Skip to main content

Ionized Plasma and Neutral Gas Coupling in the Sun’s Chromosphere and Earth’s Ionosphere/Thermosphere

Abstract

We review physical processes of ionized plasma and neutral gas coupling in the weakly ionized, stratified, electromagnetically-permeated regions of the Sun’s chromosphere and Earth’s ionosphere/thermosphere. Using representative models for each environment we derive fundamental descriptions of the coupling of the constituent parts to each other and to the electric and magnetic fields, and we examine the variation in magnetization of the components. Using these descriptions we compare related phenomena in the two environments, and discuss electric currents, energy transfer and dissipation. We present examples of physical processes that occur in both atmospheres, the descriptions of which have previously been conducted in contrasting paradigms, that serve as examples of how the chromospheric and ionospheric communities can further collaborate. We also suggest future collaborative studies that will help improve our understanding of these two different atmospheres, which while sharing many similarities, also exhibit large disparities in key quantities.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

References

  • W.P. Abbett, The magnetic connection between the convection zone and corona in the quiet Sun. Astrophys. J. 665, 1469–1488 (2007). doi:10.1086/519788

    ADS  Google Scholar 

  • H. Alfvén, C.-G. Fälthammar, Cosmical Electrodynamics (Oxford University Press, Clarendon, 1963)

    MATH  Google Scholar 

  • T.D. Arber, G.J.J. Botha, C.S. Brady, Effect of solar chromospheric neutrals on equilibrium field structures. Astrophys. J. 705, 1183–1188 (2009). doi:10.1088/0004-637X/705/2/1183

    ADS  Google Scholar 

  • T.D. Arber, M. Haynes, J.E. Leake, Emergence of a flux tube through a partially ionized solar atmosphere. Astrophys. J. 666, 541–546 (2007). doi:10.1086/520046

    ADS  Google Scholar 

  • H.C. Aveiro, J.D. Huba, Equatorial spread F studies using SAMI3 with two-dimensional and three-dimensional electrostatics. Ann. Geophys. 31, 2157-2162 (2013). doi:10.5194/angeo-31-2157-2013

    ADS  Google Scholar 

  • H.C. Aveiro, D.L. Hysell, Three-dimensional numerical simulation of equatorial F region plasma irregularities with bottomside shear flow. J. Geophys. Res. 115, 11321 (2010). doi:10.1029/2010JA015602

    Google Scholar 

  • H.C. Aveiro, D.L. Hysell, Implications of the equipotential field line approximation for equatorial spread F analysis. Geophys. Res. Lett. 39, 11106 (2012). doi:10.1029/2012GL051971

    ADS  Google Scholar 

  • E.H. Avrett, R. Loeser, Models of the solar chromosphere and transition region from SUMER and HRTS observations: formation of the extreme-ultraviolet spectrum of hydrogen, carbon, and oxygen. Astrophys. J. Suppl. Ser. 175, 229–276 (2008). doi:10.1086/523671

    ADS  Google Scholar 

  • R. Balescu, Transport Processes in Plasmas, 1 (1988).

    Google Scholar 

  • B. Basu, Characteristics of electromagnetic Rayleigh–Taylor modes in nighttime equatorial plasma. J. Geophys. Res. 110, 2303 (2005). doi:10.1029/2004JA010659

    Google Scholar 

  • T.E. Berger, G. Slater, N. Hurlburt, R. Shine, T. Tarbell, A. Title, B.W. Lites, T.J. Okamoto, K. Ichimoto, Y. Katsukawa, T. Magara, Y. Suematsu, T. Shimizu, Quiescent prominence dynamics observed with the hinode solar optical telescope. I. Turbulent upflow plumes. Astrophys. J. 716, 1288–1307 (2010). doi:10.1088/0004-637X/716/2/1288

    ADS  Google Scholar 

  • T. Berger, P. Testa, A. Hillier, P. Boerner, B.C. Low, K. Shibata, C. Schrijver, T. Tarbell, A. Title, Magneto-thermal convection in solar prominences. Nature 472, 197–200 (2011). doi:10.1038/nature09925

    ADS  Google Scholar 

  • L. Biermann, Zur Deutung der chromosphärischen Turbulenz und des Exzesses der UV-Strahlung der Sonne. Naturwissenschaften 33, 118–119 (1946). doi:10.1007/BF00738265

    ADS  Google Scholar 

  • S.I. Braginskii, Transport processes in a plasma. Rev. Plasma Phys. 1, 205 (1965).

    ADS  Google Scholar 

  • L. Brower, J.P. Thayer, J.P. St. Maurice, Frictionally heated electrons in the high-latitude D region. J. Geophys. Res. 114, A12302 (2009). doi:10.1029/2009JA014421

    ADS  Google Scholar 

  • D. Brunt, The period of simple vertical oscillations in the atmosphere. Q. J. R. Meteorol. Soc. 53, 30–32 (1927)

    ADS  Google Scholar 

  • O. Buneman, Excitation of field-aligned sound waves by electron streams. Phys. Rev. Lett. 10, 285–287 (1963). doi:10.1103/PhysRevLett.10.285

    ADS  Google Scholar 

  • M. Carlsson, J. Leenaarts, Approximations for radiative cooling and heating in the solar chromosphere. Astron. Astrophys. 539, A39 (2012). doi:10.1051/0004-6361/201118366

    ADS  Google Scholar 

  • F. Cattaneo, On the origin of magnetic fields in the quiet photosphere. Astrophys. J. 515, L39–L42 (1999).

    ADS  Google Scholar 

  • F. Cattaneo, D Hughes, Solar dynamo theory: a new look at the origin of small-scale magnetic fields. Astron. Geophys. 42, 3.18–3.22 (2001).

    Google Scholar 

  • F. Cattaneo, T Emonet, N Weiss, On the interaction between convection and magnetic fields. Astrophys. J. 588, 1183–1198 (2003).

