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Microphysics of Cosmic Plasmas: Hierarchies of Plasma Instabilities from MHD to Kinetic

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Microphysics of Cosmic Plasmas

Part of the book series: Space Sciences Series of ISSI ((SSSI,volume 47))

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Abstract

In this article, we discuss the idea of a hierarchy of instabilities that can rapidly couple the disparate scales of a turbulent plasma system. First, at the largest scale of the system, L, current carrying flux ropes can undergo a kink instability. Second, a kink instability in adjacent flux ropes can rapidly bring together bundles of magnetic flux and drive reconnection, introducing a new scale of the current sheet width, ℓ, perhaps several ion inertial lengths (δ i ) across. Finally, intense current sheets driven by reconnection electric fields can destabilize kinetic waves such as ion cyclotron waves as long as the drift speed of the electrons is large compared to the ion thermal speed, v D ≫v i . Instabilities such as these can couple MHD scales to kinetic scales, as small as the proton Larmor radius, ρ i .

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References

  • A. Al-Karkhy, P.K. Browning, G. Cunningham, S.J. Gee, M.G. Rusbridge, Observations of the magnetohydrodynamic dynamo effect in a spheromak plasma. Phys. Rev. Lett. 70, 1814–1817 (1993)

    ADS  Google Scholar 

  • T.D. Arber, A.W. Longbottom, C.L. Gerrard, A.M. Milne, A staggered grid, Lagrangian–Eulerian remap code for 3-D MHD simulations. J. Comput. Phys. 171, 151–181 (2001)

    ADS  MATH  MathSciNet  Google Scholar 

  • V. Archontis, F. Moreno-Insertis, K. Galsgaard, A.W. Hood, The three-dimensional interaction between emerging magnetic flux and a large-scale coronal field: reconnection, current sheets, and jets. Astrophys. J. 635, 1299–1318 (2005)

    ADS  Google Scholar 

  • M.R. Bareford, P.K. Browning, R.A.M. van der Linden, A nanoflare distribution generated by repeated relaxations triggered by kink instability. Astron. Astrophys. 521, 70 (2010)

    ADS  Google Scholar 

  • M.R. Bareford, P.K. Browning, R.A.M. van der Linden, The flare-energy distributions generated by kink-unstable ensembles of zero-net-current coronal loops. Sol. Phys. 273, 93–115 (2011)

    ADS  Google Scholar 

  • M.R. Bareford, A.W. Hood, P.K. Browning, Coronal heating by the partial relaxation of twisted loops. Astron. Astrophys. 550, 40 (2013)

    ADS  Google Scholar 

  • B. Basu, N.J. Grossbard, Ion-cyclotron instability in current-carrying Lorentzian (kappa) and Maxwellian plasmas with anisotropic temperatures: a comparative study. Phys. Plasmas 18, 092106 (2011)

    ADS  Google Scholar 

  • H. Baty, Magnetic topology during the reconnection process in a kinked coronal loop. Astron. Astrophys. 360, 345–350 (2000)

    ADS  Google Scholar 

  • H. Baty, J. Heyvaerts, Electric current concentration and kink instability in line-tied coronal loops. Astron. Astrophys. 308, 935–950 (1996)

    ADS  Google Scholar 

  • A.O. Benz, Flare observations. Living Rev. Sol. Phys. 5 (2008)

    Google Scholar 

  • W.F. Bergerson, C.B. Forest, G. Fiksel, D.A. Hannum, R. Kendrick, J.S. Sarff, S. Stambler, Onset and saturation of the kink instability in a current-carrying line-tied plasma. Phys. Rev. Lett. 96, 015004 (2006)

    ADS  Google Scholar 

  • I.B. Bernstein, Waves in a plasma in a magnetic field. Phys. Rev. 109, 10–21 (1958)

    ADS  MATH  MathSciNet  Google Scholar 

  • I.B. Bernstein, J.M. Greene, M.D. Kruskal, Exact nonlinear plasma oscillations. Phys. Rev. Lett. 108, 546–550 (1957)

