Astrophys. J. 585, 10731086.
Amari, T., Luciani, J. F., Aly, J. J., Mikić, Z. & Linker, J. 2003b Coronal mass ejection: initiation, magnetic helicity, and flux ropes. II. Turbulent diffusion-driven evolution. Astrophys. J. 595, 12311250.
Aparna, V. & Tripathi, D. 2016 A hot flux rope observed by SDO/AIA. Astrophys. J. 819, 71.
Asai, A., Ishii, T. T., Kurokawa, H., Yokoyama, T. & Shimojo, M. 2003 Evolution of conjugate footpoints inside flare ribbons during a great two-ribbon flare on 2001 April 10. Astrophys. J. 586, 624629.
Aulanier, G., DeLuca, E. E., Antiochos, S. K., McMullen, R. A. & Golub, L. 2000 The topology and evolution of the bastille day flare. Astrophys. J. 540, 11261142.
Aulanier, G., Démoulin, P., Schrijver, C. J., Janvier, M., Pariat, E. & Schmieder, B. 2013 The standard flare model in three dimensions. II. Upper limit on solar flare energy. Astron. Astrophys. 549, A66.
Aulanier, G., Golub, L., DeLuca, E. E., Cirtain, J. W., Kano, R., Lundquist, L. L., Narukage, N., Sakao, T. & Weber, M. A. 2007 Slipping magnetic reconnection in coronal loops. Science 318, 1588.
Aulanier, G., Janvier, M. & Schmieder, B. 2012 The standard flare model in three dimensions. I. Strong-to-weak shear transition in post-flare loops. Astron. Astrophys. 543, A110.
Aulanier, G., Pariat, E. & Démoulin, P. 2005 Current sheet formation in quasi-separatrix layers and hyperbolic flux tubes. Astron. Astrophys. 444, 961976.
Aulanier, G., Pariat, E., Démoulin, P. & DeVore, C. R. 2006 Slip-running reconnection in quasi-separatrix layers. Solar Phys. 238, 347376.
Aulanier, G., Török, T., Démoulin, P. & DeLuca, E. E. 2010 Formation of torus-unstable flux ropes and electric currents in erupting sigmoids. Astrophys. J. 708, 314333.
Baalrud, S. D., Bhattacharjee, A. & Huang, Y.-M. 2012 Reduced magnetohydrodynamic theory of oblique plasmoid instabilities. Phys. Plasmas 19 (2), 022101.
Bagalá, L. G., Mandrini, C. H., Rovira, M. G. & Démoulin, P. 2000 Magnetic reconnection: a common origin for flares and AR interconnecting arcs. Astron. Astrophys. 363, 779788.
Barnes, G., Longcope, D. W. & Leka, K. D. 2005 Implementing a magnetic charge topology model for solar active regions. Astrophys. J. 629, 561571.
Bárta, M., Vršnak, B. & Karlický, M. 2008 Dynamics of plasmoids formed by the current sheet tearing. Astron. Astrophys. 477, 649655.
Baty, H., Forbes, T. G. & Priest, E. R. 2009 Petschek reconnection with a nonlocalized resistivity. Phys. Plasmas 16 (1), 012102.
Baty, H., Forbes, T. G. & Priest, E. R. 2014 The formation and stability of Petschek reconnection. Phys. Plasmas 21 (11), 112111.
Baum, P. J. & Bratenahl, A. 1976 Laboratory solar flare experiments. Solar Phys. 47, 331343.
Baum, P. J. & Bratenahl, A. 1980 Flux linkages of bipolar sunspot groups – a computer study. Solar Phys. 67, 245258.
Baum, P. J., Bratenahl, A., Crockett, G. & Kamin, G. 1979 Magnetic flux of colinear bipolar SPOT pairs. Solar Phys. 62, 5367.
Baum, P. J., Bratenahl, A., Kao, M. & White, R. S. 1973 Plasma instability at an X-type magnetic neutral point. Phys. Fluids 16, 15011504.
Bemporad, A. 2008 Spectroscopic detection of turbulence in post-CME current sheets. Astrophys. J. 689, 572584.
Bessho, N. & Bhattacharjee, A. 2005 Collisionless reconnection in an electron–positron plasma. Phys. Rev. Lett. 95 (24), 245001.
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 (11), 112102.
Bierwage, A., Hamaguchi, S., Wakatani, M., Benkadda, S. & Leoncini, X. 2005 Nonlinear evolution of $q=1$ triple tearing modes in a tokamak plasma. Phys. Rev. Lett. 94 (6), 065001.
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, 37153720.
Birn, J. & Hesse, M. 2001 Geospace environment modeling (GEM) magnetic reconnection challenge: resistive tearing, anisotropic pressure and Hall effects. J. Geophys. Res. 106, 37373750.
Biskamp, D. 1986 Magnetic reconnection via current sheets. Phys. Fluids 29, 15201531.
Bommier, V., Landi Degl’Innocenti, E., Landolfi, M. & Molodij, G. 2007 UNNOFIT inversion of spectro-polarimetric maps observed with THEMIS. Astron. Astrophys. 464, 323339.
Büchner, J. 2007 Astrophysical reconnection and collisionless dissipation. Plasma Phys. Control. Fusion 49, B325B339.
Cai, H. & Li, D. 2008 Magnetic reconnection with electron viscosity in electron magnetohydrodynamics. Phys. Plasmas 15 (3), 032301.
Carmichael, H. 1964 A process for flares. NASA Special Publication 50, 451.
Chandra, R., Schmieder, B., Aulanier, G. & Malherbe, J. M. 2009 Evidence of magnetic helicity in emerging flux and associated flare. Solar Phys. 258, 5367.
Chandra, R., Schmieder, B., Mandrini, C. H., Démoulin, P., Pariat, E., Török, T. & Uddin, W. 2011 Homologous flares and magnetic field topology in active region NOAA 10501 on 20 November 2003. Solar Phys. 269, 83104.
Comisso, L. & Bhattacharjee, A.2016 On the value of the reconnection rate. Preprint.
Cowling, T. G. 1945 On the Sun’s general magnetic field. Mon. Not. R. Astron. Soc. 105, 166.
Craig, I. J. D. & Effenberger, F. 2014 Current singularities at quasi-separatrix layers and three-dimensional magnetic nulls. Astrophys. J. 795, 129.
Cremades, H. & Bothmer, V. 2004 On the three-dimensional configuration of coronal mass ejections. Astron. Astrophys. 422, 307322.