    ADS  Google Scholar 

  • P. Charbonneau, Dynamo models of the solar cycle. Living Rev. Sol. Phys. 7, 3 (2010). doi:10.12942/lrsp-2010-3

    ADS  Google Scholar 

  • J.R. Conrad, R.W. Schunk, Diffusion and heat flow equations with allowance for large temperature differences between interacting species. J. Geophys. Res. 84(A3), 811–822 (1979). doi:10.1029/JA084iA03p00811

    ADS  Google Scholar 

  • T.G. Cowling, The dissipation of magnetic energy in an ionized gas. Mon. Not. R. Astron. Soc. 116, 114–124 (1956)

    MATH  MathSciNet  ADS  Google Scholar 

  • S.R. Cranmer, S.R. van Ballegooijen, On the generation, propagation, and reflection of Alfvén waves from the solar photosphere to the distant heliospher. Mon. Not. R. Astron. Soc. 156, 265–293 (2005)

    ADS  Google Scholar 

  • R.B. Dahlburg, J.A. Klimchuk, S.K. Antiochos, Coronal energy release via ideal three-dimensional instability. Adv. Space Res. 32, 1029–1034 (2003). doi:10.1016/S0273-1177(03)00305-3

    ADS  Google Scholar 

  • R.B. Dahlburg, J.A. Klimchuk, S.K. Antiochos, An explanation for the “switch-on” nature of magnetic energy release and its application to coronal heating. Astrophys. J. 622, 1191 (2005)

    ADS  Google Scholar 

  • B. De Pontieu, Numerical simulations of spicules driven by weakly-damped Alfvén waves. I. WKB approach. Astron. Astrophys. 347, 696–710 (1999)

    ADS  Google Scholar 

  • B. De Pontieu, S.W. McIntosh, M. Carlsson, V.H. Hansteen, T.D. Tarbell, C.J. Schrijver, A.M. Title, R.A. Shine, S. Tsuneta, Y. Katsukawa, K. Ichimoto, Y. Suematsu, T. Shimizu, S. Nagata, Chromospheric Alfvénic waves strong enough to power the solar wind. Science 318, 1574 (2007a). doi:10.1126/science.1151747

    ADS  Google Scholar 

  • B. De Pontieu, S.W. McIntosh, M. Carlsson, V.H. Hansteen, C.J. Schrijver, T.D. Tarbell, A. Title, SOT Team, Observational evidence for the ubiquity of strong Alfvén waves in the magnetized chromosphere, in American Astronomical Society Meeting Abstracts #210. Bull. Am. Astron. Soc., vol. 39, 2007b, p. 219

    Google Scholar 

  • B. De Pontieu, A.M. Title, J. Lemen, J. Wuelser, T.D. Tarbell, C.J. Schrijver, L. Golub, C. Kankelborg, M. Carlsson, V.H. Hansteen, S. Worden, IRIS team, The Interface Region Imaging Spectrograph (IRIS), in AAS/Solar Physics Division Meeting. AAS/Solar Physics Division Meeting, vol. 44, 2013, p. 3

    Google Scholar 

  • Y.S. Dimant, R.N. Sudan, Kinetic theory of the Farley–Buneman instability in the E region of the ionosphere. J. Geophys. Res. 100, 14605–14624 (1995). doi:10.1029/95JA00794

    ADS  Google Scholar 

  • Y.S. Dimant, M.M. Oppenheim, Magnetosphere-ionosphere coupling through E region turbulence: 1. Energy budget. J. Geophys. Res. 116, 9303 (2011). doi:10.1029/2011JA016648

    Google Scholar 

  • D.P. Drob, D. Broutman, M.A. Hedlin, N.W. Winslow, R.G. Gibson, A method for specifying atmospheric gravity wavefields for long-range infrasound propagation calculations. J. Geophys. Res., Atmos. 118, 3933–3943 (2013). doi:10.1029/2012JD018077

    ADS  Google Scholar 

  • J.K. Edmondson, B.J. Lynch, C.R. DeVore, M. Velli, Reconnection-Driven Alfvén (RDA) Waves in the Solar Corona. AGU Fall Meeting Abstracts, 1990 (2011)

  • R.E. Erlandson, L.J. Zanetti, M.H. Acuña, A.I. Eriksson, L. Eliasson, M.H. Boehm, L.G. Blomberg, Freja observations of electromagnetic ion cyclotron ELF waves and transverse oxygen ion acceleration on auroral field lines. Geophys. Res. Lett. 21, 1855–1858 (1994). doi:10.1029/94GL01363

    ADS  Google Scholar 

  • D.T. Farley Jr., A plasma instability resulting in field-aligned irregularities in the ionosphere. J. Geophys. Res. 68, 6083 (1963)

    MATH  ADS  Google Scholar 

  • J.M. Fontenla, Chromospheric plasma and the Farley–Buneman instability in solar magnetic regions. Astron. Astrophys. 442, 1099–1103 (2005). doi:10.1051/0004-6361:20053669

    ADS  Google Scholar 

  • J.M. Fontenla, E.H. Avrett, R. Loeser, Energy balance in the solar transition region. III—Helium emission in hydrostatic, constant-abundance models with diffusion. Astrophys. J. 406, 319–345 (1993). doi:10.1086/172443

    ADS  Google Scholar 

  • J.M. Fontenla, W.K. Peterson, J. Harder, Chromospheric heating by the Farley–Buneman instability. Astron. Astrophys. 480, 839–846 (2008). doi:10.1051/0004-6361:20078517

    ADS  Google Scholar 

  • J.M. Fontenla, E. Avrett, G. Thuillier, J. Harder, Semiempirical models of the solar atmosphere. I. The quiet- and active Sun photosphere at moderate resolution. Astrophys. J. 639, 441–458 (2006). doi:10.1086/499345