    ADS  MATH  MathSciNet  Google Scholar 

  • A. Bhattacharjee, Y.-M. Huang, H. Yang, B. Rogers, Fast reconnection in high-lundquist-number plasmas due to the plasmoid instability. Phys. Plasmas 16, 112102 (2009)

    ADS  Google Scholar 

  • J. Birn, E.R. Priest, Reconnection of Magnetic Fields (Cambridge University Press, Cambridge, 2007)

    Google Scholar 

  • D. Biskamp, Magnetic Reconnection in Plasmas (Cambridge University Press, Cambridge, 2005)

    Google Scholar 

  • G.J.J. Botha, T.D. Arber, A.W. Hood, Thermal conduction effects on the kink instability in coronal loops. Astron. Astrophys. 525, 96 (2011)

    ADS  Google Scholar 

  • D. Brennan, P.K. Browning, R.A.M. van der Linden, A.W. Hood, S. Woodruff, Stability studies and the origin of the n=1 mode in the SPHEX spheromak experiment. Phys. Plasmas 6, 4248–4259 (1999)

    ADS  Google Scholar 

  • D.P. Brennan, P.K. Browning, R.A.M. van der Linden, A two-dimensional magnetohydrodynamic stability model for helicity-injected devices with open flux. Phys. Plasmas 9, 3526–3535 (2002)

    ADS  Google Scholar 

  • D.P. Brennan, P.K. Browning, J. Gates, R.A.M. van der Linden, Helicity-injected current drive and open flux instabilities in spherical tokamaks. Plasma Phys. Control. Fusion 51, 045004 (2009)

    ADS  Google Scholar 

  • M.R. Brown, Experimental studies of magnetic reconnection. Phys. Plasmas 6, 1717–1724 (1999)

    ADS  Google Scholar 

  • P.K. Browning, Mechanisms of solar coronal heating. Plasma Phys. Control. Fusion 33, 539–571 (1991)

    ADS  Google Scholar 

  • P.K. Browning, R.A.M. van der Linden, Solar coronal heating by relaxation events. Astron. Astrophys. 400, 355–367 (2003)

    ADS  Google Scholar 

  • P.K. Browning, G. Cunningham, R. Duck, S.J. Gee, K.J. Gibson, D.A. Kitson, R. Martin, M.G. Rusbridge, Injection and sustainment of plasma in a preexisting toroidal field using a coaxial helicity source. Phys. Rev. Lett. 68, 1722–1725 (1992)

    ADS  Google Scholar 

  • P.K. Browning, C. Gerrard, A.W. Hood, R. Kevis, R.A.M. van der Linden, Heating the corona by nanoflares: simulations of energy release triggered by a kink instability. Astron. Astrophys. 485, 837–848 (2008)

    ADS  MATH  Google Scholar 

  • O. Buneman, Instability, turbulence and conductivity in current-carrying plasma. Phys. Rev. Lett. 1, 8–9 (1959)

    ADS  Google Scholar 

  • B.I. Cohen, C.A. Romero-Talamás, D.D. Ryutov, E.B. Hooper, L.L. Lodestro, H.S. McLean, T.L. Stewart, R.D. Wood, The role of the n=1 column mode in spheromak formation. Phys. Plasmas 16, 042501 (2009)

    ADS  Google Scholar 

  • I.J.D. Craig, P.G. Watson, Flare-like energy release by flux pile-up reconnection. Sol. Phys. 191, 359–379 (2000)

    ADS  Google Scholar 

  • I.J.D. Craig, R.B. Fabling, P.G. Watson, The power output of spine and fan magnetic reconnection solutions. Astrophys. J. 485, 383 (1997)

    ADS  Google Scholar 

  • W. Daughton, V. Roytershteyn, H. Karimabadi, L. Yin, B.J. Albright, B. Bergen, K.J. Bowers, Role of electron physics in the development of turbulent magnetic reconnection in collisionless plasmas. Nat. Phys. 7, 539–542 (2011)