Dasso, S., Mandrini, C. H., Démoulin, P., Luoni, M. L. & Gulisano, A. M. 2005 Large scale MHD properties of interplanetary magnetic clouds. Adv. Space Res. 35, 711724.
Daughton, W., Roytershteyn, V., Karimabadi, H., Yin, L., Albright, B. J., Bergen, B. & Bowers, K. J. 2011 Role of electron physics in the development of turbulent magnetic reconnection in collisionless plasmas. Nat. Phys. 7, 539542.
de La Beaujardiere, J.-F., Canfield, R. C. & Leka, K. D. 1993 The morphology of flare phenomena, magnetic fields, and electric currents in active regions. III – NOAA active region 6233 (1990 August). Astrophys. J. 411, 378382.
Del Sarto, D., Pucci, F., Tenerani, A. & Velli, M. 2016 ‘Ideal’ tearing and the transition to fast reconnection in the weakly collisional MHD and EMHD regimes. J. Geophys. Res. 121, 18571873.
Del Zanna, L., Landi, S., Papini, E., Pucci, F. & Velli, M. 2016 The ideal tearing mode: theory and resistive MHD simulations. J. Phys.: Conf. Ser. 719 (1), 012016.
Delzanno, G. L. & Finn, J. M. 2008 The effect of line-tying on tearing modes. Phys. Plasmas 15 (3), 032904.
Démoulin, P. 2005 Magnetic Topologies: where Will Reconnection Occur? In Chromospheric and Coronal Magnetic Fields (ed. Innes, D. E., Lagg, A. & Solanki, S. A.), ESA Special Publication, vol. 596, p. 22.1.
Démoulin, P., Bagala, L. G., Mandrini, C. H., Hénoux, J. C. & Rovira, M. G. 1997 Quasi-separatrix layers in solar flares. II. Observed magnetic configurations. Astron. Astrophys. 325, 305317.
Démoulin, P., Hénoux, J. C. & Mandrini, C. H. 1994a Are magnetic null points important in solar flares? Astron. Astrophys. 285, p. 1023.
Démoulin, P., Hénoux, J. C., Priest, E. R. & Mandrini, C. H. 1996a Quasi-separatrix layers in solar flares. I. Method. Astron. Astrophys. 308, 643655.
Démoulin, P., Mandrini, C. H., Rovira, M. G., Hénoux, J. C. & Machado, M. E. 1994b Interpretation of multiwavelength observations of November 5, 1980 solar flares by the magnetic topology of AR 2766. Solar Phys. 150, 221243.
Démoulin, P., Priest, E. R. & Lonie, D. P. 1996b Three-dimensional magnetic reconnection without null points 2. Application to twisted flux tubes. J. Geophys. Res. 101, 76317646.
Démoulin, P., van Driel-Gesztelyi, L., Schmieder, B., Hénoux, J. C., Csepura, G. & Hagyard, M. J. 1993 Evidence for magnetic reconnection in solar flares. Astron. Astrophys. 271, 292.
Drake, J. F., Shay, M. A. & Swisdak, M. 2008 The Hall fields and fast magnetic reconnection. Phys. Plasmas 15 (4), 042306.
Dudík, J., Janvier, M., Aulanier, G., Del Zanna, G., Karlický, M., Mason, H. E. & Schmieder, B. 2014 Slipping magnetic reconnection during an X-class solar flare observed by SDO/AIA. Astrophys. J. 784, 144.
Dudík, J., Polito, V., Janvier, M., Mulay, S. M., Karlický, M., Aulanier, G., Del Zanna, G., Dzifčáková, E., Mason, H. E. & Schmieder, B. 2016 Slipping magnetic reconnection, chromospheric evaporation, implosion, and precursors in the 2014 September 10 X1.6-Class Solar Flare. Astrophys. J. 823, 41.
Dungey, J. W. 1953 The motion of magnetic fields. Mon. Not. R. Astron. Soc. 113, 679.
Edmondson, J. K., Antiochos, S. K., DeVore, C. R. & Zurbuchen, T. H. 2010 Formation and reconnection of three-dimensional current sheets in the solar corona. Astrophys. J. 718, 7285.
Effenberger, F., Thust, K., Arnold, L., Grauer, R. & Dreher, J. 2011 Numerical simulation of current sheet formation in a quasiseparatrix layer using adaptive mesh refinement. Phys. Plasmas 18 (3), 032902.
Emslie, A. G., Dennis, B. R., Holman, G. D. & Hudson, H. S. 2005 Refinements to flare energy estimates: a followup to ‘Energy partition in two solar flare/CME events’ by A. G. Emslie et al. J. Geophys. Res. 110, A11103.
Feng, L., Wang, Y., Shen, F., Shen, C., Inhester, B., Lu, L. & Gan, W. 2015 Why does the apparent mass of a coronal mass ejection increase? Astrophys. J. 812, 70.
Fermo, R. L., Drake, J. F. & Swisdak, M. 2010 A statistical model of magnetic islands in a current layer. Phys. Plasmas 17 (1), 010702.
Forbes, T. 2000 Solar Flare Models. p. 2295. Institute of Physics Publishing.
Forbes, T. G., Priest, E. R., Seaton, D. B. & Litvinenko, Y. E. 2013 Indeterminacy and instability in Petschek reconnection. Phys. Plasmas 20 (5), 052902.
Friedman, M. & Hamberger, S. M. 1968 On the neutral-point region in Petschek’s model of magnetic-field annihilation. Astrophys. J. 152, 667.
Furth, H. P., Killeen, J. & Rosenbluth, M. N. 1963 Finite-resistivity instabilities of a sheet pinch. Phys. Fluids 6, 459484.
Fuselier, S. A., Lewis, W. S., Schiff, C., Ergun, R., Burch, J. L., Petrinec, S. M. & Trattner, K. J. 2016 Magnetospheric multiscale science mission profile and operations. Space Sci. Rev. 199, 77103.
Galsgaard, K. & Pontin, D. I. 2011 Steady state reconnection at a single 3D magnetic null point. Astron. Astrophys. 529, A20.
Gekelman, W., Lawrence, E. & Van Compernolle, B. 2012 Three-dimensional reconnection involving magnetic flux ropes. Astrophys. J. 753, 131.
Gibson, S. E. & Fan, Y. 2006 Coronal prominence structure and dynamics: a magnetic flux rope interpretation. J. Geophys. Res. 111, A12103.
