- Open Access
A self-similar solution of expanding cylindrical flux ropes for any polytropic index value
Earth, Planets and Space volume 54, pages783–790(2002)
We found a new class of solutions for MHD equations that satisfies the condition that cylindrical flux ropes can expand self-similarly even when the polytropic index γ is larger than 1. We achieved this by including the effects of elongation along the symmetry axis as well as radial expansion and assuming that the radial expansion rate is the same as the elongation rate. In previous studies (Osherovich et al., 1993a, 1995), a class of self-similar solutions was described for which cylindrical flux ropes expand only in the medium where γ is less than 1. We compare the models including elongation and excluding elongation observationally by using the WIND key parameters. The difference in the fitting results of the magnetic field between these two models is slight. However the fitting of the velocity is improved when elongation is included and when new geometric parameters that are necessary to represent the elongation are introduced. The values of these parameters are almost the same scale as the radius of flux ropes, which is consistent with the assumption of the isotropic expansion. This new exact solution to a time-dependent two-dimensional MHD problem can also be used to test numerical codes.
Berdichevsky, D. B., R. P. Lepping, and C. J. Farrugia, On geometric considerations of the evolution of magnetic flux reopes, Phys. Rev. Lett., 2002 (submitted)
Bernstein, I. B. and R. M. Kulsrud, On the explosion of a supernova into the interstellar magnetic field. I, Astrophys. J., 142, 479–490, 1965.
Burlaga, L. F., Magnetic clouds and force-free fields with constant alpha, J. Geophys. Res., 93, 7217–7224, 1988.
Burlaga, L., E. Sittler, F. Mariani, and R. Schwenn, Magnetic loop behind an interplanetary shock: Voyager, Helios, and IMP 8 observations, J. Geophys. Res., 86, 6673–6684, 1981.
Cargill, P. J., J. Chen, D. S. Spicer, and S. T. Zalesak, Magnetohydrodynamic simulations of the motion of magnetic flux tubes through a magnetized plasma, J. Geophys. Res., 101, 4855–4870, 1996.
Chen, J., Theory of prominence eruption and propagation: Interplanetary consequences, J. Geophys. Res., 101, 27,499–27,519, 1996.
Chen, J. and D. A. Garren, Interplanetary magnetic clouds: Topology and driving mechanism, Geophys. Res. Lett., 20, 2319–2322, 1993.
Farrugia, C. J., L. F. Burlaga, V. A. Osherovich, and R. P. Lepping, A comparative study of dynamically expanding force-free, constant-alpha magnetic configurations with applications to magnetic clouds, in Solar Wind Seven, edited by E. Marsch and R. Schwenn, COSPAR, vol. 3, pp. 611–614, Pergamon, New York, 1992.
Farrugia, C. J., L. F. Burlaga, V. A. Osherovich, I. G. Richardson, M. P. Freeman, R. P. Lepping, and A. J. Lazarus, A study of an expanding interplanetary magnetic cloud and its interaction with the earth’s magnetosphere: The interplanetary aspect, J. Geophys. Res., 98, 7621–7632, 1993.
Gibson, S. E. and B. C. Low, A time-dependent three-dimensional magnetohydrodynamic model of the coronal mass ejection, Astrophys. J., 493, 460–473, 1998.
Goldstein, H., On the field configuration in magnetic clouds, Solar Wind Five, NASA Conf. Publ., 2280, 731–733, 1983.
Gosling, J. T., On the determination of electron polytrope indices within coronal mass ejections in the solar wind, J. Geophys. Res., 104, 19,851–19,857, 1999.
Gosling, J. T., P. Riley, and R. M. Skoug, Reply, J. Geophys. Res., 106, 3709–3713, 2001.
Kulsrud, R. M., I. B. Bernstein, M. Kruskal, J. Fanucci, and N. Ness, On the explosion of a supernova into the interstellar magnetic field. II, Astrophys. J., 142, 491–506, 1965.
Kumar, A., and D. M. Rust, Interplanetary magnetic clouds, helicity conservation, and current-core flux-ropes, J. Geophys. Res., 101, 15,667–15,684, 1996.
Larson, D. E., R. P. Lin, J. M. McTiernan, J. P. McFadden, R. E. Ergun, M. McCarthy, H. Rème, T. R. Sanderson, M. Kaiser, R. P. Lepping, and J. Mazur, Tracing the topology of the October 18–20, 1995, magnetic cloud with ~0.1–102 keV electrons, Geophys. Res. Lett., 24, 1911–1914, 1997.
Lepping, R. P., J. A. Jones, and L. F. Burlaga, Magnetic field structure of interplanetary magnetic clouds at 1 AU, J. Geophys. Res., 95, 11,957–11,965, 1990.