    ADS  Google Scholar 

  • A. Fossum, M. Carlsson, Are high frequency acoustic waves sufficient to heat the solar chromosphere? in The Dynamic Sun: Challenges for Theory and Observations. ESA Special Publication, vol. 600, 2005a

    Google Scholar 

  • A. Fossum, M. Carlsson, High-frequency acoustic waves are not sufficient to heat the solar chromosphere. Nature 435, 919–921 (2005b). doi:10.1038/nature03695

    ADS  Google Scholar 

  • A. Fossum, M. Carlsson, Determination of the acoustic wave flux in the lower solar chromosphere. Astrophys. J. 646, 579–592 (2006). doi:10.1086/504887

    ADS  Google Scholar 

  • R. Fujii, S. Nozawa, S.C. Buchert, A. Brekke, Statistical characteristics of electromagnetic energy transfer between the magnetosphere, the ionosphere, and the thermosphere. J. Geophys. Res. 104, 2357–2366 (1999). doi:10.1029/98JA02750

    ADS  Google Scholar 

  • T. Fuller-Rowell, C.J. Schrijver, On the ionosphere and chromosphere, in Heliophysics I: Plasma Physics of the Local Cosmos, ed. by C. J. Schrijver, G. L. Siscoe (Cambridge University Press, New York, 2009), pp. 324–359

    Google Scholar 

  • T.J. Fuller-Rowell, D. Rees, S. Quegan, G.J. Bailey, R.J. Moffett, The effect of realistic conductivities on the high-latitude neutral thermospheric circulation. Planet. Space Sci. 32, 469–480 (1984). doi:10.1016/0032-0633(84)90126-0

    ADS  Google Scholar 

  • T.J. Fuller-Rowell, D. Rees, S. Quegan, R.J. Moffett, M.V. Codrescu, A Coupled Thermosphere–Ionosphere Model (CTIM), STEP Handbook of Ionospheric Models 1996, pp. 217–238

  • H. Gilbert, G. Kilper, D. Alexander, Observational evidence supporting cross-field diffusion of neutral material in solar filaments. Astrophys. J. 671, 978–989 (2007). doi:10.1086/522884

    ADS  Google Scholar 

  • H.R. Gilbert, V.H. Hansteen, T.E. Holzer, Neutral atom diffusion in a partially ionized prominence plasma. Astrophys. J. 577, 464–474 (2002). doi:10.1086/342165

    ADS  Google Scholar 

  • G. Gogoberidze, Y. Voitenko, S. Poedts, M. Goossens, Farley–Buneman instability in the solar chromosphere. Astrophys. J. Lett. 706, 12–16 (2009). doi:10.1088/0004-637X/706/1/L12

    ADS  Google Scholar 

  • M.L. Goodman, On the mechanism of chromospheric network heating and the condition for its onset in the Sun and other solar-type stars. Astrophys. J. 533, 501–522 (2000). doi:10.1086/308635

    ADS  Google Scholar 

  • M.L. Goodman, The necessity of using realistic descriptions of transport processes in modeling the solar atmosphere, and the importance of understanding chromospheric heating*. Space Sci. Rev. 95, 70 (2001).

    ADS  Google Scholar 

  • M.L. Goodman, On the efficiency of plasma heating by Pedersen current dissipation from the photosphere to the lower corona. Astron. Astrophys. 416, 1159–1178 (2004). doi:10.1051/0004-6361:20031719

    ADS  Google Scholar 

  • M.L. Goodman, On the creation of the chromospheres of solar type stars. Astron. Astrophys. 424, 691–712 (2004). doi:10.1051/0004-6361:20040310

    MATH  ADS  Google Scholar 

  • M.L. Goodman, Conditions for photospherically driven Alfvénic oscillations to heat the solar chromosphere by Pedersen current dissipation. Astrophys. J. 735, 45 (2011). doi:10.1088/0004-637X/735/1/45

    ADS  Google Scholar 

  • M.L. Goodman, P.G. Judge, Radiating current sheets in the solar chromosphere. Astrophys. J. 751, 75 (2012). doi:10.1088/0004-637X/751/1/75

    ADS  Google Scholar 

  • G. Haerendel, Commonalities between ionosphere and chromosphere. Space Sci. Rev. 124, 317–331 (2006). doi:10.1007/s11214-006-9092-z

    ADS  Google Scholar 

  • M.E. Hagan, M.D. Burrage, J.M. Forbes, J. Hackney, W.J. Randel, X. Zhang, GSWM-98: results for migrating solar tides. J. Geophys. Res. 104, 6813–6828 (1999). doi:10.1029/1998JA900125

    ADS  Google Scholar 

  • A.M. Hamza, J.-P. St. Maurice, A fully self-consistent fluid theory of anomalous transport in Farley–Buneman turbulence. J. Geophys. Res. 100, 9653–9668 (1995). doi:10.1029/94JA03031

    ADS  Google Scholar 

  • S.S. Hasan, A.A. van Ballegooijen, Dynamics of the solar magnetic network. II. Heating the magnetized chromosphere. Astrophys. J. 680, 1542–1552 (2008). doi:10.1086/587773

    ADS  Google Scholar 

  • J.C. Henoux, B.V. Somov, The photospheric dynamo. I. Magnetic flux-tube generation. Astron. Astrophys. 241, 613–617 (1991)

    ADS  Google Scholar 

  • J.C. Henoux, B.V. Somov, The photospheric dynamo. I. Physics of thin magnetic flux tubes. Astron. Astrophys. 318, 947–956 (1997)

    ADS  Google Scholar 

  • A. Hillier, H. Isobe, K. Shibata, T. Berger, Numerical simulations of the magnetic Rayleigh–Taylor instability in the Kippenhahn–Schlüter prominence model. Astrophys. J. Lett. 736, 1 (2011). doi:10.1088/2041-8205/736/1/L1