Gibson, S. E., Kucera, T. A., Rastawicki, D., Dove, J., de Toma, G., Hao, J., Hill, S., Hudson, H. S., Marqué, C. & McIntosh, P. S. 2010 Three-dimensional morphology of a coronal prominence cavity. Astrophys. J. 724, 11331146.
Gilchrist, S. A. & Wheatland, M. S. 2013 A magnetostatic grad-rubin code for coronal magnetic field extrapolations. Solar Phys. 282, 283302.
Giovanelli, R. G. 1947 Magnetic and electric phenomena in the Sun’s atmosphere associated with sunspots. Mon. Not. R. Astron. Soc. 107, 338.
Gold, T. & Hoyle, F. 1960 On the origin of solar flares. Mon. Not. R. Astron. Soc. 120, 89.
Gonzalez, W. & Parker, E.(Eds) 2016 Magnetic Reconnection, Astrophysics and Space Science Library, vol. 427.
Gorbachev, V. S. & Somov, B. V. 1988 Photospheric vortex flows as a cause for two-ribbon flares – a topological model. Solar Phys. 117, 7788.
Gosling, J. T., Mccomas, D. J., Phillips, J. L. & Bame, S. J. 1991 Geomagnetic activity associated with earth passage of interplanetary shock disturbances and coronal mass ejections. J. Geophys. Res. 96, 78317839.
Graham, D. R. & Cauzzi, G. 2015 Temporal evolution of multiple evaporating ribbon sources in a solar flare. Astrophys. J. Lett. 807, L22.
Green, L. M. & Kliem, B. 2009 Flux rope formation preceding coronal mass ejection onset. Astrophys. J. Lett. 700, L83L87.
Green, L. M., Kliem, B., Török, T., van Driel-Gesztelyi, L. & Attrill, G. D. R. 2007 Transient coronal sigmoids and rotating erupting flux ropes. Solar Phys. 246, 365391.
Green, R. M. & Sweet, P. A. 1967 Note on the dissipation of magnetic fields at neutral lines. Astrophys. J. 147, 1153.
Hagyard, M. J. 1988 Observed nonpotential magnetic fields and the inferred flow of electric currents at a location of repeated flaring. Solar Phys. 115, 107124.
Hahm, T. S. & Kulsrud, R. M. 1985 Forced magnetic reconnection. Phys. Fluids 28, 24122418.
Hayashi, T. 1981 Numerical simulations of forced coalescence of magnetic islands generated by a tearing mode instability. J. Phys. Soc. Japan 50, 3124.
Hazeltine, R. D., Meiss, J. D. & Morrison, P. J. 1986 Analytic theory of the nonlinear $m=1$ tearing mode. Phys. Fluids 29, 16331639.
Heerikhuisen, J. & Craig, I. J. D. 2004 Magnetic reconnection in three dimensions – spine, fan and separator solutions. Solar Phys. 222 (1), 95114.
Hénoux, J. C., Demoulin, P., Mandrini, C. H. & Rovira, M. G. 1993 Observational evidence for magnetic reconnection in solar flares (invited). In IAU Colloq. 141: The Magnetic and Velocity Fields of Solar Active Regions (ed. Zirin, H., Ai, G. & Wang, H.), Astronomical Society of the Pacific Conference Series, vol. 46, p. 333.
Hénoux, J. C. & Somov, B. V. 1987 Generation and structure of the electric currents in a flaring activity complex. Astron. Astrophys. 185, 306314.
Hesse, M., Forbes, T. G. & Birn, J. 2005 On the relation between reconnected magnetic flux and parallel electric fields in the solar corona. Astrophys. J. 631, 12271238.
Hesse, M., Kuznetsova, M. & Birn, J. 2004 The role of electron heat flux in guide-field magnetic reconnection. Phys. Plasmas 11, 53875397.
Hesse, M. & Schindler, K. 1988 A theoretical foundation of general magnetic reconnection. J. Geophys. Res. 93, 55595567.
Hirayama, T. 1974 Theoretical model of flares and prominences. I: evaporating flare model. Solar Phys. 34, 323338.
Hofmann, A., Grigor’ev, V. M. & Selivanov, V. L. 1988 Analysis and results of cooperative magnetographic measurements. II – comparison and interpretation of the current densities. Astron. Nachr. 309, 373379.
Hood, A. W. & Priest, E. R. 1979 Kink instability of solar coronal loops as the cause of solar flares. Solar Phys. 64, 303321.
Hu, Q., Qiu, J., Dasgupta, B., Khare, A. & Webb, G. M. 2014 Structures of interplanetary magnetic flux ropes and comparison with their solar sources. Astrophys. J. 793, 53.
Huba, J. D. 2003 Hall Magnetohydrodynamics – A Tutorial, pp. 166192. Springer.
Ishii, Y., Azumi, M. & Kishimoto, Y. 2002 Structure-driven nonlinear instability of double tearing modes and the abrupt growth after long-time-scale evolution. Phys. Rev. Lett. 89 (20), 205002.
Jaggi, R. K. 1963 The role of plasma instabilities in the origin of solar flares. J. Geophys. Res. 68, 4429.
Janvier, M., Aulanier, G., Bommier, V., Schmieder, B., Démoulin, P. & Pariat, E. 2014a Electric currents in flare ribbons: observations and three-dimensional standard model. Astrophys. J. 788, 60.
Janvier, M., Aulanier, G., Pariat, E. & Démoulin, P. 2013 The standard flare model in three dimensions. III. Slip-running reconnection properties. Astron. Astrophys. 555, A77.
Janvier, M., Démoulin, P. & Dasso, S. 2014b Are there different populations of flux ropes in the solar wind? Solar Phys. 289, 26332652.
Janvier, M., Kishimoto, Y. & Li, J. Q. 2011 Structure-driven nonlinear instability as the origin of the explosive reconnection dynamics in resistive double tearing modes. Phys. Rev. Lett. 107 (19), 195001.
Janvier, M., Savcheva, A., Pariat, E., Tassev, S., Millholland, S., Bommier, V., McCauley, P., McKillop, S. & Dougan, F. 2016 Evolution of flare ribbons, electric currents, and quasi-separatrix layers during an X-class flare. Astron. Astrophys. 591, A141.
Karlický, M., Fárník, F. & Mészárosová, H. 2002 High-frequency slowly drifting structures in solar flares. Astron. Astrophys. 395, 677683.
Kerr, G. S., Fletcher, L., Russell, A. J. B. & Allred, J. C. 2016 Simulations of the Mg II k and Ca II 8542 lines from an AlfvÉn Wave-heated Flare Chromosphere. Astrophys. J. 827, 101.