Lepping, R. P., M. H. Acũna, L. F. Burlaga, W. M. Farrell, J. A. Slavin, K. H. Schatten, F. Mariani, N. F. Ness, F. M. Neubauer, Y. C. Whang, J. B. Byrnes, R. S. Kennon, P. V. Panetta, J. Scheifele, and E. M. Worley, The WIND magnetic field investigation, Space Sci. Rev., 71, 207–229, 1995.
Low, B. C., Self-similar magnetohydrodynamics. I. The γ = 4/3 polytrope and the coronal transient, Astrophys. J., 254, 796–805, 1982.
Marubashi, K., Structure of the interplanetary magnetic clouds and their solar origins, Adv. Space Res., 6(6), 335–338, 1986.
Marubashi, K., Interplanetary magnetic flux ropes and solar filaments, in Coronal Mass Ejections (Geophysical monograph 99), edited by N. Crooker, J. A. Joselyn, and J. Feynman, pp. 147–156, American Geophysical Union, Washington, D.C., 1997.
Odstrčil, D. and V. J. Pizzo, Three-dimensional propagation of coronal mass ejections (CMEs) in a structured solar wind flow 1. CME launched within the streamer belt, J. Geophys. Res., 104, 483–492, 1999.
Ogilvie, K. W., D. J. Chornay, R. J. Fritzenreiter, F. Hunsaker, J. Keller, J. Lobell, G. Miller, J. D. Scudder, E. C. Sittler, Jr., R. B. Torbert, D. Bodet, G. Needell, A. J. Lazarus, J. T. Steinberg, J. H. Tappan, A. Mavretic, and E. Gergin, SWE, a comprehensive plasma instrument for the WIND spacecraft, Space Sci. Rev., 71, 55–77, 1995.
Osherovich, V., Comment on “On the determination of electron polytrope indices within coronal mass ejections in the solar wind”, J. Geophys. Res., 106, 3703–3707, 2001.
Osherovich, V. A., C. J. Farrugia, and L. F. Burlaga, Nonlinear evolution of magnetic flux ropes 1. Low-beta limit, J. Geophys. Res., 98, 13,225–13,231, 1993a.
Osherovich, V. A., C. J. Farrugia, L. F. Burlaga, R. P. Lepping, J. Fainberg, and R. G. Stone, Polytropic relationship in interplanetary magnetic clouds, J. Geophys. Res., 98, 15,331–15,342, 1993b.
Osherovich, V. A., C. J. Farrugia, and L. F. Burlaga, Nonlinear evolution of magnetic flux ropes 2. Finite beta plasma, J. Geophys. Res., 100, 12,307–12,318, 1995.
Shimazu, H. and K. Marubashi, New method for detecting interplanetary flux ropes, J. Geophys. Res., 105, 2365–2373, 2000.
Skoug, R. M., W. C. Feldman, J. T. Gosling, D. J. McComas, and C. W. Smith, Solar wind electron characteristics inside and outside coronal mass ejections, J. Geophys. Res., 105, 23,069–23,084, 2000a.
Skoug, R. M., W. C. Feldman, J. T. Gosling, D. J. McComas, D. B. Reisenfeld, C. W. Smith, R. P. Lepping, and A. Balogh, Radial variation of solar wind electrons inside a magnetic cloud observed at 1 and 5 AU, J. Geophys. Res., 105, 27,269–27,275, 2000b.
Tsurutani, B. T., W. D. Gonzalez, F. Tang, S. I. Akasofu, and E. J. Smith, Origin of interplanetary southward magnetic fields responsible for major magnetic storms near solar maximum (1978–1979), J. Geophys. Res., 93, 8519–8531, 1988.
Vandas, M. and D. Odstrčil, Magnetic cloud evolution: A comparison of analytical and numerical solutions, J. Geophys. Res., 105, 12,605–12,616, 2000.
Vandas, M., S. Fischer, M. Dryer, Z. Smith, and T. Detman, Simulation of magnetic cloud propagation in the inner heliosphere in two-dimensions 1. A loop perpendicular to the ecliptic plane, J. Geophys. Res., 100, 12,285–12,292, 1995.
Vandas, M., S. Fischer, M. Dryer, Z. Smith, and T. Detman, Parametric study of loop-like magnetic cloud propagation, J. Geophys. Res., 101, 15,645–15,652, 1996.
Wu, S. T., W. P. Guo, and M. Dryer, Dynamical evolution of a coronal streamer—flux rope system II. A self-consistent non-planar magnetohydrodynamic simulation, Solar Phys., 170, 265–282, 1997.
About this article
Cite this article
Shimazu, H., Vandas, M. A self-similar solution of expanding cylindrical flux ropes for any polytropic index value. Earth Planet Sp 54, 783–790 (2002). https://doi.org/10.1186/BF03351731
- Solar Wind
- Coronal Mass Ejection
- Magnetic Cloud
- Flux Rope
- Interplanetary Space