    ADS  Google Scholar 

  • A. Hillier, T. Berger, H. Isobe, K. Shibata, Numerical simulations of the magnetic Rayleigh–Taylor instability in the Kippenhahn–Schlüter prominence model. I. Formation of upflows. Astrophys. J. 746, 120 (2012a). doi:10.1088/0004-637X/746/2/120

    ADS  Google Scholar 

  • A. Hillier, H. Isobe, K. Shibata, T. Berger, Numerical simulations of the magnetic Rayleigh–Taylor instability in the Kippenhahn–Schlüter prominence model. II. Reconnection-triggered downflows. Astrophys. J. 756, 110 (2012b). doi:10.1088/0004-637X/756/2/110

    ADS  Google Scholar 

  • J.D. Huba, G. Joyce, Global modeling of equatorial plasma bubbles. Geophys. Res. Lett. 37 17104 (2013). doi:10.1029/2010GL044281. http://adsabs.harvard.edu/abs/2010GeoRL..3717104H

    ADS  Google Scholar 

  • H. Isobe, T. Miyagoshi, K. Shibata, T. Yokoyama, Filamentary structure on the Sun from the magnetic Rayleigh–Taylor instability. Nature 434, 478–481 (2005). doi:10.1038/nature03399

    ADS  Google Scholar 

  • H. Isobe, T. Miyagoshi, K. Shibata, T. Yokoyama, Three-dimensional simulation of solar emerging flux using the Earth simulator I. Magnetic Rayleigh–Taylor instability at the top of the emerging flux as the origin of filamentary structure. Publ. Astron. Soc. Jpn. 58, 423–438 (2006)

    ADS  Google Scholar 

  • W. Kalkofen, Is the solar chromosphere heated by acoustic waves? Astrophys. J. 671, 2154–2158 (2007). doi:10.1086/523259

    ADS  Google Scholar 

  • Y. Kamide, The relationship between field-aligned currents and the auroral electrojets—a review. Space Sci. Rev. 31, 127–243 (1982). doi:10.1007/BF00215281

    ADS  Google Scholar 

  • A. Keiling, J.R. Wygant, C.A. Cattell, F.S. Mozer, C.T. Russell, The global morphology of wave poynting flux: powering the aurora. Science 299, 383–386 (2003). doi:10.1126/science.1080073

    ADS  Google Scholar 

  • M.C Kelley, D.J Knudsen, J.F Vickrey, Poynting flux measurements on a satellite. A diagnostic tool for space research. J. Geophys. Res. 96, 201–207 (1991).

    ADS  Google Scholar 

  • M.C. Kelley, R.A. Hellis, The Earth’s Ionosphere: Plasma Physics and Electrodynamics (second Addition) (Academic Press, New York, 2009)

    Google Scholar 

  • E. Khomenko, M. Collados, Heating of the magnetized solar chromosphere by partial ionization effects. Astrophys. J. 747, 87 (2012). doi:10.1088/0004-637X/747/2/87

    ADS  Google Scholar 

  • H. Kigure, K. Takahashi, K. Shibata, T. Yokoyama, S. Nozawa, Generation of Alfvén waves by magnetic reconnection. Publ. Astron. Soc. Jpn. 62, 993 (2010)

    ADS  Google Scholar 

  • J.A. Klimchuk, On solving the coronal heating problem. Sol. Phys. 234, 41–77 (2006). doi:10.1007/s11207-006-0055-z

    ADS  Google Scholar 

  • D.J. Knipp, W.K. Tobiska, B. Emery, Direct and indirect thermospheric heating sources for solar cycles 21–23. Sol. Phys. 224, 495–505 (2004).

    ADS  Google Scholar 

  • V. Krasnoselskikh, G. Vekstein, H.S. Hudson, S.D. Bale, W.P. Abbett, Generation of electric currents in the chromosphere via neutral-ion drag. Astrophys. J. 724, 1542–1550 (2010). doi:10.1088/0004-637X/724/2/1542

    ADS  Google Scholar 

  • A.P. Kropotkin, The generation of magnetic field via convective motions in the photosphere, Alfvén waves, and the origin of chromospheric spicules. Astron. Rep. 55, 1132–1143 (2011). doi:10.1134/S1063772911120079

    ADS  Google Scholar 

  • J.E. Leake, T.D. Arber, The emergence of magnetic flux through a partially ionised solar atmosphere. Astron. Astrophys. 450, 805–818 (2006). doi:10.1051/0004-6361:20054099

    ADS  Google Scholar 

  • J.E. Leake, M.G. Linton, Effect of ion-neutral collisions in simulations of emerging active regions. Astrophys. J. 764, 54 (2013). doi:10.1088/0004-637X/764/1/54

    ADS  Google Scholar 

  • J.E. Leake, T.D. Arber, M.L. Khodachenko, Collisional dissipation of Alfvén waves in a partially ionised solar chromosphere. Astron. Astrophys. 442, 1091–1098 (2005). doi:10.1051/0004-6361:20053427

    ADS  Google Scholar 

  • J.E. Leake, V.S. Lukin, M.G. Linton, Magnetic reconnection in a weakly ionized plasma. Phys. Plasmas 20(6), 061202 (2013)

    ADS  Google Scholar 

  • J.E. Leake, V.S. Lukin, M.G. Linton, E.T. Meier, Multi-fluid simulations of chromospheric magnetic reconnection in a weakly ionized reacting plasma. Astrophys. J. 760, 109 (2012). doi:10.1088/0004-637X/760/2/109

    ADS  Google Scholar 

  • J. Lei, R.G. Noble, B.A. Wang, S.R. Zhang, Electron temperature climatology at Millstone Hill and Arecibo. J. Geophys. Res. 112, A02302 (2007). doi:10.1029/2006JA012041

    ADS  Google Scholar 

  • G. Lu, A.D. Richmond, B.A. Emery, R.G. Roble, Magnetosphere-ionosphere-thermosphere coupling: effect of neutral winds on energy transfer and field-aligned current. J. Geophys. Res. 100, 19643–19660 (1995). doi:10.1029/95JA00766

