Solar Physics

, Volume 278, Issue 2, pp 435–446 | Cite as

Implications of Non-cylindrical Flux Ropes for Magnetic Cloud Reconstruction Techniques and the Interpretation of Double Flux Rope Events

  • M. J. OwensEmail author
  • P. Démoulin
  • N. P. Savani
  • B. Lavraud
  • A. Ruffenach


Magnetic clouds (MCs) are a subset of interplanetary coronal mass ejections (ICMEs) which exhibit signatures consistent with a magnetic flux rope structure. Techniques for reconstructing flux rope orientation from single-point in situ observations typically assume the flux rope is locally cylindrical, e.g., minimum variance analysis (MVA) and force-free flux rope (FFFR) fitting. In this study, we outline a non-cylindrical magnetic flux rope model, in which the flux rope radius and axial curvature can both vary along the length of the axis. This model is not necessarily intended to represent the global structure of MCs, but it can be used to quantify the error in MC reconstruction resulting from the cylindrical approximation. When the local flux rope axis is approximately perpendicular to the heliocentric radial direction, which is also the effective spacecraft trajectory through a magnetic cloud, the error in using cylindrical reconstruction methods is relatively small (≈ 10). However, as the local axis orientation becomes increasingly aligned with the radial direction, the spacecraft trajectory may pass close to the axis at two separate locations. This results in a magnetic field time series which deviates significantly from encounters with a force-free flux rope, and consequently the error in the axis orientation derived from cylindrical reconstructions can be as much as 90. Such two-axis encounters can result in an apparent ‘double flux rope’ signature in the magnetic field time series, sometimes observed in spacecraft data. Analysing each axis encounter independently produces reasonably accurate axis orientations with MVA, but larger errors with FFFR fitting.