Kliem, B. 1995 Coupled Magnetohydrodynamic and Kinetic Development of Current Sheets in the Solar Corona, pp. 93114. Springer.
Kliem, B., Su, Y. N., van Ballegooijen, A. A. & DeLuca, E. E. 2013 Magnetohydrodynamic modeling of the solar eruption on 2010 April 8. Astrophys. J. 779, 129.
Kopp, R. A. & Pneuman, G. W. 1976 Magnetic reconnection in the corona and the loop prominence phenomenon. Solar Phys. 50, 8598.
Kosovichev, A. G. & Zharkova, V. V. 1999 Variations of photospheric magnetic field associated with flares and CMEs. Solar Phys. 190, 459466.
Kretzschmar, M. 2011 The Sun as a star: observations of white-light flares. Astron. Astrophys. 530, A84.
Kulsrud, R. M. 2001 Magnetic reconnection: Sweet–Parker versus Petschek. Earth Planets Space 53, 417422.
Kusano, K., Bamba, Y., Yamamoto, T. T., Iida, Y., Toriumi, S. & Asai, A. 2012 Magnetic field structures triggering solar flares and coronal mass ejections. Astrophys. J. 760, 31.
La Rosa, T. N. 1990 Impulsive phase heating by uni-directional current systems in solar flares. Solar Phys. 126 (1), 153175.
Landi, S., Del Zanna, L., Papini, E., Pucci, F. & Velli, M. 2015 Resistive magnetohydrodynamics simulations of the ideal tearing mode. Astrophys. J. 806, 131.
Lau, Y.-T. & Finn, J. M. 1990 Three-dimensional kinematic reconnection in the presence of field nulls and closed field lines. Astrophys. J. 350, 672691.
Lazarian, A. & Vishniac, E. T. 1999 Reconnection in a weakly stochastic field. Astrophys. J. 517, 700718.
Leake, J. E., Lukin, V. S. & Linton, M. G. 2013 Magnetic reconnection in a weakly ionized plasma. Phys. Plasmas 20 (6), 061202.
Lemen, J. R., Title, A. M., Akin, D. J., Boerner, P. F., Chou, C., Drake, J. F., Duncan, D. W., Edwards, C. G., Friedlaender, F. M., Heyman, G. F. et al. 2012 The atmospheric imaging assembly (AIA) on the solar dynamics observatory (SDO). Solar Phys. 275, 1740.
Li, T., Yang, K., Hou, Y. & Zhang, J.2016 Slipping magnetic reconnection of flux rope structures as a precursor to an eruptive X-class solar flare. Preprint.
Li, T. & Zhang, J. 2014 Slipping magnetic reconnection triggering a solar eruption of a triangle-shaped flag flux rope. Astrophys. J. Lett. 791, L13.
Liang, Y., Koslowski, H. R., Krämer-Flecken, A., Zimmermann, O., Löwenbrück, K., Bertschinger, G., Wolf, R. C. & TEXTOR-team 2007 LETTER: observations of secondary structures after collapse events occurring at the $q=2$ magnetic surface in the TEXTOR tokamak. Nucl. Fusion 47, L21L25.
Lin, J. & Forbes, T. G. 2000 Effects of reconnection on the coronal mass ejection process. J. Geophys. Res. 105, 23752392.
Liu, W., Chen, Q. & Petrosian, V. 2013 Plasmoid ejections and loop contractions in an eruptive M7.7 solar flare: evidence of particle acceleration and heating in magnetic reconnection outflows. Astrophys. J. 767, 168.
Liu, W., Jiang, Y. W., Liu, S. & Petrosian, V. 2004 RHESSI observations of a simple large X-ray flare on 2003 November 3. Astrophys. J. Lett. 611, L53L56.
Longcope, D. W. 2005 Topological methods for the analysis of solar magnetic fields. Living Rev. Solar Phys. 2, 7.
Longcope, D. W. & Cowley, S. C. 1996 Current sheet formation along three-dimensional magnetic separators. Phys. Plasmas 3, 28852897.
Loureiro, N. F., Cowley, S. C., Dorland, W. D., Haines, M. G. & Schekochihin, A. A. 2005 X-point collapse and saturation in the nonlinear tearing mode reconnection. Phys. Rev. Lett. 95 (23), 235003.
Loureiro, N. F., Samtaney, R., Schekochihin, A. A. & Uzdensky, D. A. 2012 Magnetic reconnection and stochastic plasmoid chains in high-Lundquist-number plasmas. Phys. Plasmas 19 (4), 042303.
Loureiro, N. F. & Uzdensky, D. A. 2016 Magnetic reconnection: from the Sweet–Parker model to stochastic plasmoid chains. Plasma Phys. Control. Fusion 58 (1), 014021.
Lynch, B. J., Antiochos, S. K., DeVore, C. R., Luhmann, J. G. & Zurbuchen, T. H. 2008 Topological evolution of a fast magnetic breakout CME in three dimensions. Astrophys. J. 683, 11921206.
Lynch, B. J., Edmondson, J. K., Kazachenko, M. D. & Guidoni, S. E. 2016 Reconnection properties of large-scale current sheets during coronal mass ejection eruptions. Astrophys. J. 826, 43.
Ma, Z. W. & Bhattacharjee, A. 1996 Role of photospheric footpoint shear in the impulsive dynamics of the solar corona. Geophys. Res. Lett. 23, 29552958.
Mandrini, C. H., Demoulin, P., Henoux, J. C. & Machado, M. E. 1991 Evidence for the interaction of large scale magnetic structures in solar flares. Astron. Astrophys. 250, 541547.
Mandrini, C. H., Demoulin, P., Schmieder, B., Deluca, E. E., Pariat, E. & Uddin, W. 2006 Companion Event and Precursor of the X17 Flare on 28 October 2003. Solar Phys. 238, 293312.
Mandrini, C. H., Pohjolainen, S., Dasso, S., Green, L. M., Démoulin, P., van Driel-Gesztelyi, L., Copperwheat, C. & Foley, C. 2005 Interplanetary flux rope ejected from an X-ray bright point. The smallest magnetic cloud source-region ever observed. Astron. Astrophys. 434, 725740.
Mandrini, C. H., Rovira, M. G., Demoulin, P., Henoux, J. C., Machado, M. E. & Wilkinson, L. K. 1993 Evidence for magnetic reconnection in large-scale magnetic structures in solar flares. Astron. Astrophys. 272, 609.
