Abstract
Very often space plasma is treated as collisionless. We check the validity of this paradigm considering various regimes of tearing mode (spontaneous reconnection) including effects of particle collisions and shear of magnetic field. We briefly describe Pitaevskii’s effect of effective modification of collision frequency due to the finite particle Larmor radius in the presence of magnetic field. This effect results in a significant increase of the role of collisionality, especially in a weakly magnetized systems. Another popular paradigm is related with application of MHD description to collisionless or weakly collisional systems. We show, that for current sheets observed in the Earth magnetotail and magnetopause as well as for current sheets formed in Solar corona and in laboratory devices most appropriate is the kinetic semi-collisional tearing regime. Role of “collisions” could play usual Coulomb pair collisions of electrons and ions (e.g. in Solar corona) or effective collisions (scattering) of electrons with the microturbulence wave modes. Transition to real MHD modes requires either very large collisions frequencies and/or very large amplitudes of the magnetic field shear. The largest domain in the parameter space is occupied by the kinetic regimes of tearing mode growth where dissipation is provided either by Landau damping or by real (or effective) collisions.
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V. Angelopoulos, J.P. McFadden, D. Larson, et al., Tail reconnection triggering substorm onset. Science 321, 931–935 (2008). doi:10.1126/science.1160495
A.Y. Aydemir, Nonlinear studies of m=1 modes in high-temperature plasmas. Phys. Fluids B 4, 3469–3472 (1992). doi:10.1063/1.860355
J. Berchem, C.T. Russell, Magnetic field rotation through the magnetopause—ISEE 1 and 2 observations. J. Geophys. Res. 87, 8139–8148 (1982). doi:10.1029/JA087iA10p08139
P.L. Bhatnagar, E.P. Gross, M. Krook, A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Phys. Rev. 94, 511–525 (1954). doi:10.1103/PhysRev.94.511
J. Birn, E.R. Priest, Reconnection of Magnetic Fields: Magnetohydrodynamics and Collisionless Theory and Observations (2007)
D. Biskamp, Magnetic Reconnection in Plasmas (2000)
D. Biskamp, E. Schwarz, J.F. Drake, Two-fluid theory of collisionless magnetic reconnection. Phys. Plasmas 4, 1002–1009 (1997). doi:10.1063/1.872211
A.H. Boozer, Magnetic reconnection in space. Phys. Plasmas 19(9), 092902 (2012a). doi:10.1063/1.4754715
A.H. Boozer, Theory of Tokamak disruptions. Phys. Plasmas 19(5), 058101 (2012b). doi:10.1063/1.3703327
J. Büchner, Astrophysical reconnection and collisionless dissipation. Plasma Phys. Control. Fusion 49, 325–339 (2007). doi:10.1088/0741-3335/49/12B/S30
V.P. Budaev, S.P. Savin, L.M. Zelenyi, Investigation of intermittency and generalized self-similarity of turbulent boundary layers in laboratory and magnetospheric plasmas: towards a quantitative definition of plasma transport features. Phys. Usp. 54, 875–918 (2011). doi:10.3367/UFNe.0181.201109a.0905
B. Coppi, Current-driven instabilities in configurations with sheared magnetic fields. Phys. Fluids 8, 2273–2280 (1965). doi:10.1063/1.1761195
B. Coppi, J.M. Greene, J.L. Johnson, Resistive instabilities in a diffuse linear pinch. Nucl. Fusion 6, 101–117 (1966a)
B. Coppi, G. Laval, R. Pellat, Dynamics of the geomagnetic tail. Phys. Rev. Lett. 16, 1207–1210 (1966b). doi:10.1103/PhysRevLett.16.1207