    ADS  Google Scholar 

  • V.S. Lukin, Computational study of the internal kink mode evolution and associated magnetic reconnection phenomena, PhD thesis, Princeton University, 2008

  • S. Lundquist, Studies in magneto-hydrodynamics. Ark. Fys. 5, 297–347 (1952)

    MATH  MathSciNet  Google Scholar 

  • C.A. Madsen, Y.S. Dimant, M.M. Oppenheim, J.M. Fontenla, The Multi-Species Farley–Buneman Instability in the Solar Chromosphere. ArXiv e-prints (2013)

  • J.J. Makela, B.M. Ledvina, M.C. Kelley, P.M. Kintner, Analysis of the seasonal variations of equatorial plasma bubble occurrence observed from Haleakala, Hawaii. Ann. Geophys. 22, 3109–3121 (2004). doi:10.5194/angeo-22-3109-2004

    ADS  Google Scholar 

  • J. Martínez-Sykora, B. De Pontieu, V. Hansteen, Two-dimensional radiative magnetohydrodynamic simulations of the importance of partial ionization in the chromosphere. Astrophys. J. 753, 161 (2012). doi:10.1088/0004-637X/753/2/161

    ADS  Google Scholar 

  • E.T. Meier, U. Shumlak, A general nonlinear fluid model for reacting plasma–neutral mixtures. Phys. Plasmas 19, 072508 (2012)

    ADS  Google Scholar 

  • G.H. Millward, R.J. Moffett, S. Quegan, T.J. Fuller-Rowell, A Coupled Thermosphere–Ionosphere Model (CTIM), STEP Handbook of Ionospheric Models 1996, pp. 239–280

  • M. Mitchner, C.H. Kruger, Partially Ionized Gases (Wiley, New York, 1973)

    Google Scholar 

  • V.M. Nakariakov, L. Ofman, E.E. Deluca, B. Roberts, J.M. Davila, TRACE observation of damped coronal loop oscillations: implications for coronal heating. Science 285, 862–864 (1999). doi:10.1126/science.285.5429.862

    ADS  Google Scholar 

  • U. Narain, P. Ulmschneider, Chromospheric and coronal heating mechanisms. Space Sci. Rev. 54, 377–445 (1990). doi:10.1007/BF00177801

    ADS  Google Scholar 

  • L. Ofman, Chromospheric leakage of Alfvén waves in coronal loops. Astrophys. J. Lett. 568, 135–138 (2002). doi:10.1086/340329

    ADS  Google Scholar 

  • M.M. Oppenheim, Y.S. Dimant, Kinetic simulations of 3-D Farley–Buneman turbulence and anomalous electron heating. J. Geophys. Res. 118, 1306–1318 (2013). doi:10.1002/jgra.50196

    Google Scholar 

  • S.L. Ossakow, Spread F theories: a review. J. Atmos. Terr. Phys. 43, 437–452 (1981)

    ADS  Google Scholar 

  • N.F. Otani, M. Oppenheim, Saturation of the Farley–Buneman instability via three-mode coupling. J. Geophys. Res. 111, 3302 (2006). doi:10.1029/2005JA011215

    Google Scholar 

  • E.N. Parker, Magnetic neutral sheets in evolving fields. I. General theory. Astrophys. J. 264, 635–647 (1983). doi:10.1086/160636

    ADS  Google Scholar 

  • E.N. Parker, Dynamical oscillation and propulsion of magnetic fields in the convective zone of a star. VI. Small flux bundles, network fields, and ephemeral active regions. Astrophys. J. 326, 407–411 (1988). doi:10.1086/166103

    ADS  Google Scholar 

  • E.N. Parker, The alternative paradigm for magnetospheric physics. J. Geophys. Res. 101, 10587–10626 (1996). doi:10.1029/95JA02866

    ADS  Google Scholar 

  • E.N. Parker, Conversations on Electric and Magnetic Fields in the Cosmos (Princeton University Press, Princeton, 2007)

    Google Scholar 

  • S.V. Poliakov, V.O. Rapoport, The ionospheric Alfvén resonator. Geomagn. Aeron. 21, 816–822 (1981)

    ADS  Google Scholar 

  • J.W.S. Rayleigh, Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density. Proc. Lond. Math. Soc. 14, 170–177 (1882)

    MathSciNet  Google Scholar 

  • A.D. Richmond, J.P. Thayer, Ionospheric electrodynamics: a tutorial, in Magnetospheric Current Systems, ed. by S. Ohtani, R. Fujii, M. Hesse, R. L. Lysak, Geophysical Monograph, vol. 118 (American Geophysical Union, Washington, 2000), pp. 131–146

    Google Scholar 

  • A.D. Richmond, E.C. Ridley, R.G. Roble, A thermosphere/ionosphere general circulation model with coupled electrodynamics. Geophys. Res. Lett. 19, 601–604 (1992). doi:10.1029/92GL00401

    ADS  Google Scholar 

  • H. Rishbeth, Thermospheric targets. Eos 88, 189–193 (2007). doi:10.1029/2007EO170002

    ADS  Google Scholar 

  • R.G. Roble, E.C. Ridley, A thermosphere–ionosphere-mesosphere-electrodynamics general circulation model (TIMEGCM): equinox solar cycle minimum simulations (30–500 km). Geophys. Res. Lett. 21, 417–420 (1994). doi:10.1029/93GL03391

    ADS  Google Scholar 

  • R.G. Roble, E.C. Ridley, A.D. Richmond, R.E. Dickinson, A coupled thermosphere/ionosphere general circulation model. Geophys. Res. Lett. 15, 1325–1328 (1988). doi:10.1029/GL015i012p01325

    ADS  Google Scholar 

  • A.J.B Russell, L. Fletcher, Propagation of Alfvénic waves from corona to chromosphere and consequences for solar flares. Astrophys. J. 765, 81 (2013). doi:10.1088/0004-637X/765/2/81

    ADS  Google Scholar 

  • R.W. Schunk, Transport equations for aeronomy. Planet. Space Sci. 23, 437 (1975).