Masson, S., Pariat, E., Aulanier, G. & Schrijver, C. J. 2009 The nature of flare ribbons in coronal null-point topology. Astrophys. J. 700, 559578.
Masuda, S., Kosugi, T., Hara, H., Tsuneta, S. & Ogawara, Y. 1994 A loop-top hard X-ray source in a compact solar flare as evidence for magnetic reconnection. Nature 371, 495497.
McKenzie, D. E. 2011 Observational studies of reconnection in the solar corona. Phys. Plasmas 18 (11), 111205.
McKenzie, D. E. & Canfield, R. C. 2008 Hinode XRT observations of a long-lasting coronal sigmoid. Astron. Astrophys. 481, L65L68.
Miklenic, C., Veronig, A. M., Temmer, M., Möstl, C. & Biernat, H. K. 2011 Coronal dimmings and the early phase of a CME observed with STEREO and Hinode/EIS. Solar Phys. 273, 125142.
Militello, F., Grasso, D. & Borgogno, D. 2014 The deceiving $\unicode[STIX]{x1D6E5}$ ’: on the equilibrium dependent dynamics of nonlinear magnetic islands. Phys. Plasmas 21 (10), 102514.
Moreton, G. E. & Severny, A. B. 1968 Magnetic fields and flares in the region CMP 20 September 1963. Solar Phys. 3, 282297.
Musset, S., Vilmer, N. & Bommier, V. 2015 Hard X-ray emitting energetic electrons and photospheric electric currents. Astron. Astrophys. 580, A106.
Ni, L., Germaschewski, K., Huang, Y.-M., Sullivan, B. P., Yang, H. & Bhattacharjee, A. 2010 Linear plasmoid instability of thin current sheets with shear flow. Phys. Plasmas 17 (5), 052109.
Nindos, A., Patsourakos, S., Vourlidas, A. & Tagikas, C. 2015 How common are hot magnetic flux ropes in the low solar corona? A statistical study of EUV observations. Astrophys. J. 808, 117.
Nishida, K., Nishizuka, N. & Shibata, K. 2013 The role of a flux rope ejection in a three-dimensional magnetohydrodynamic simulation of a solar flare. Astrophys. J. Lett. 775, L39.
Nishizuka, N., Karlický, M., Janvier, M. & Bárta, M. 2015 Particle acceleration in plasmoid ejections derived from radio drifting pulsating structures. Astrophys. J. 799, 126.
Pariat, E., Aulanier, G. & Démoulin, P. 2006 A new concept for magnetic reconnection: slip-running reconnection. In SF2A-2006: Semaine de l’Astrophysique Francaise (ed. Barret, D., Casoli, F., Lagache, G., Lecavelier, A. & Pagani, L.), p. 559.
Pariat, E. & Démoulin, P. 2012 Estimation of the squashing degree within a three-dimensional domain. Astron. Astrophys. 541, A78.
Parker, E. N. 1957a Acceleration of cosmic rays in solar flares. Phys. Rev. 107, 830836.
Parker, E. N. 1957b Sweet’s mechanism for merging magnetic fields in conducting fluids. J. Geophys. Res. 62, 509520.
Parker, E. N. 1963 The solar-flare phenomenon and the theory of reconnection and annihiliation of magnetic fields. Astrophys. J. Suppl. 8, 177.
Parker, E. N. & Krook, M. 1956 Diffusion and severing of magnetic lines of force. Astrophys. J. 124, 214.
Parnell, C. E., Haynes, A. L. & Galsgaard, K. 2010 Structure of magnetic separators and separator reconnection. J. Geophys. Res. 115, 2102.
Parnell, C. E., Smith, J. M., Neukirch, T. & Priest, E. R. 1996 The structure of three-dimensional magnetic neutral points. Phys. Plasmas 3, 759770.
Petrie, G. J. D. 2013 A spatio-temporal description of the abrupt changes in the photospheric magnetic and Lorentz-force vectors during the 15 February 2011 X2.2 flare. Solar Phys. 287, 415440.
Petrie, G. J. D. & Sudol, J. J. 2010 Abrupt longitudinal magnetic field changes in flaring active regions. Astrophys. J. 724, 12181237.
Petschek, H. E. 1964 Magnetic field annihilation. NASA Special Publication 50, 425.
Petschek, H. E. & Thorne, R. M. 1967 The existence of intermediate waves in neutral sheets. Astrophys. J. 147, 1157.
Piddington, J. H. 1954a Electromagnetic field equations for a moving medium with Hall conductivity. Mon. Not. R. Astron. Soc. 114, 638.
Piddington, J. H. 1954b The motion of ionized gas in combined magnetic, electric and mechanical fields of force. Mon. Not. R. Astron. Soc. 114, 651.
Pontin, D. I. 2012 Theory of magnetic reconnection in solar and astrophysical plasmas. Phil. Trans. R. Soc. Lond. A 370, 31693192.
Pontin, D. I., Bhattacharjee, A. & Galsgaard, K. 2007 Current sheet formation and nonideal behavior at three-dimensional magnetic null points. Phys. Plasmas 14 (5), 052106.
Pontin, D. I. & Craig, I. J. D. 2006 Dynamic three-dimensional reconnection in a separator geometry with two null points. Astrophys. J. 642 (1), 568.
Pontin, D. I., Hornig, G. & Priest, E. R. 2004 Kinematic reconnection at a magnetic null point: spine-aligned current. Geophys. Astrophys. Fluid Dyn. 98, 407428.
Pontin, D. I., Hornig, G. & Priest, E. R. 2005 Kinematic reconnection at a magnetic null point: fan-aligned current. Geophys. Astrophys. Fluid Dyn. 99, 7793.
Pontin, D. I., Priest, E. R. & Galsgaard, K. 2013 On the nature of reconnection at a solar coronal null point above a separatrix dome. Astrophys. J. 774, 154.
Porcelli, F., Borgogno, D., Califano, F., Grasso, D., Ottaviani, M. & Pegoraro, F. 2002 Recent advances in collisionless magnetic reconnection. Plasma Phys. Control. Fusion 44, 389405.
Prangé, R., Pallier, L., Hansen, K. C., Howard, R., Vourlidas, A., Courtin, R. & Parkinson, C. 2004 An interplanetary shock traced by planetary auroral storms from the Sun to Saturn. Nature 432, 7881.