F.V. Coroniti, Space plasma turbulent dissipation—reality or myth? Space Sci. Rev. 42, 399–410 (1985). doi:10.1007/BF00214995
W. Daughton, The unstable eigenmodes of a neutral sheet. Phys. Plasmas 6, 1329–1343 (1999). doi:10.1063/1.873374
W. Daughton, H. Karimabadi, Kinetic theory of collisionless tearing at the magnetopause. J. Geophys. Res. (Space Phys.) 110, 3217 (2005). doi:10.1029/2004JA010751
X.H. Deng, H. Matsumoto, Rapid magnetic reconnection in the Earth’s magnetosphere mediated by whistler waves. Nature 410, 557–560 (2001). doi:10.1038/35069018
M. Dobrowolny, Instability of a neutral sheet. Nuovo Cim., B 55, 427–442 (1968). doi:10.1007/BF02711653
J.F. Drake, R.G. Kleva, Collisionless reconnection and the sawtooth crash. Phys. Rev. Lett. 66, 1458–1461 (1991). doi:10.1103/PhysRevLett.66.1458
J.F. Drake, Y.C. Lee, Kinetic theory of tearing instabilities. Phys. Fluids 20, 1341–1353 (1977). doi:10.1063/1.862017
J.P. Eastwood, T.D. Phan, S.D. Bale, A. Tjulin, Observations of turbulence generated by magnetic reconnection. Phys. Rev. Lett. 102(3), 035001 (2009). doi:10.1103/PhysRevLett.102.035001
A.G. Frank, Dynamics of current sheets underlying flare-type events in magnetized plasmas. Phys. Usp. 53, 941–947 (2010). doi:10.3367/UFNe.0180.201009h.0982
A.G. Frank, N.P. Kyrie, S.N. Satunin, Plasma dynamics in laboratory-produced current sheets. Phys. Plasmas 18(11), 111209 (2011). doi:10.1063/1.3647576
A.G. Frank, S.Y. Bogdanov, V.S. Markov, G.V. Ostrovskaya, G.V. Dreiden, Experimental study of plasma compression into the sheet in three-dimensional magnetic fields with singular X lines. Phys. Plasmas 12(5), 052316 (2005). doi:10.1063/1.1896376
M. Fujimoto, I. Shinohara, H. Kojima, Reconnection and waves: a review with a perspective. Space Sci. Rev. 160, 123–143 (2011). doi:10.1007/s11214-011-9807-7
H.P. Furth, The ‘mirror instability’ for finite particle gyro-radius. Nucl. Fusion 1, 169–174 (1962)
H.P. Furth, J. Killeen, M.N. Rosenbluth, Finite-resistivity instabilities of a sheet pinch. Phys. Fluids 6, 459–485 (1963)
A.A. Galeev, Reconnection in the magnetotail. Space Sci. Rev. 23, 411–425 (1979). doi:10.1007/BF00172248
A.A. Galeev, L.M. Zelenyi, Tearing instability in plasma configurations. Sov. Phys. JETP 43, 1113 (1976)
A.A. Galeev, L.M. Zelenyi, Model of magnetic-field reconnection in a plane layer of collisionless plasma. JETP Lett. 25, 380 (1977)
A.A. Galeev, L.M. Zelenyi, Magnetic reconnection in a space plasma, in Theoretical and Computational Plasma Physics (1978), pp. 93–116
A.A. Galeev, M.M. Kuznetsova, L.M. Zelenyi, Magnetopause stability threshold for patchy reconnection. Space Sci. Rev. 44, 1–41 (1986). doi:10.1007/BF00227227
R.G. Giovanelli, Magnetic and electric phenomena in the Sun’s atmosphere associated with sunspots. Mon. Not. R. Astron. Soc. 107, 338 (1947)
D. Grasso, F. Pegoraro, F. Porcelli, F. Califano, Hamiltonian magnetic reconnection. Plasma Phys. Control. Fusion 41, 1497–1515 (1999). doi:10.1088/0741-3335/41/12/306
E.G. Harris, On a plasma sheet separating regions of oppositely directed magnetic field. Nuovo Cimento 23, 115–123 (1962)
W. Horton, T. Tajima, Decay of correlations and the collisionless conductivity in the geomagnetic tail. Geophys. Res. Lett. 17, 123–126 (1990). doi:10.1029/GL017i002p00123
S.Y. Huang, et al., Observations of turbulence within reconnection jet in the presence of guide field. Geophys. Res. Lett. 39, 11104 (2012). doi:10.1029/2012GL052210