    Google Scholar 

  • J.M. Dawson, Particle simulation of plasmas. Rev. Mod. Phys. 55, 403–447 (1983)

    ADS  Google Scholar 

  • P. Demoulin, J.C. Henoux, E.R. Priest, C.H. Mandrini, Quasi-separatrix layers in solar flares. I. Method. Astron. Astrophys. 308, 643–655 (1996)

    ADS  Google Scholar 

  • M.E. Dieckmann, B. Eliasson, A. Stathopoulos, A. Ynnerman, Connecting shock velocities to electron-injection mechanisms. Phys. Rev. Lett. 92, 065006 (2004a)

    ADS  Google Scholar 

  • M.E. Dieckmann, A. Ynnerman, S.C. Chapman, G. Rowlands, N. Andersson, Simulating thermal noise. Phys. Scr. 69, 456 (2004b)

    ADS  Google Scholar 

  • M.E. Dieckmann, A. Bret, G. Sarri, E. Perez Alvaro, I. Kourakis, M. Borghesi, Particle simulation study of electron heating by counter-streaming ion beams ahead of supernova remnant shocks. Plasma Phys. Control. Fusion 54, 085015 (2012)

    ADS  Google Scholar 

  • J.F. Drake, M. Swisdak, C. Cattell, M.A. Shay, B.N. Rogers, A. Zeiler, Formation of electron holes and particle energization during magnetic reconnection. Science 299, 873–877 (2003)

    ADS  Google Scholar 

  • W.E. Drummond, M.N. Rosenbluth, Anomalous diffusion arising from microinstabilities in a plasma. Phys. Fluids 5, 1507–1513 (1962)

    ADS  MATH  Google Scholar 

  • R.C. Duck, P.K. Browning, G. Cunningham, S.J. Gee, A. al-Karkhy, R. Martin, M.G. Rusbridge, Structure of the n=1 mode responsible for relaxation and current drive during sustainment of the SPHEX spheromak. Plasma Phys. Control. Fusion 39, 715–736 (1997)

    ADS  Google Scholar 

  • R.E. Ergun, C.W. Carlson, J.P. McFadden, F.S. Mozer, L. Muschietti, I. Roth, R.J. Strangeway, Debye-scale plasma structures associated with magnetic-field-aligned electric fields. Phys. Rev. Lett. 81, 826–829 (1998)

    ADS  Google Scholar 

  • D.W. Forslund, C.R. Shonk, Numerical simulation of electrostatic counterstreaming instabilities in ion beams. Phys. Rev. Lett. 25, 281–284 (1970)

    ADS  Google Scholar 

  • I. Furno, T. Intrator, E. Torbert, C. Carey, M.D. Cash, J.K. Campbell, W.J. Fienup, C.A. Werley, G.A. Wurden, G. Fiksel, Reconnection scaling experiment: a new device for three-dimensional magnetic reconnection studies. Rev. Sci. Instrum. 74, 2324–2331 (2003)

    ADS  Google Scholar 

  • I. Furno, T.P. Intrator, E.W. Hemsing, S.C. Hsu, S. Abbate, Coalescence of two magnetic flux ropes via collisional magnetic reconnection. Phys. Plasmas 12, 055702 (2005)

    ADS  Google Scholar 

  • I. Furno, T.P. Intrator, D.D. Ryutov, S. Abbate, T. Madziwa-Nussinov, A. Light, L. Dorf, G. Lapenta, Current-driven rotating-kink mode in a plasma column with a non-line-tied free end. Phys. Rev. Lett. 97, 015002 (2006)

    ADS  Google Scholar 

  • H.P. Furth, J. Killeen, M.N. Rosenbluth, Finite-resistivity instabilities of a sheet pinch. Phys. Fluids 6, 459–484 (1963)

    ADS  Google Scholar 

  • C.G. Gimblett, R.J. Hastie, P. Helander, Model for current-driven edge-localized modes. Phys. Rev. Lett. 96, 035006 (2006a)