Priest, E. 2016 MHD structures in three-dimensional reconnection. In Astrophysics and Space Science Library (ed. Gonzalez, W. & Parker, E.), Astrophysics and Space Science Library, vol. 427, p. 101.
Priest, E. R. & Démoulin, P. 1995 Three-dimensional magnetic reconnection without null points. 1. Basic theory of magnetic flipping. J. Geophys. Res. 100, 2344323464.
Priest, E. R. & Forbes, T. G. 1992 Magnetic flipping – reconnection in three dimensions without null points. J. Geophys. Res. 97, 15211531.
Priest, E. R., Hornig, G. & Pontin, D. I. 2003 On the nature of three-dimensional magnetic reconnection. J. Geophys. Res. 108, 1285.
Priest, E. R. & Pontin, D. I. 2009 Three-dimensional null point reconnection regimes. Phys. Plasmas 16 (12), 122101.
Priest, E. R. & Raadu, M. A. 1975 Preflare current sheets in the solar atmosphere. Solar Phys. 43, 177188.
Priest, E. R. & Titov, V. S. 1996 Magnetic reconnection at three-dimensional null points. Proc. R. Soc. Lond. A 354, 29512992.
Pritchett, P. L., Lee, Y. C. & Drake, J. F. 1980 Linear analysis of the double-tearing mode. Phys. Fluids 23, 13681374.
Pucci, F. & Velli, M. 2014 Reconnection of quasi-singular current sheets: the ‘ideal’ tearing mode. Astrophys. J. Lett. 780, L19.
Qiu, J., Hu, Q., Howard, T. A. & Yurchyshyn, V. B. 2007 On the magnetic flux budget in low-corona magnetic reconnection and interplanetary coronal mass ejections. Astrophys. J. 659, 758772.
Reeves, K. K., Linker, J. A., Mikić, Z. & Forbes, T. G. 2010 Current sheet energetics, flare emissions, and energy partition in a simulated solar eruption. Astrophys. J. 721, 15471558.
Restante, A. L., Aulanier, G. & Parnell, C. E. 2009 How skeletons turn into quasi-separatrix layers in source models. Astron. Astrophys. 508, 433443.
Rosenbluth, M. N., Dagazian, R. Y. & Rutherford, P. H. 1973 Nonlinear properties of the internal $m=1$ kink instability in the cylindrical tokamak. Phys. Fluids 16, 18941902.
Sakurai, T. & Uchida, Y. 1977 Magnetic field and current sheets in the corona above active regions. Solar Phys. 52, 397416.
Samtaney, R., Loureiro, N. F., Uzdensky, D. A., Schekochihin, A. A. & Cowley, S. C. 2009 Formation of plasmoid chains in magnetic reconnection. Phys. Rev. Lett. 103 (10), 105004.
Savage, S. L., Holman, G., Reeves, K. K., Seaton, D. B., McKenzie, D. E. & Su, Y. 2012a Low-altitude reconnection inflow-outflow observations during a 2010 November 3 solar eruption. Astrophys. J. 754, 13.
Savage, S. L., McKenzie, D. E. & Reeves, K. K. 2012b Re-interpretation of supra-arcade downflows in solar flares. Astrophys. J. Lett. 747, L40.
Savcheva, A., Pariat, E., McKillop, S., McCauley, P., Hanson, E., Su, Y. & Deluca, E. E. 2016 The relation between solar eruption topologies and observed flare features. II. Dynamical evolution. Astrophys. J. 817, 43.
Savcheva, A., Pariat, E., McKillop, S., McCauley, P., Hanson, E., Su, Y., Werner, E. & Deluca, E. E. 2015 The relation between solar eruption topologies and observed flare features. I. Flare Ribbons. Astrophys. J. 810, 96.
Savcheva, A., Pariat, E., van Ballegooijen, A., Aulanier, G. & DeLuca, E. 2012a Sigmoidal active region on the sun: comparison of a magnetohydrodynamical simulation and a nonlinear force-free field model. Astrophys. J. 750, 15.
Savcheva, A. & van Ballegooijen, A. 2009 Nonlinear force-free modeling of a long-lasting coronal sigmoid. Astrophys. J. 703, 17661777.
Savcheva, A. S., Green, L. M., van Ballegooijen, A. A. & DeLuca, E. E. 2012b Photospheric flux cancellation and the build-up of sigmoidal flux ropes on the sun. Astrophys. J. 759, 105.
Savcheva, A. S., MCkillop, S. C., McCauley, P. I., Hanson, E. M. & Deluca, E. E. 2014 A new sigmoid catalog from hinode and the solar dynamics observatory: statistical properties and evolutionary histories. Solar Phys. 289, 32973311.
Schindler, K., Hesse, M. & Birn, J. 1988 General magnetic reconnection, parallel electric fields, and helicity. J. Geophys. Res. 93, 55475557.
Schmidt, H. U. 1964 On the observable effects of magnetic energy storage and release connected with solar flares. NASA Special Publication 50, 107.
Schmieder, B., Aulanier, G., Demoulin, P., van Driel-Gesztelyi, L., Roudier, T., Nitta, N. & Cauzzi, G. 1997 Magnetic reconnection driven by emergence of sheared magnetic field. Astron. Astrophys. 325, 12131225.
Schmieder, B., Démoulin, P. & Aulanier, G. 2013 Solar filament eruptions and their physical role in triggering coronal mass ejections. Adv. Space Res. 51, 19671980.
Schou, J., Scherrer, P. H., Bush, R. I., Wachter, R., Couvidat, S., Rabello-Soares, M. C., Bogart, R. S., Hoeksema, J. T., Liu, Y., Duvall, T. L. et al. 2012 Design and ground calibration of the helioseismic and magnetic imager (HMI) instrument on the solar dynamics observatory (SDO). Solar Phys. 275, 229259.
Schrijver, C. J., Beer, J., Baltensperger, U., Cliver, E. W., Güdel, M., Hudson, H. S., Mccracken, K. G., Osten, R. A., Peter, T., Soderblom, D. R. et al. 2012 Estimating the frequency of extremely energetic solar events, based on solar, stellar, lunar, and terrestrial records. J. Geophys. Res. 117, 8103.
Sergeev, V., Kubyshkina, M., Alexeev, I., Fazakerley, A., Owen, C., Baumjohann, W., Nakamura, R., Runov, A., VöRöS, Z., Zhang, T. L. et al. 2008 Study of near-Earth reconnection events with Cluster and Double Star. J. Geophys. Res. 113, A07S36.