J.D. Huba, N.T. Gladd, K. Papadopoulos, The lower-hybrid-drift instability as a source of anomalous resistivity for magnetic field line reconnection. Geophys. Res. Lett. 4, 125–126 (1977). doi:10.1029/GL004i003p00125
V. Igochine, O. Dumbrajs, H. Zohm, A. Flaws, ASDEX Upgrade Team, Stochastic sawtooth reconnection in ASDEX upgrade. Nucl. Fusion 47, 23–32 (2007). doi:10.1088/0029-5515/47/1/004
H. Ji, S. Terry, M. Yamada, R. Kulsrud, A. Kuritsyn, Y. Ren, Electromagnetic fluctuations during fast reconnection in a laboratory plasma. Phys. Rev. Lett. 92(11), 115001 (2004). doi:10.1103/PhysRevLett.92.115001
B.B. Kadomtsev, Disruptive instability in tokamaks. Sov. J. Plasma Phys. 1, 710–715 (1975)
B.B. Kadomtsev, Review article: magnetic field line reconnection. Rep. Prog. Phys. 50, 115–143 (1987). doi:10.1088/0034-4885/50/2/001
H. Karimabadi, W. Daughton, K.B. Quest, Physics of saturation of collisionless tearing mode as a function of guide field. J. Geophys. Res. 110, 3214 (2005). doi:10.1029/2004JA010749
R.G. Kleva, J.F. Drake, F.L. Waelbroeck, Fast reconnection in high temperature plasmas. Phys. Plasmas 2, 23–34 (1995). doi:10.1063/1.871095
A.P. Kropotkin, H.V. Malova, M.I. Sitnov, Self-consistent structure of a thin anisotropic current sheet. J. Geophys. Res. 102, 22099–22106 (1997). doi:10.1029/97JA01316
J. Labelle, R.A. Treumann, Plasma waves at the dayside magnetopause. Space Sci. Rev. 47, 175–202 (1988). doi:10.1007/BF00223240
G. Lapenta, J.U. Brackbill, A kinetic theory for the drift-kink instability. J. Geophys. Res. 102, 27099–27108 (1997). doi:10.1029/97JA02140
G. Laval, R. Pellat, M. Vuillemin, Instabilités Électromagnétiques des Plasmas Sans Collisions (cn-21/71), in Plasma Physics and Controlled Nuclear Fusion Research, vol. II (1966), pp. 259–277
F.M. Levinton, L. Zakharov, S.H. Batha, J. Manickam, M.C. Zarnstorff, Stabilization and onset of sawteeth in TFTR. Phys. Rev. Lett. 72, 2895–2898 (1994). doi:10.1103/PhysRevLett.72.2895
A.S. Lipatov, L.M. Zelenyi, The study of magnetic islands dynamics. Plasma Phys. 24, 1082–1089 (1982)
A.B. Mikhailovskii, Review of instability theory for high pressure Tokamak plasma, Technical report, 1978
R. Nakamura, et al., Cluster observations of an ion-scale current sheet in the magnetotail under the presence of a guide field. J. Geophys. Res. 113, 7 (2008). doi:10.1029/2007JA012760
W.A. Newcomb, Hydromagnetic stability of a diffuse linear pinch. Ann. Phys. 10, 232–267 (1960). doi:10.1016/0003-4916(60)90023-3
R. Numata, Z. Yoshida, Chaos-induced resistivity in collisionless magnetic reconnection. Phys. Rev. Lett. 88(4), 045003 (2002). doi:10.1103/PhysRevLett.88.045003
E.V. Panov, et al., CLUSTER observation of collisionless transport at the magnetopause. Geophys. Res. Lett. 33, 15109 (2006). doi:10.1029/2006GL026556
E.V. Panov, J. Büchner, M. Fränz, et al., High-latitude earth’s magnetopause outside the cusp: cluster observations. J. Geophys. Res. 113, 1220 (2008). doi:10.1029/2006JA012123
H.K. Park, A.J.H. Donné, N.C. Luhmann Jr., I.G.J. Classen, C.W. Domier, E. Mazzucato, T. Munsat, M.J. van de Pol, Z. Xia, Comparison study of 2D images of temperature fluctuations during sawtooth oscillation with theoretical models. Phys. Rev. Lett. 96(19), 195004 (2006a). doi:10.1103/PhysRevLett.96.195004