    ADS  Google Scholar 

  • C.G. Gimblett, R.J. Hastie, P. Helander, The role of edge current-driven modes in ELM activity. Plasma Phys. Control. Fusion 48, 1531–1550 (2006b)

    ADS  Google Scholar 

  • T. Gray, M.R. Brown, D. Dandurand, Observation of a relaxed plasma state in a quasi-infinite cylinder. Phys. Rev. Lett. 110, (2013)

    Google Scholar 

  • T.S. Hahm, R.M. Kulsrud, Forced magnetic reconnection. Phys. Fluids 28, 2412–2418 (1985)

    ADS  MATH  Google Scholar 

  • E.W. Hemsing, I. Furno, T.P. Intrator, Fast camera images of flux ropes during plasma relaxation. IEEE Trans. Plasma Sci. 33, 448–449 (2005)

    ADS  Google Scholar 

  • H.W. Hendel, M. Yamada, S.W. Seiler, H. Ikezi, Ion-beam-driven resonant ion-cyclotron instability. Phys. Rev. Lett. 36, 319–322 (1976)

    ADS  Google Scholar 

  • J. Heyvaerts, E.R. Priest, Coronal heating by reconnection in DC current systems—a theory based on Taylor’s hypothesis. Astron. Astrophys. 137, 63–78 (1984)

    ADS  Google Scholar 

  • A.W. Hood, E.R. Priest, Kink instability of solar coronal loops as the cause of solar flares. Sol. Phys. 64, 303–321 (1979)

    ADS  Google Scholar 

  • A.W. Hood, P.K. Browning, R.A.M. van der Linden, Coronal heating by magnetic reconnection in loops with zero net current. Astron. Astrophys. 506, 913–925 (2009)

    ADS  Google Scholar 

  • E.B. Hooper, L.D. Pearlstein, R.H. Bulmer, MHD equilibria in a spheromak sustained by coaxial helicity injection. Nucl. Fusion 39, 863–871 (1999)

    ADS  Google Scholar 

  • S.C. Hsu, P.M. Bellan, Experimental identification of the kink instability as a poloidal flux amplification mechanism for coaxial gun spheromak formation. Phys. Rev. Lett. 90, 215002 (2003)

    ADS  Google Scholar 

  • T.P. Intrator, X. Sun, L. Dorf, G. Lapenta, I. Furno, Experimental onset threshold and magnetic pressure pileup for 3D reconnection. Nat. Phys. 5, 521–526 (2009)

    Google Scholar 

  • S. Ishiguro, T. Sato, H. Takamaru, Complexity Simulation Group, V-shaped dc potential structure caused by current-driven electrostatic ion-cyclotron instability. Phys. Rev. Lett. 78, 4761–4764 (1997b)

    ADS  Google Scholar 

  • S. Ishiguro, T. Sato, H. Takamaru, K. Watanabe, Complexity Simulation Group, Formation of wave-front pattern accompanied by current-driven electrostatic ion-cyclotron instabilities. Phys. Plasmas 4, 2886–2892 (1997a). doi:10.1063/1.872613

    ADS  Google Scholar 

  • O. Ishihara, A. Hirose, A.B. Langdon, Nonlinear saturation of the Buneman instability. Phys. Rev. Lett. 44, 1404–1407 (1980)

    ADS  Google Scholar 

  • M. Karlický, B. Kliem, Reconnection of a kinking flux rope triggering the ejection of a microwave and hard X-ray source I. Observations and interpretation. Sol. Phys. 266, 71–89 (2010)

    ADS  Google Scholar 

  • J.M. Kindel, C.F. Kennel, Topside current instabilities. J. Geophys. Res. 76, 3055 (1971)

    ADS  Google Scholar 

  • J.A. Klimchuk, On solving the coronal heating problem. Sol. Phys. 234, 41–77 (2006)