    ADS  Google Scholar 

  • R.W. Schunk, Mathematical structure of transport equations for multispecies flows. Rev. Geophys. 15, 429 (1977).

    ADS  Google Scholar 

  • R.W. Schunk, J.J. Sojka, Ion temperature variations in the daytime high-latitude F region. J. Geophys. Res. 87(A7), 5169-5183 (1982). doi:10.1029/JA087iA07p05169.

    ADS  Google Scholar 

  • R.W. Schunk, A.F. Nagy, Ionospheres: Physics, Plasma Physics, and Chemistry (Cambridge University Press, New York, 2000)

    Google Scholar 

  • M. Schwarzschild, On noise arising from the solar granulation. Astrophys. J. 107, 1 (1948). doi:10.1086/144983

    ADS  Google Scholar 

  • P. Song, V.M. Vasyliūnas, Heating of the solar atmosphere by strong damping of Alfvén waves. J. Geophys. Res. 116, 9104 (2011). doi:10.1029/2011JA016679

    Google Scholar 

  • P. Song, T.I. Gombosi, A.J. Ridley, Three-fluid Ohm’s law. J. Geophys. Res. 106, 8149–8156 (2001). doi:10.1029/2000JA000423

    ADS  Google Scholar 

  • P. Song, V.M. Vasyliūnas, L. Ma, Solar wind-magnetosphere-ionosphere coupling: neutral atmosphere effects on signal propagation. J. Geophys. Res. 110, 9309 (2005). doi:10.1029/2005JA011139

    Google Scholar 

  • B.U.O. Sonnerup, G. Paschmann, I. Papamastorakis, N. Sckopke, G. Haerendel, S.J. Barne, J.R. Asbridge, J.T. Gosling, C.T. Russelll, Evidence for magnetic field reconnection at the earth’s magnetopause. J. Geophys. Res. 86, 10049 (1981). doi:10.1029/JA086iA12p10049

    ADS  Google Scholar 

  • J.P. St. Maurice, R.W. Schunk, Ion-neutral momentum coupling near discrete high latitude ionospheric features. J. Geophys. Res. 86, 11299 (1981).

    ADS  Google Scholar 

  • J.P. St. Maurice, W.B. Hanson, Ion frictional heating at high latitudes and its possible use for an in situ determination of neutral thermospheric winds and temperatures. J. Geophys. Res. 87(A9), 7580 (1982). doi:10.1029/JA087iA09p07580.

    ADS  Google Scholar 

  • J.P. St. Maurice, W.B. Hanson, A statistical study of F region ion temperatures at high latitudes based on atmosphere explorer C data. J. Geophys. Res. 89(A2), 987 (1984). doi:10.1029/JA089iA02p00987.

    ADS  Google Scholar 

  • R.F. Stein, Solar surface magneto-convection. Living Rev. Sol. Phys. 9, 4 (2012). doi:10.12942/lrsp-2012-4

    ADS  Google Scholar 

  • P.J. Sultan, Linear theory and modeling of the Rayleigh–Taylor instability leading to the occurrence of equatorial spread F. J. Geophys. Res. 101, 26875–26892 (1996)

    ADS  Google Scholar 

  • G. Taylor, The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I. Proc. Phys. Soc. Lond. 201, 192–196 (1950). doi:10.1098/rspa.1950.0052

    MATH  ADS  Google Scholar 

  • J.P. Thayer, High-latitude currents and their energy exchange with the ionosphere-thermosphere system. J. Geophys. Res. 105, 23015–23024 (2000). doi:10.1029/1999JA000409

    ADS  Google Scholar 

  • J.P. Thayer, J. Semeter, The convergence of magnetospheric energy flux in the polar atmosphere. J. Atmos. Sol.-Terr. Phys. 66, 807–824 (2004). doi:10.1016/j.jastp.2004.01.035

    ADS  Google Scholar 

  • J.P. Thayer, J.F. Vickrey, R.A. Heelis, J.B. Gary, Interpretation and modeling of the high-latitude electromagnetic energy flux. J. Geophys. Res. 100, 19715–19728 (1995). doi:10.1029/95JA01159

    ADS  Google Scholar 

  • W.K. Tobiska, T. Woods, F. Eparvier, R. Viereck, L. Floyd, D. Bouwer, G. Rottman, O.R. White, The SOLAR2000 empirical solar irradiance model and forecast tool. J. Atmos. Sol.-Terr. Phys. 62, 1233–1250 (2000). doi:10.1016/S1364-6826(00)00070-5

    ADS  Google Scholar 

  • S. Tomczyk, S.W. McIntosh, S.L. Keil, P.G. Judge, T. Schad, D.H. Seeley, J. Edmondson, Alfvén waves in the solar corona. AGU Fall Meeting Abstracts, 289 (2007)

  • M.R. Torr, D.G. Torr, The seasonal behaviour of the F2 layer of the ionosphere. J. Atmos. Terr. Phys. 35, 2237–2251 (1973)

    ADS  Google Scholar 

  • J. Tu, P. Song, On the concept of penetration electric field. Radio Sound. Plasma Phys. 974, 81–85 (2008).