H.K. Park, N.C. Luhmann Jr., A.J.H. Donné, I.G.J. Classen, C.W. Domier, E. Mazzucato, T. Munsat, M.J. van de Pol, Z. Xia, Observation of high-field-side crash and heat transfer during sawtooth oscillation in magnetically confined plasmas. Phys. Rev. Lett. 96(19), 195003 (2006b). doi:10.1103/PhysRevLett.96.195003
E.N. Parker, Spontaneous current sheets in magnetic fields: with applications to stellar x-rays, in Spontaneous Current Sheets in Magnetic Fields: With Applications to Stellar X-rays. International Series in Astronomy and Astrophysics, vol. 1 (Oxford University Press, New York, 1994)
F. Pegoraro, T.J. Schep, Theory of resistive modes in the ballooning representation. Plasma Phys. Control. Fusion 28, 647–667 (1986). doi:10.1088/0741-3335/28/4/003
R. Pellat, F.V. Coroniti, P.L. Pritchett, Does ion tearing exist? Geophys. Res. Lett. 18, 143–146 (1991). doi:10.1029/91GL00123
A.A. Petrukovich, Origins of plasma sheet B y . J. Geophys. Res. 116, 7217 (2011). doi:10.1029/2010JA016386
H.E. Petschek, Magnetic field annihilation. NASA Spec. Publ. 50, 425 (1964)
L.P. Pitaevskii, Effect of collisions on perturbation of body rotating in plasma. J. Exp. Theor. Phys. 44, 969–979 (1963) (in Russian)
L.P. Pitaevskii, E.M. Lifshitz, Physical Kinetics, Course of Theoretical Physics, vol. 10 (Pergamon Press, New York, 1981)
F. Porcelli, Collisionless m=1 tearing mode. Phys. Rev. Lett. 66, 425–428 (1991). doi:10.1103/PhysRevLett.66.425
F. Porcelli, D. Borgogno, F. Califano, D. Grasso, M. Ottaviani, F. Pegoraro, Recent advances in collisionless magnetic reconnection. Plasma Phys. Control. Fusion 44, 389 (2002)
E. Priest, T. Forbes, Magnetic Reconnection (2000)
P.L. Pritchett, F.V. Coroniti, Plasma sheet disruption by interchange-generated flow intrusions. Geophys. Res. Lett. 381, 10102 (2011). doi:10.1029/2011GL047527
K.B. Quest, H. Karimabadi, M. Brittnacher, Consequences of particle conservation along a flux surface for magnetotail tearing. J. Geophys. Res. 101, 179–184 (1996). doi:10.1029/95JA02986
M.N. Rosenbluth, R.Y. Dagazian, P.H. Rutherford, Nonlinear properties of the internal m=1 kink instability in the cylindrical tokamak. Phys. Fluids 16, 1894–1902 (1973). doi:10.1063/1.1694231
M. Roth, J. de Keyser, M.M. Kuznetsova, Vlasov theory of the equilibrium structure of tangential discontinuities in space plasmas. Space Sci. Rev. 76, 251–317 (1996). doi:10.1007/BF00197842
P.H. Rutherford, Nonlinear growth of the tearing mode. Phys. Fluids 16, 1903–1908 (1973). doi:10.1063/1.1694232
K. Schindler, A theory of the substorm mechanism. J. Geophys. Res. 79, 2803–2810 (1974). doi:10.1029/JA079i019p02803
K. Schindler, Physics of Space Plasma Activity (Cambridge University Press, Cambridge, 2006). doi:10.2277/0521858976
K. Schindler, M. Soop, Stability of plasma sheaths. Phys. Fluids 11, 1192–1195 (1968). doi:10.1063/1.1692083
M.I. Sitnov, K. Schindler, Tearing stability of a multiscale magnetotail current sheet. Geophys. Res. Lett. 37, 8102 (2010). doi:10.1029/2010GL042961
M.I. Sitnov, L.M. Zelenyi, H.V. Malova, A.S. Sharma, Thin current sheet embedded within a thicker plasma sheet: self-consistent kinetic theory. J. Geophys. Res. 105, 13029–13044 (2000). doi:10.1029/1999JA000431
B.U.Ö. Sonnerup, Adiabatic particle orbits in a magnetic null sheet. J. Geophys. Res. 76, 8211–8222 (1971). doi:10.1029/JA076i034p08211
L.C. Steinhauer, Review of field-reversed configurations. Phys. Plasmas 18(7), 070501 (2011). doi:10.1063/1.3613680