Magnetic cloud Magnetic flux rope Coronal mass ejection Solar wind 


  1. Bothmer, V., Schwenn, R.: 1998, The structure and origin of magnetic clouds in the solar wind. Ann. Geophys. 16, 1 – 24. ADSCrossRefGoogle Scholar
  2. Burlaga, L.F.: 1988, Magnetic clouds: Constant alpha force-free configurations. J. Geophys. Res. 93, 7217 – 7224. ADSCrossRefGoogle Scholar
  3. Burlaga, L.F., Sittler, E., Mariani, F., Schwenn, R.: 1981, Magnetic loop behind an interplanetary shock: Voyager, Helios, and IMP 8 observations. J. Geophys. Res. 86, 6673 – 6684. ADSCrossRefGoogle Scholar
  4. Cane, H.V., Richardson, I.G.: 2003, Interplanetary coronal mass ejections in the near-Earth solar wind during 1996 – 2002. J. Geophys. Res. 108, 1156. doi: 10.1029/2002JA009817. CrossRefGoogle Scholar
  5. Cremades, H., Bothmer, V.: 2004, On the three-dimensional configuration of coronal mass ejections. Astron. Astrophys. 422, 307 – 322. doi: 10.1051/0004-6361:20035776. ADSCrossRefGoogle Scholar
  6. Dungey, J.W.: 1961, Interplanetary magnetic field and the auroral zones. Phys. Rev. Lett. 6, 47. ADSCrossRefGoogle Scholar
  7. Farrugia, C.J., Osherovich, V.A., Burlaga, L.F.: 1995, Magnetic flux rope versus the spheromak as models for interplanetary magnetic clouds. J. Geophys. Res. 100, 12293. doi: 10.1029/95JA00272. ADSCrossRefGoogle Scholar
  8. Gosling, J.T.: 1993, The solar flare myth. J. Geophys. Res. 98, 18937 – 18950. doi: 10.1029/93JA01896. ADSCrossRefGoogle Scholar
  9. Gosling, J.T., Baker, D.N., Bame, S.J., Feldman, W.C., Zwickl, R.D.: 1987, Bidirectional solar wind electron heat flux events. J. Geophys. Res. 92, 8519 – 8535. ADSCrossRefGoogle Scholar
  10. Gulisano, A.M., Dasso, S., Mandrini, C.H., Démoulin, P.: 2007, Estimation of the bias of the minimum variance technique in the determination of magnetic clouds global quantities and orientation. Adv. Space Res. 40, 1881 – 1890. doi: 10.1016/j.asr.2007.09.001. ADSCrossRefGoogle Scholar
  11. Hidalgo, M.A., Cid, C., Vinas, A.F., Sequeiros, J.: 2002, A non-force-free approach to the topology of magnetic clouds. J. Geophys. Res. 107, 1002 – 1009. doi: 10.1029/2001JA900100. CrossRefGoogle Scholar
  12. Hu, Q., Sonnerup, B.U.O.: 2001, Reconstruction of magnetic flux ropes in the solar wind. Geophys. Res. Lett. 28, 1443. CrossRefGoogle Scholar
  13. Hundhausen, A.J.: 1993, Sizes and locations of coronal mass ejections – SMM observations from 1980 and 1984 – 1989. J. Geophys. Res. 98, 13177 – 13200. ADSCrossRefGoogle Scholar
  14. Klein, L.W., Burlaga, L.F.: 1982, Interplanetary magnetic clouds at 1 AU. J. Geophys. Res. 87, 613 – 624. ADSCrossRefGoogle Scholar
  15. Lavraud, B., Borovsky, J.E.: 2008, Altered solar wind-magnetosphere interaction at low Mach numbers: Coronal mass ejections. J. Geophys. Res. 113, A00B08. doi: 10.1029/2008JA013192. CrossRefGoogle Scholar
  16. Lavraud, B., Owens, M.J., Rouillard, A.P.: 2011, In situ signatures of interchange reconnection between magnetic clouds and open magnetic fields: A mechanism for the erosion of polar coronal holes? Solar Phys. 270, 285 – 296. doi: 10.1007/s11207-011-9717-6. ADSCrossRefGoogle Scholar
  17. Lepping, R.P., Jones, J.A., Burlaga, L.F.: 1990, Magnetic field structure of interplanetary clouds at 1 AU. J. Geophys. Res. 95, 11957 – 11965. ADSCrossRefGoogle Scholar
  18. Lynch, B.J., Gruesbeck, J.R., Zurbuchen, T.H., Antiochos, S.K.: 2005, Solar cycle dependent helicity transport by magnetic clouds. J. Geophys. Res. 110, A08107. doi: 10.1029/2005JA011137. CrossRefGoogle Scholar
  19. Marubashi, K., Lepping, R.P.: 2007, Long-duration magnetic clouds: A comparison of analyses using torus- and cylinder-shaped flux rope models. Ann. Geophys. 25, 2453 – 2477. doi: 10.5194/angeo-25-2453-2007. ADSCrossRefGoogle Scholar
  20. Mulligan, T., Russell, C.T.: 2001, Mulitspacecraft modeling of the flux rope structure of interplanetary coronal mass ejections: Cylindrical symmetric versus nonsymmetric topologies. J. Geophys. Res. 106, 10581 – 10596. ADSCrossRefGoogle Scholar
  21. Owens, M.J.: 2008, Combining remote and in situ observations of coronal mass ejections to better constrain magnetic cloud reconstruction. J. Geophys. Res. 113, A12102. doi: 10.1029/2008JA013589. ADSCrossRefGoogle Scholar
  22. Owens, M.J., Cargill, P.J.: 2004, Non-radial solar wind flows induced by the motion of interplanetary coronal mass ejections. Ann. Geophys. 22, 4395 – 4397. ADSGoogle Scholar