Severny, A. 1964a Solar magnetic fields. Space Sci. Rev. 3, 451486.
Severny, A. B. 1964b Solar flares. Annu. Rev. Astron. Astrophys. 2, 363.
Shay, M. A., Drake, J. F., Swisdak, M. & Rogers, B. N. 2004 The scaling of embedded collisionless reconnection. Phys. Plasmas 11, 21992213.
Shibata, K. & Tanuma, S. 2001 Plasmoid-induced-reconnection and fractal reconnection. Earth Planets Space 53, 473482.
Sobotka, M., Dudík, J., Denker, C., Balthasar, H., Jurčák, J., Liu, W., Berkefeld, T., Collados Vera, M., Feller, A., Hofmann, A. et al. 2016 Slipping reconnection in a solar flare observed in high resolution with the GREGOR solar telescope. Preprint.
Sonnerup, B. U. Ö. 1970 Magnetic-field re-connexion in a highly conducting incompressible fluid. J. Plasma Phys. 4, 161174.
Spicer, D. S. 1981 First phase heating and particle acceleration during solar flares by fast tearing modes. Solar Phys. 71, 115124.
Spitzer, L. 1956 Physics of Fully Ionized Gases.
Stenzel, R. L., Urrutia, J. M., Griskey, M. & Strohmaier, K. 2002 A new laboratory experiment on magnetic reconnection. Phys. Plasmas 9, 19251930.
Stevenson, J. E. H. & Parnell, C. E. 2015 Spontaneous reconnection at a separator current layer: 1. Nature of the reconnection. J. Geophys. Res. 120, 10.
Sturrock, P. A. 1966 Model of the high-energy phase of solar flares. Nature 211, 695697.
Sturrock, P. A. 1968 A model of solar flares. In Structure and Development of Solar Active Regions (ed. Kiepenheuer, K. O.), IAU Symposium, vol. 35, p. 471.
Su, Y., Golub, L., van Ballegooijen, A., Deluca, E. E., Reeves, K. K., Sakao, T., Kano, R., Narukage, N. & Shibasaki, K. 2007 Evolution of the sheared magnetic fields of two X-class flares observed by Hinode/XRT. Pub. Astron. Soc. Japan 59, 785.
Su, Y. N., Golub, L., van Ballegooijen, A. A. & Gros, M. 2006 Analysis of magnetic shear in An X17 solar flare on October 28, 2003. Solar Phys. 236, 325349.
Sudol, J. J. & Harvey, J. W. 2005 Longitudinal magnetic field changes accompanying solar flares. Astrophys. J. 635, 647658.
Sun, X., Hoeksema, J. T., Liu, Y., Wiegelmann, T., Hayashi, K., Chen, Q. & Thalmann, J. 2012 Evolution of magnetic field and energy in a major eruptive active region based on SDO/HMI observation. Astrophys. J. 748, 77.
Svestka, Z. 1986 On the varieties of solar flares. In The Lower Atmosphere of Solar Flares; Proceedings of the Solar Maximum Mission Symposium, Sunspot, NM, Aug. 20–24, 1985 (A87-26201 10-92). Sunspot, NM, National Solar Observatory, 1986, pp. 332–355 (ed. Neidig, D. F.), pp. 332355.
Sweet, P. A. 1950 The effect of turbulence on a magnetic field. Mon. Not. R. Astron. Soc. 110, 6983.
Sweet, P. A. 1956 Proceedings of the International Astronomical Union Symposium on Electromagnetic Phenomena in Cosmical Physics, Stockholm, 1956, IAU Symposium; unpublished.
Sweet, P. A. 1958a The neutral point theory of solar flares. In Electromagnetic Phenomena in Cosmical Physics (ed. Lehnert, B.), IAU Symposium, vol. 6, p. 123.
Sweet, P. A. 1958b The production of high energy particles in solar flares. In Supplemento al volume VIII, Serie X Del Nuovo Cimento, vol. 8, pp. 188196.
Sweet, P. A. 1958c The topology of force-free magnetic fields. Observatory 78, 3032.
Sweet, P. A. 1969 Mechanisms of solar flares. Annu. Rev. Astron. Astrophys. 7, 149.
Syrovatskii, S. I. 1966 Dynamic dissipation of a magnetic field and particle acceleration. Sov. Astron. 10, 270.
Syrovatskii, S. I., Frank, A. G. & Khodzhaev, A. Z. 1972 Development of a current layer when plasma moves in a magnetic field with a neutral line. Sov. J. Exp. Theoret. Phys. Lett. 15, 94.
Syrovatskiǐ, S. I. 1971 Formation of current sheets in a plasma with a frozen-in strong magnetic field. Sov. J. Exp. Theoret. Phys. 33, 933.
Takasao, S., Asai, A., Isobe, H. & Shibata, K. 2012 Simultaneous observation of reconnection inflow and outflow associated with the 2010 August 18 solar flare. Astrophys. J. Lett. 745, L6.
Tassev, S. & Savcheva, A.2016 QSL squasher: a fast quasi-separatrix layer map calculator. Preprint.
Titov, V. S., Forbes, T. G., Priest, E. R., Mikić, Z. & Linker, J. A. 2009 Slip-squashing factors as a measure of three-dimensional magnetic reconnection. Astrophys. J. 693, 10291044.
Titov, V. S., Hornig, G. & Démoulin, P. 2002 Theory of magnetic connectivity in the solar corona. J. Geophys. Res. 107, 1164.
Török, T. & Kliem, B. 2005 Confined and ejective eruptions of kink-unstable flux ropes. Astrophys. J. Lett. 630, L97L100.
Tripathi, D., Isobe, H. & Mason, H. E. 2006 On the propagation of brightening after filament/prominence eruptions, as seen by SoHO-EIT. Astron. Astrophys. 453, 11111116.
Tripathi, D., Kliem, B., Mason, H. E., Young, P. R. & Green, L. M. 2009 Temperature tomography of a coronal sigmoid supporting the gradual formation of a flux rope. Astrophys. J. Lett. 698, L27L32.
Tsiklauri, D. & Haruki, T. 2007 Magnetic reconnection during collisionless, stressed, X-point collapse using particle-in-cell simulation. Phys. Plasmas 14 (11), 112905112905.
Tur, T. J. & Priest, E. R. 1976 The formation of current sheets during the emergence of new magnetic flux from below the photosphere. Solar Phys. 48, 89100.