    ADS  Google Scholar 

  • S.O. Knox, C.W. Barnes, G.J. Marklin, T.R. Jarboe, I. Henins, H.W. Hoida, B.L. Wright, Observations of spheromak equilibria which differ from the minimum-energy state and have internal kink distortions. Phys. Rev. Lett. 56, 842–845 (1986)

    ADS  Google Scholar 

  • G. Lapenta, L. Bettarini, Spontaneous transition to a fast 3D turbulent reconnection regime. Europhys. Lett. 93, 65001 (2011)

    ADS  Google Scholar 

  • G. Lapenta, S. Markidis, A. Divin, M. Goldman, D. Newman, Scales of guide field reconnection at the hydrogen mass ratio. Phys. Plasmas 17, 082106 (2010)

    ADS  Google Scholar 

  • K.D. Leka, R.C. Canfield, A.N. McClymont, L. van Driel-Gesztelyi, Evidence for current-carrying emerging flux. Astrophys. J. 462, 547 (1996)

    ADS  Google Scholar 

  • Y. Liang, C.G. Gimblett, P.K. Browning, P. Devoy, H.R. Koslowski, S. Jachmich, Y. Sun, C. Wiegmann, Multiresonance effect in type-I edge-localized mode control with low n fields on JET. Phys. Rev. Lett. 105, 065001 (2010)

    ADS  Google Scholar 

  • Y. Liang, C.G. Gimblett, P.K. Browning, P. Devoy, A. Alfier, G. Calabrò, C. Giroud, D. Harting, H.R. Koslowski, S. Jachmich, J. Pearson, Y. Sun, C. Wiegmann, T. Zhang, JET-EFDA contributors, Observations of multi-resonance effect in ELM control with magnetic perturbation fields on the JET tokamak. Nucl. Fusion 51, 073001 (2011)

    ADS  Google Scholar 

  • M.G. Linton, R.B. Dahlburg, G.H. Fisher, D.W. Longcope, Nonlinear evolution of kink-unstable magnetic flux tubes and solar delta-spot active regions. Astrophys. J. 507, 404–416 (1998)

    ADS  Google Scholar 

  • R. Lionello, M. Velli, G. Einaudi, Z. Mikic, Nonlinear magnetohydrodynamic evolution of line-tied coronal loops. Astrophys. J. 494, 840 (1998)

    ADS  Google Scholar 

  • R. Liu, D. Alexander, Hard X-ray emission in kinking filaments. Astrophys. J. 697, 999–1009 (2009)

    ADS  Google Scholar 

  • D.W. Longcope, Separator current sheets: generic features in minimum-energy magnetic fields subject to flux constraints. Phys. Plasmas 8, 5277–5290 (2001)

    ADS  Google Scholar 

  • N.F. Loureiro, A.A. Schekochihin, S.C. Cowley, Instability of current sheets and formation of plasmoid chains. Phys. Plasmas 14, 100703 (2007)

    ADS  Google Scholar 

  • F. Moreno-Insertis, T. Emonet, The rise of twisted magnetic tubes in a stratified medium. Astrophys. J. 472, 53 (1996)

    ADS  Google Scholar 

  • A.L. Moser, P.M. Bellan, Magnetic reconnection from a multiscale instability cascade. Nature 482, 379–381 (2012)

    ADS  Google Scholar 

  • E.N. Parker, Nanoflares and the solar X-ray corona. Astrophys. J. 330, 474–479 (1988)

    ADS  Google Scholar 

  • C.E. Parnell, A.L. Haynes, K. Galsgaard, Structure of magnetic separators and separator reconnection. J. Geophys. Res. 115, 2102 (2010)

    Google Scholar 

  • D.I. Pontin, Three-dimensional magnetic reconnection regimes: a review. Adv. Space Res. 47, 1508–1522 (2011)

    ADS  Google Scholar 

  • D.I. Pontin, A. Bhattacharjee, K. Galsgaard, Current sheet formation and nonideal behavior at three-dimensional magnetic null points. Phys. Plasmas 14, 052106 (2007)

    ADS  Google Scholar 

  • E. Priest, T. Forbes, Magnetic Reconnection (Cambridge University Press, Cambridge, 2000)