    ADS  Google Scholar 

  • J. Tu, P. Song, V.M. Vasyliūnas, Ionosphere/thermosphere heating determined from dynamic magnetosphere-ionosphere/thermosphere coupling. J. Geophys. Res. 116, 9311 (2011). doi:10.1029/2011JA016620

    Google Scholar 

  • J. Tu, P. Song, A study of Alfvén wave propagation and heating the chromosphere. Astrophys. J. 777, 53 (2013). doi:10.1088/0004-637X/777/1/53

    ADS  Google Scholar 

  • Y.-K. Tung, C.W. Carlson, J.P. McFadden, D.M. Klumpar, G.K. Parks, W.J. Peria, K. Liou, Auroral polar cap boundary ion conic outflow observed on FAST. J. Geophys. Res. 106, 3603–3614 (2001). doi:10.1029/2000JA900115

    ADS  Google Scholar 

  • P. Ulmschneider, Acoustic heating of stellar chromospheres and coronae, in Cool Stars, Stellar Systems, and the Sun, ed. by G. Wallerstein, Astron. Soc. Pac. Conf. Ser., vol. 9 (ASP, San Francisco, 1990), pp. 3–14

    Google Scholar 

  • V. Väisälä, Über die Wirkung der Windschwankungen auf die Pilotbeobachtungen. Soc. Sci. Fenn. Comment. Math. Phys. 2, 19–37 (1925)

    Google Scholar 

  • V.M. Vasyliūnas, Electric field and plasma flow: what drives what? Geophys. Res. Lett. 28, 2177–2180 (2001). doi:10.1029/2001GL013014

    ADS  Google Scholar 

  • V.M. Vasyliūnas, Time evolution of electric fields and currents and the generalized Ohm’s law. Ann. Geophys. 23, 1347–1354 (2005). doi:10.5194/angeo-23-1347-2005

    ADS  Google Scholar 

  • V.M. Vasyliūnas, P. Song, Meaning of ionospheric Joule heating. J. Geophys. Res. 110, 2301 (2005). doi:10.1029/2004JA010615

    Google Scholar 

  • V.M. Vasyliūnas, Physics of magnetospheric variability. J. Geophys. Res. 158, 91–118 (2011). doi:10.1007/s11214-010-9696-1

    Google Scholar 

  • V.M. Vasyliūnas, The physical basis of ionospheric electrodynamics. Ann. Geophys. 30, 3157–3369 (2012). doi:10.5194/angeo-30-357-2012

    Google Scholar 

  • J.E. Vernazza, E.H. Avrett, R. Loeser, Structure of the solar chromosphere. III. Models of the EUV brightness components of the quiet Sun. Astrophys. J. Suppl. Ser. 45, 635–725 (1981). doi:10.1086/190731

    ADS  Google Scholar 

  • Y. Voitenko, M. Goossens, Excitation of high-frequency Alfvén waves by plasma outflows from coronal reconnection events. Sol. Phys. 206, 285–313 (2002). doi:10.1023/A:1015090003136

    ADS  Google Scholar 

  • J. Vranjes, P.S. Krstic, Collisions, magnetization, and transport coefficients in the lower solar atmosphere. Astron. Astrophys. 554, 22 (2013). doi:10.1051/0004-6361/201220738

    ADS  Google Scholar 

  • W. Wang, A.G. Burns, M. Wiltberger, S.C. Solomon, T.L. Killeen, Altitude variations of the horizontal thermospheric winds during geomagnetic storms. J. Geophys. Res. 113, 2301 (2008). doi:10.1029/2007JA012374

    Google Scholar 

  • R.F. Woodman, Spread F—an old equatorial aeronomy problem finally resolved? Ann. Geophys. 27, 1915–1934 (2009). doi:10.5194/angeo-27-1915-2009

    ADS  Google Scholar 

  • T.V. Zaqarashvili, M.L. Khodachenko, H.O. Rucker, Magnetohydrodynamic waves in solar partially ionized plasmas: two-fluid approach. Astrophysics 529, 82 (2011). doi:10.1051/0004-6361/201016326

    Google Scholar 

Download references

Acknowledgements

This work was supported by NASA’s Living with a Star (LWS) Targeted Research and Technology (TR&T) program. Numerical simulations were performed under a grant of computer time from the Department of Defense (DoD) High Performance Computing (HPC) program. The Authors thank the anonymous referees who contributed significantly to the improvement of this manuscript.

This work was funded by NASA’s “Living with a Star” Targeted Research and Technology program “Plasma–Neutral Gas Coupling in the Chromosphere and Ionosphere”. Numerical simulations were performed using a grant of computer time from the DoD High Performance Computing Program. NCAR is sponsored by the National Science Foundation.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to J. E. Leake.

Appendix

Appendix

The two-dimensional simulation results shown in Figs. 14 and 15 were performed with the HiFi spectral-element multi-fluid model (Lukin 2008). Effective grid sizes of 480×1920 and 180×720 were used in the solar-prominence and ionosphere cases, respectively, along the horizontal (y) and vertical (x) directions. Periodic conditions were applied at the side boundaries (y), while closed, reflecting, free-slip, perfect-conductor conditions were applied at the top and bottom boundaries (x), which were placed sufficiently far from the unstable layer to have negligible effect on the Rayleigh–Taylor evolution. Details of the plasma and neutral profiles and parameters used in the simulations are given below.

A.1 Prominence

Normalization constants for this case are number density n 0=1×1015 m−3, length scale L 0=1×106 m, and magnetic field B 0=1×10−3 T. Using these in a hydrogen plasma, normalization values for the time t 0=1.45 s and temperature T 0=5.76×107 K can be derived. The ion inertial scale is so much smaller than any scale of interest that, in this case, its value has been set explicitly to zero, d i =(c/ω pi0)/L 0=0. This is equivalent to neglecting the Hall term in the Ohm’s law. Using the ratio of Hall term to Pedersen in the center of mass Ohm’s law (47), and the simplifications used in Sect. 4.3, this is equivalent to \(\xi_{n}^{2}k_{in} \gg1\), which is valid for these simulations.