P.A. Sweet, The neutral point theory of solar flares, in Electromagnetic Phenomena in Cosmical Physics, ed. by B. Lehnert. IAU Symposium, vol. 6 (1958), p. 123
S.I. Syrovatskii, Dynamic dissipation of a magnetic field and particle acceleration. Sov. Astron. 10, 270 (1966)
D.A. Uzdensky, Petschek-like reconnection with current-driven anomalous resistivity and its application to solar flares. Astrophys. J. 587, 450–457 (2003). doi:10.1086/368075
S. von Goeler, W. Stodiek, N. Sauthoff, Studies of internal disruptions and m=1 oscillations in tokamak discharges with soft-X-ray techniques. Phys. Rev. Lett. 33, 1201–1203 (1974). doi:10.1103/PhysRevLett.33.1201
R. Wang, et al., Asymmetry in the current sheet and secondary magnetic flux ropes during guide field magnetic reconnection. J. Geophys. Res. 117, 7223 (2012). doi:10.1029/2011JA017384
J. Wesson, Finite resistive instabilities of a sheet pinch. Nucl. Fusion 6, 130–134 (1966)
J.A. Wesson, Sawtooth reconnection. Nucl. Fusion 30, 2545–2549 (1990)
J. Wesson, Tokamaks, 3rd edn. (Oxford University Press, London, 2004). doi:10.1017/S0022377804003058
M. Yamada, R. Kulsrud, H. Ji, Magnetic reconnection. Rev. Mod. Phys. 82, 603–664 (2010). doi:10.1103/RevModPhys.82.603
P.H. Yoon, A.T.Y. Lui, Quasi-linear theory of anomalous resistivity. J. Geophys. Res. 111, 2203 (2006). doi:10.1029/2005JA011482
L. Zakharov, B. Rogers, S. Migliuolo, The theory of the early nonlinear stage of m=1 reconnection in tokamaks. Phys. Fluids B 5, 2498–2505 (1993). doi:10.1063/1.860735
L.E. Zakharov, On the nature of disruptive instability in a tokamak. JETP Lett. 31, 714 (1980)
L.M. Zelenyi, M.M. Kuznetsova, Large-scale instabilities of the plasma sheet driven by particle fluxes at the boundary of the magnetosphere. Sov. J. Plasma Phys. 10, 326–334 (1984)
L.M. Zelenyi, A.L. Taktakishvili, The influence of dissipative processes on the development of the tearing mode in current sheets. Sov. J. Plasma Phys. 7, 1064–1075 (1981)
L.M. Zelenyi, A.L. Taktakishvili, Spontaneous magnetic reconnection mechanisms in plasma. Astrophys. Space Sci. 134, 185–196 (1987). doi:10.1007/BF00636466
L.M. Zelenyi, M.I. Sitnov, H.V. Malova, A.S. Sharma, Thin and superthin ion current sheets. Quasi-adiabatic and nonadiabatic models. Nonlinear Process. Geophys. 7, 127–139 (2000)
L.M. Zelenyi, A.V. Artemyev, H.V. Malova, V.Y. Popov, Marginal stability of thin current sheets in the Earth’s magnetotail. J. Atmos. Sol.-Terr. Phys. 70, 325–333 (2008). doi:10.1016/j.jastp.2007.08.019
L.M. Zelenyi, A.V. Artemyev, K.V. Malova, A.A. Petrukovich, R. Nakamura, Metastability of current sheets. Phys. Usp. 53, 933–941 (2010). doi:10.3367/UFNe.0180.201009g.0973
L.M. Zelenyi, H.V. Malova, A.V. Artemyev, V.Y. Popov, A.A. Petrukovich, Thin current sheets in collisionless plasma: equilibrium structure, plasma instabilities, and particle acceleration. Plasma Phys. Rep. 37, 118–160 (2011). doi:10.1134/S1063780X1102005X
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Zelenyi, L., Artemyev, A. (2013). Mechanisms of Spontaneous Reconnection: From Magnetospheric to Fusion Plasma. In: Balogh, A., Bykov, A., Cargill, P., Dendy, R., Dudok de Wit, T., Raymond, J. (eds) Microphysics of Cosmic Plasmas. Space Sciences Series of ISSI, vol 47. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-7413-6_14
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