Uzdensky, D. A., Loureiro, N. F. & Schekochihin, A. A. 2010 Fast magnetic reconnection in the plasmoid-dominated regime. Phys. Rev. Lett. 105 (23), 235002.
van Ballegooijen, A. A. 2004 Observations and modeling of a filament on the sun. Astrophys. J. 612, 519529.
van Hoven, G. & Cross, M. A. 1973 Energy release by magnetic tearing: the nonlinear limit. Phys. Rev. A 7, 13471352.
Vekstein, G., Priest, E. R. & Amari, T. 1991 Formation of current sheets in force-free magnetic fields. Astron. Astrophys. 243, 492500.
Waelbroeck, F. L. 1989 Current sheets and nonlinear growth of the $m=1$ kink-tearing mode. Phys. Fluids B 1, 23722380.
Wang, H., Spirock, T. J., Qiu, J., Ji, H., Yurchyshyn, V., Moon, Y.-J., Denker, C. & Goode, P. R. 2002 Rapid changes of magnetic fields associated with six X-class flares. Astrophys. J. 576, 497504.
Wang, S., Liu, C., Liu, R., Deng, N., Liu, Y. & Wang, H. 2012 Response of the photospheric magnetic field to the X2.2 flare on 2011 February 15. Astrophys. J. Lett. 745, L17.
Wang, S., Yokoyama, T. & Isobe, H. 2015 Three-dimensional MHD magnetic reconnection simulations with a finite guide field: proposal of the shock-evoking positive-feedback model. Astrophys. J. 811, 31.
Wang, T., Sui, L. & Qiu, J. 2007 Direct observation of high-speed plasma outflows produced by magnetic reconnection in solar impulsive events. Astrophys. J. Lett. 661 (2), L207.
Wang, X., Ma, Z. W. & Bhattacharjee, A. 1996 Fast magnetic reconnection and sudden enhancement of current sheets due to inward boundary flows. Phys. Plasmas 3, 21292134.
Wang, Z. X., Wang, X. G., Dong, J. Q., Lei, Y. A., Long, Y. X., Mou, Z. Z. & Qu, W. X. 2007 Fast resistive reconnection regime in the nonlinear evolution of double tearing modes. Phys. Rev. Lett. 99 (18), 185004.
Warren, H. P., O’Brien, C. M. & Sheeley, N. R. Jr. 2011 Observations of reconnecting flare loops with the atmospheric imaging assembly. Astrophys. J. 742, 92.
Watanabe, K., Sato, T. & Nakayama, Y. 1995 Current profile flattening and hot core shift due to non-linear development of resistive kink mode. Nucl. Fusion 35, 251259.
Webb, D. F. & Howard, T. A. 2012 Coronal mass ejections: observations. Living Rev. Solar Phys. 9 (3), 3.
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 (12), 122105.
Wentzel, D. G. 1963 Dissipation of magnetic energy in a solar flare. Astronom. J. 68, 299.
Wild, J. P., Smerd, S. F. & Weiss, A. A. 1963 Solar bursts. Annu. Rev. Astron. Astrophys. 1, 291.
Wilmot-Smith, A. L., Hornig, G. & Pontin, D. I. 2009 Magnetic braiding and quasi-separatrix layers. Astrophys. J. 704, 12881295.
Wyper, P. F., DeVore, C. R., Karpen, J. T. & Lynch, B. J. 2016 Three-dimensional simulations of tearing and intermittency in coronal jets. Astrophys. J. 827, 4.
Wyper, P. F. & Pontin, D. I. 2014 Dynamic topology and flux rope evolution during non-linear tearing of 3D null point current sheets. Phys. Plasmas 21 (10), 102102.
Yamada, M. 2007 Progress in understanding magnetic reconnection in laboratory and space astrophysical plasmas. Phys. Plasmas 14 (5), 058102.
Yamada, M., Ji, H., Hsu, S., Carter, T., Kulsrud, R., Bretz, N., Jobes, F., Ono, Y. & Perkins, F. 1997 Study of driven magnetic reconnection in a laboratory plasma. Phys. Plasmas 4, 19361944.
Yamada, M., Kulsrud, R. & Ji, H. 2010 Magnetic reconnection. Rev. Mod. Phys. 82, 603664.
Yamada, M., Yoo, J., Jara-Almonte, J., Daughton, W., Ji, H., Kulsrud, R. M. & Myers, C. E. 2015 Study of energy conversion and partitioning in the magnetic reconnection layer of a laboratory plasma). Phys. Plasmas 22 (5), 056501.
Yamada, M., Yoo, J. & Zenitani, S. 2016 Energy conversion and inventory of a prototypical magnetic reconnection layer. In Astrophysics and Space Science Library (ed. Gonzalez, W. & Parker, E.), Astrophysics and Space Science Library, vol. 427, p. 143.
Yashiro, S., Akiyama, S., Gopalswamy, N. & Howard, R. A. 2006 Different power-law indices in the frequency distributions of flares with and without coronal mass ejections. Astrophys. J. Lett. 650, L143L146.
Yeh, T. 1976 Diffusive hydromagnetic flow in the vicinity of a neutral point. Astrophys. J. 207, 837847.
Yeh, T. & Axford, W. I. 1970 On the re-connexion of magnetic field lines in conducting fluids. J. Plasma Phys. 4, 207229.
Yokoyama, T., Akita, K., Morimoto, T., Inoue, K. & Newmark, J. 2001 Clear evidence of reconnection inflow of a solar flare. Astrophys. J. Lett. 546, L69L72.
Zhao, J., Gilchrist, S. A., Aulanier, G., Schmieder, B., Pariat, E. & Li, H. 2016 Hooked flare ribbons and flux-rope-related QSL footprints. Astrophys. J. 823, 62.
Zheng, R., Chen, Y. & Wang, B. 2016 Slipping magnetic reconnections with multiple flare ribbons during an X-class solar flare. Astrophys. J. 823, 136.
Zurbuchen, T. H. & Richardson, I. G. 2006 In-situ solar wind and magnetic field signatures of interplanetary coronal mass ejections. Space Sci. Rev. 123, 3143.
Zweibel, E. G. 2015 Ambipolar diffusion. In Magnetic Fields in Diffuse Media (ed. Lazarian, A., de Gouveia Dal Pino, E. M. & Melioli, C.), Astrophysics and Space Science Library, vol. 407, p. 285.
Zweibel, E. G. & Yamada, M. 2009 Magnetic reconnection in astrophysical and laboratory plasmas. Annu. Rev. Astron. Astrophys. 47, 291332.