  23. Owens, M.J., Crooker, N.U., Horbury, T.S.: 2009, The expected imprint of flux rope geometry on suprathermal electrons in magnetic clouds. Ann. Geophys. 27, 4057 – 4067. doi: 10.5194/angeo-27-4057-2009. ADSCrossRefGoogle Scholar
  24. Owens, M.J., Merkin, V.G., Riley, P.: 2006, A kinematically distorted flux rope model for magnetic clouds. J. Geophys. Res. 111, A03104. doi: 10.1029/2005JA011460. CrossRefGoogle Scholar
  25. Owens, M.J., Schwadron, N.A., Crooker, N.U., Hughes, W.J., Spence, H.E.: 2007, Role of coronal mass ejections in the heliospheric Hale cycle. Geophys. Res. Lett. 34, L06104. doi: 10.1029/2006GL028795. CrossRefGoogle Scholar
  26. Rees, A., Forsyth, R.J.: 2004, Two examples of magnetic clouds with double rotations observed by the Ulysses spacecraft. Geophys. Res. Lett. 31, L06804. doi: 10.1029/2003GL018330. CrossRefGoogle Scholar
  27. Riley, P., Crooker, N.U.: 2004, Kinematic treatment of CME evolution in the solar wind. Astrophys. J. 600, 1035 – 1042. ADSCrossRefGoogle Scholar
  28. Riley, P., Linker, J.A., Lionello, R., Mikic, Z., Odstrcil, D., Hidalgo, M.A., Hu, Q., Lepping, R.P., Lynch, B.J., Rees, A.: 2004, Fitting flux-ropes to a global MHD solution: A comparison of techniques. J. Atmos. Solar-Terr. Phys. 66, 1321 – 1332. ADSCrossRefGoogle Scholar
  29. Romashets, E., Vandas, M.: 2009, Linear force-free field of a toroidal symmetry. Astron. Astrophys. 499, 17 – 20. doi: 10.1051/0004-6361/200911701. ADSzbMATHCrossRefGoogle Scholar
  30. Russell, C.T., Mulligan, T.: 2002, On the magnetosheath thicknesses of interplanetary coronal mass ejections. Planet. Space Sci. 50, 527 – 534. ADSCrossRefGoogle Scholar
  31. Savani, N.P., Owens, M.J., Rouillard, A.P., Forsyth, R.J., Davies, J.A.: 2010, Observational evidence of a coronal mass ejection distortion directly attributable to a structured solar wind. Astrophys. J. Lett. 714, L128 – L132. doi: 10.1088/2041-8205/714/1/L128. ADSCrossRefGoogle Scholar
  32. Sonnerup, B.U.O., Cahill, L.J.: 1967, Magnetopause structure and attitude from Explorer 12 observations. J. Geophys. Res. 72, 171. ADSCrossRefGoogle Scholar
  33. Vandas, M., Romashets, E.P.: 2003, A force-free field with constant alpha in an oblate cylinder: A generalization of the Lundquist solution. Astron. Astrophys. 398, 801 – 807. doi: 10.1051/0004-6361:20021691. ADSCrossRefGoogle Scholar
  34. Vandas, M., Fischer, S., Geranios, A.: 1991, Spherical and cylindrical models of magnetized plasma clouds and their comparison with spacecraft data. Planet. Space Sci. 39, 1147 – 1154. doi: 10.1016/0032-0633(91)90166-8. ADSCrossRefGoogle Scholar
  35. Vandas, M., Fischer, S., Dryer, M., Smith, Z., Detman, T.: 1998, Propagation of a spheromak 2. Three-dimensional structure of a spheromak. J. Geophys. Res. 103, 23717 – 23726. doi: 10.1029/98JA01902. ADSCrossRefGoogle Scholar
  36. Wang, Y., Zhou, G., Ye, P., Wang, S., Wang, J.: 2006, A study of the orientation of interplanetary magnetic clouds and solar filaments. Astrophys. J. 651, 1245 – 1255. doi: 10.1086/507668. ADSCrossRefGoogle Scholar
  37. Wimmer-Schweingruber, R.F., Crooker, N.U., Balogh, A., Bothmer, V., Forsyth, R.J., Gazis, P., Gosling, J.T., Horbury, T., Kilchmann, A., Richardson, I.G., Riley, P., Rodriguez, L., von Steiger, R., Wurz, P., Zurbuchen, T.H.: 2006, Understanding interplanetary coronal mass ejection signatures. Space Sci. Rev. 123, 177 – 216. doi: 10.1007/s11214-006-9017-x. ADSGoogle Scholar
  38. Yamamoto, T.T., Kataoka, R., Inoue, S.: 2010, Helical lengths of magnetic clouds from the magnetic flux conservation. Astrophys. J. 710, 456 – 461. doi: 10.1088/0004-637X/710/1/456. ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • M. J. Owens
    • 1
    • 2
    Email author
  • P. Démoulin
    • 3
  • N. P. Savani
    • 4
  • B. Lavraud
    • 5
    • 6
  • A. Ruffenach
    • 5
    • 6
  1. 1.Space Environment Physics Group, Department of MeteorologyUniversity of ReadingReadingUK
  2. 2.Space and Atmospheric PhysicsImperial College LondonLondonUK
  3. 3.Observatoire de Paris, Section de MeudonMeudon CedexFrance
  4. 4.Solar-Terrestrial Environment LaboratoryNagoya UniversityNagoyaJapan
  5. 5.Institut de Recherche en Astrophysique et Planétologie (IRAP)Université de Toulouse (UPS)ToulouseFrance
  6. 6.UMR 5277Centre National de la Recherche ScientifiqueToulouseFrance

Personalised recommendations