The electron and ion density profiles are given by atmospheric stratification,

$$ n_i(x) = n_e(x) = n_0 \exp \biggl( - \frac{x}{x_0} \biggr). $$
(124)

The scale height x 0 is set by the solar gravitational acceleration, g S =2.74×102 m s−2, and the assumed background temperature of the corona, T b =3.5×10−3 T 0=2.02×105 K, scaled to the normalization length L 0; its value is x 0=12.2. The density profile of the neutral fluid that constitutes the prominence is given by a prescribed function of x plus a very low uniform background value,

$$ n_n(x) = n_{n0} \operatorname{sech}^2 ( 2x-1 ) + n_{nb}. $$
(125)

The peak neutral number density enhancement is taken to be n n0=1×1016 m−3=10n 0, while n nb =3.5×10−7 n n0, corresponding to the neutral fraction obtained in the HiFi ionization/recombination equilibrium at the background temperature T b . We chose an artificially low value of T b (compared to a typical coronal temperature of about 2×106 K) in order to prevent the background neutral density n nb from being far smaller still.

The electron, ion, and neutral temperatures are all assumed to be equal to each other initially. The temperature profile is given by a prescribed function f(x),

$$ T(x) = T_b f(x) = T_b \frac{\cosh^2(x-0.5)}{\cosh^2(x-0.5) + \lambda}, $$
(126)

which approaches T b away from the prominence and attains a minimum value T p =T b /(1+λ) within the prominence. To obtain a temperature approximately corresponding to that observed on the Sun, with an associated low ionization fraction (n e0/(n e0+n n0))=0.091, we set the parameter λ=20. The resulting prominence temperature T p =9.60×103 K.

The magnetic field is initialized to lie in the out-of-plane direction \(\hat{ \mathbf{e}}_{z}\), so that it is perpendicular to both gravity in the \(-\hat{\mathbf{e}}_{x}\) direction and the instability wavenumber k in the \(\hat{\mathbf{e}}_{y}\) direction. It is given by

$$ \mathbf{B}= B_0 \hat{\mathbf{e}}_z \biggl[ 1 + \beta \biggl\{ \frac {n_e(x)}{n_0} \bigl[ 1 - f(x) \bigr] - \frac{n_n(x)}{2n_0}f(x) - \frac{1}{x_0} \frac{n_{n0}}{2n_0} \bigl[ \tanh ( 2x-1 ) - 1 \bigr] \biggr\} \biggr]^{1/2}, $$
(127)

where β=1.4×10−2 is the plasma beta evaluated using the background plasma pressure at x=0 and B 0. The magnetic field profile so constructed accommodates (1) the plasma pressure change from the isothermal hydrostatic profile (2) the neutral pressure, and (3) the gravitational force exerted on the bulk of the neutral fluid (neglecting the small background contribution n nb ) throughout the atmosphere.

This initial condition is not an exact solution to the multi-fluid model which includes ionization, recombination, and viscous forces, but would be if only gravity, pressure gradients, and Lorentz forces were considered. It is close enough to the full solution, however, that any flows such as those created by pressure gradients driven by ionization/recombination of the initial condition are small compared to the flows initiated by the instability. The instability is initiated by introducing a small neutral density perturbation localized in x on the bottom side of the prominence,

$$ \Delta n_n(x,y) = \delta n_n(x) \exp \bigl[-4x^2\bigr]\frac{1}{5}\sum_{j=1}^5 \sin[j \pi y], $$
(128)

where we chose δ=10−2, and y is the normalized distance along the gravitational equipotential surface.

A.2 Ionosphere

The normalization constants are number density n 0=1×1016 m−3, length scale L 0=2×104 m, and magnetic field B 0=3×10−5 T. Using these in a hydrogen plasma, normalization values for the time t 0=3.06 s, temperature T 0=5.19×103 K, and ion inertial scale length d i =(c/ω pi0)/L 0=1.14×10−4 can be derived.

The neutral density profile is given by atmospheric stratification,

$$ n_n(x) = n_{0} \exp \biggl( -\frac{x}{x_0} \biggr). $$
(129)

The scale height x 0 is set by Earth’s gravitational acceleration, g E =9.81 m s−2, and the assumed background temperature of the ionosphere, T b =0.225T 0=1.17×103 K, scaled to the normalization length L 0; its value is x 0=49.1. The electron/ion density profile of the plasma is given by a prescribed function of x plus a low uniform background value,

$$ n_e(x) = n_i(x) = n_{e0} \operatorname{sech}^2 ( 2x-1 ) + n_{eb}. $$
(130)

The peak electron number density is taken to be n e0=1×1012 m−3=10−4 n 0, while n eb =0.05n e0. The electron, ion, and neutral temperatures are all assumed to be equal and uniform initially, at T b =1.17×103 K.

As before, the magnetic field is initialized to lie in the out-of-plane direction. It is given by

$$ \mathbf{B}= B_0 \hat{\mathbf{e}}_z \biggl[ 1 - \beta \biggl\{ \frac{2n_e(x)}{n_0} + \frac{1}{2x_0} \bigl[ \tanh ( 2x - 1 ) - 1 \bigr] \biggr\} \biggr]^{1/2}, $$
(131)

where β=0.450 is the neutral beta calculated using the background neutral pressure at x=0 and B 0. The magnetic field profile so constructed accommodates (1) the plasma pressure and (2) the gravitational force exerted on the bulk of the plasma (neglecting the small background contribution n eb ) throughout the atmosphere.

The instability is initiated with a small electron density perturbation localized in x on the bottom side of the ionization layer,

$$ \Delta n_e(x,y) = -\delta n_e(x) \exp \bigl[-4x^2\bigr]\frac{1}{5}\sum_{j=1}^5 \sin[j \pi y], $$
(132)

where again we chose δ=10−2, and y is the normalized distance along the gravitational equipotential surface.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Leake, J.E., DeVore, C.R., Thayer, J.P. et al. Ionized Plasma and Neutral Gas Coupling in the Sun’s Chromosphere and Earth’s Ionosphere/Thermosphere. Space Sci Rev 184, 107–172 (2014). https://doi.org/10.1007/s11214-014-0103-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11214-014-0103-1

Keywords

  • Sun
  • Ionosphere
  • Thermosphere
  • Chromosphere