    MATH  Google Scholar 

  • E.R. Priest, D.I. Pontin, Three-dimensional null point reconnection regimes. Phys. Plasmas 16, 122101 (2009)

    ADS  Google Scholar 

  • E.R. Priest, V.S. Titov, Magnetic reconnection at three-dimensional null points. Proc. R. Soc. Lond. Ser. A, Math. Phys. Sci. 354, 2951–2992 (1996)

    ADS  MATH  MathSciNet  Google Scholar 

  • J.J. Rasmussen, R.W. Schrittwieser, On the current-driven ion-cyclotron instability—a review. IEEE Trans. Plasma Sci. 19, 457–501 (1991)

    ADS  Google Scholar 

  • K.V. Roberts, H.L. Berk, Nonlinear evolution of a two-stream instability. Phys. Rev. Lett. 19, 297–300 (1967)

    ADS  Google Scholar 

  • R. Samtaney, N.F. Loureiro, D.A. Uzdensky, A.A. Schekochihin, S.C. Cowley, Formation of plasmoid chains in magnetic reconnection. Phys. Rev. Lett. 103, 105004 (2009)

    ADS  Google Scholar 

  • J.C. Santos, J. Büchner, A. Otto, Development of electric currents in a magnetic field configuration containing a magnetic null point. Astron. Astrophys. 525, 3 (2011)

    ADS  Google Scholar 

  • G. Sarri, M.E. Dieckmann, C.R.D. Brown, C.A. Cecchetti, D.J. Hoarty, S.F. James, R. Jung, I. Kourakis, H. Schamel, O. Willi, M. Borghesi, Observation and characterization of laser-driven phase space electron holes. Phys. Plasmas 17, 010701 (2010)

    ADS  Google Scholar 

  • H. Schamel, Electron holes, ion holes and double-layers phase-space structures in theory and experiment. Phys. Rep. 140, 161–191 (1986)

    ADS  Google Scholar 

  • H. Schamel, S. Bujarbarua, Solitary plasma hole via ion-vortex distribution. Phys. Fluids 23, 2498 (1980)

    ADS  Google Scholar 

  • K. Schindler, M. Hesse, J. Birn, General magnetic reconnection, parallel electric fields, and helicity. J. Geophys. Res. 93, 5547–5557 (1988)

    ADS  Google Scholar 

  • C.E. Seyler, J. Providakes, Particle and fluid simulations of resistive current-driven electrostatic ion cyclotron waves. Phys. Fluids 30, 3113–3128 (1987)

    ADS  MATH  Google Scholar 

  • C.E. Seyler, J.-E. Wahlund, Theory of nearly perpendicular plasma waves and comparison to Freja satellite observations. J. Geophys. Res. 101, 21795–21813 (1996)

    ADS  Google Scholar 

  • A.K. Srivastava, T.V. Zaqarashvili, P. Kumar, M.L. Khodachenko, Observation of kink instability during small B5.0 solar flare on 2007 June 4. Astrophys. J. 715, 292–299 (2010)

    ADS  Google Scholar 

  • B.W. Stallard, E.B. Hooper, S. Woodruff, R.H. Bulmer, D.N. Hill, H.S. McLean, R.D. Wood, Magnetic helicity balance in the sustained spheromak plasma experiment. Phys. Plasmas 10, 2912–2924 (2003)

    ADS  Google Scholar 

  • X. Sun, T. Intrator, L. Dorf, I. Furno, G. Lapenta, Transition of mhd kink stability properties between line-tied and non line tied boundary conditions. Phys. Rev. Lett. 100, 205004 (2008)

    ADS  Google Scholar 

  • X. Sun, T.P. Intrator, L. Dorf, J. Sears, I. Furno, G. Lapenta, Flux rope dynamics: experimental study of bouncing and merging. Phys. Rev. Lett. 105, 255001 (2010)

    ADS  Google Scholar 

  • J.B. Taylor, Relaxation of toroidal plasma and generation of reverse magnetic fields. Phys. Rev. Lett. 33, 1139–1141 (1974)

    ADS  Google Scholar 

  • J.B. Taylor, Relaxation and magnetic reconnection in plasmas. Rev. Mod. Phys. 58, 741–763 (1986)

    ADS  Google Scholar 

  • T. Török, B. Kliem, Confined and ejective eruptions of kink-unstable flux ropes. Astrophys. J. 630, 97–100 (2005)

    Google Scholar 

  • T. Török, B. Kliem, V.S. Titov, Ideal kink instability of a magnetic loop equilibrium. Astron. Astrophys. 413, 27–30 (2004)

    Google Scholar 

  • G.E. Vekstein, R. Jain, Energy release and plasma heating by forced magnetic reconnection. Phys. Plasmas 5, 1506–1513 (1998)

    ADS  Google Scholar 

  • M. Velli, R. Lionello, G. Einaudi, Kink modes and current sheets in coronal loops. Sol. Phys. 172, 257–266 (1997)

    ADS  Google Scholar 

  • Z. Wang, C.W. Barnes, G.A. Wurden, D.N. Hill, E.B. Hooper, H.S. McLean, R.D. Wood, S. Woodruff, Large-amplitude electron density and H fluctuations in the sustained spheromak physics experiment. Nucl. Fusion 42, 643–652 (2002)

    ADS  Google Scholar 

  • E.S. Weibel, Ion cyclotron instability. Phys. Fluids 13, 3003–3006 (1970)

    ADS  Google Scholar 

  • D.M. Willett, P.K. Browning, S. Woodruff, K.J. Gibson, The internal magnetic structure and current drive in the SPHEX spheromak. Plasma Phys. Control. Fusion 41, 595–612 (1999)

    ADS  Google Scholar 

  • P.H. Yoon, R. Gaelzer, T. Umeda, Y. Omura, H. Matsumoto, Harmonic Langmuir waves. I. Nonlinear dispersion relation. Phys. Plasmas 10, 364–372 (2003)

    ADS  MathSciNet  Google Scholar 

  • E.G. Zweibel, M. Yamada, Magnetic reconnection in astrophysical and laboratory plasmas. Astron. Astrophys. Rev. 47, 291–332 (2009)

    ADS  Google Scholar 

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Authors and Affiliations

  1. Dept. of Physics and Astronomy, Swarthmore Coll., Swarthmore, PA, 19081, USA

    M. R. Brown

  2. Univ. of Manchester, Jodrell Bank Ctr. Astrophys., Manchester, M13 9PL, UK

    P. K. Browning

  3. Dept. of Science and Technology (ITN), Linkoping University, Campus Norrkoping, 60174, Norrkoping, Sweden

    M. E. Dieckmann

  4. Ecole Polytech Fed Lausanne, CRPP, Ctr Rech Phys Plasmas, Lausanne, Switzerland

    I. Furno

  5. Los Alamos Natl. Lab, Los Alamos, NM, 87545, USA

    T. P. Intrator

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  1. M. R. Brown
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  2. P. K. Browning
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  3. M. E. Dieckmann
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  4. I. Furno
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  5. T. P. Intrator
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Correspondence to M. R. Brown .

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Editors and Affiliations

  1. Imperial College London, London, UK

    André Balogh  & Peter Cargill  & 

  2. Russian Academy of Sciences, St. Petersburg, Russia

    Andrei Bykov

  3. Euratom/UKAEA Fusion Association, Abingdon, UK

    Richard Dendy

  4. LPC2E/CNRS-University of Orleans, Orleans Cedex 2, France

    Thierry Dudok de Wit

  5. Harvard-Smithsonian Center for Astrophysics, Cambridge, MA, USA

    John Raymond

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Brown, M.R., Browning, P.K., Dieckmann, M.E., Furno, I., Intrator, T.P. (2013). Microphysics of Cosmic Plasmas: Hierarchies of Plasma Instabilities from MHD to Kinetic. 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_11

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