Abstract
The resistive MHD equations are numerically solved in two dimensions for an initial-boundary-value problem which simulates reconnection between an emerging magnetic flux region and an overlying coronal magnetic field. The emerging region is modelled by a cylindrical flux tube with a poloidal magnetic field lying in the same plane as the external, coronal field. The plasma betas of the emerging and coronal regions are 1.0 and 0.1, respectively, and the magnetic Reynolds number for the system is 2 × 103. At the beginning of the simulation the tube starts to emerge through the base of the rectangular computational domain, and, when the tube is halfway into the computational domain, its position is held fixed so that no more flux of plasma enters through the base. Because the time-scale of the emergence is slower than the Alfvén time-scale, but faster than the reconnection time-scale, a region of closed loops forms at the base. These loops are gradually opened and reconnected with the overlying, external magnetic field as time proceeds.
The evolution of the plasma can be divided into four phases as follows: First, an initial, quasi-steady phase during which most of the emergence is completed. During this phase, reconnection initially occurs at the slow rate predicted by the Sweet model of diffusive reconnection, but increases steadily until the fast rate predicted by the Petschek model of slow-shock reconnection is approached. Second, an impulsive phase with large-scale, super-magnetosonic flows. This phase appears to be triggered when the internal mechanical equilibrium inside the emerging flux tube is upset by reconnection acting on the outer layers of the flux tube. During the impulsive phase most of the flux tube pinches off from the base to form a cylindrical magnetic island, and temporarily the reconnection rate exceeds the steady-state Petschek rate. (At the time of the peak reconnection rate, the diffusion region at the X-line is not fully resolved, and so this may be a numerical artifact.) Third, a second quasi-steady phase during which the magnetic island created in the impulsive phase is slowly dissipated by continuing, but low-level, reconnection. And fourth, a static, non-evolving phase containing a potential, current-free field and virtually no flow.
During the short time in the impulsive phase when the reconnection rate exceeds the steady-state Petschek rate, a pile-up of magnetic flux at the neutral line occurs. At the same time the existing Petschek-slow-mode shocks are shed and replaced by new ones; and, for a while, both new and old sets of slow shocks coexist.
Similar content being viewed by others
References
Bayliss, A. and Turkel, E.: 1982, J. Comp. Phys. 48, 182.
Biskamp, D.: 1982, Phys. Letters A87, 357.
Boris, J. P. and Book, D. L.: 1973, J. Comp. Phys. 11, 38.
Boris, J. P. and Book, D. L.: 1976, J. Comp. Phys. 20, 397.
Canfield, R. C., Priest, E. R., and Rust, D. M.: 1974, in Y. Nakagawa and D. M. Rust (eds.), Flare-Related Magnetic Field Dynamics, NCAR, Boulder, Colo., U.S.A.
Chu, C. K.: 1978, Adv. Appl. Mech. 18, 285.
Chu, C. K. and Sereny, A.: 1974, J. Comp. Phys. 15, 476.
Forbes, T. G. and Priest, E. R.: 1982, Solar Phys. 81, 303.
Forbes, T. G. and Priest, E. R.: 1983, Solar Phys. 84, 170.
Fyfe, D., Montgomery, D., and Joyce, G.: 1977, J. Plasma Phys. 17, 369.
Glackin, D. L.: 1975, Solar Phys. 43, 317.
Han, S. M., Wu, S. T., and Nakagawa, Y.: 1982, Computer Fluids 10, 195.
Heyvaerts, J., Priest, E. R., and Rust, D. M.: 1977, Astrophys. J. 216, 123.
Kessler, T. J.: 1968, Numerical Experiments of Plane Shock Diffraction from Two-Dimensional Obstacles, MM 68–5425–24, Bell Telephone Labs, Whippany, New Jersey.
Israeli, M. and Orszag, S. A.: 1981, J. Comp. Phys. 41, 115.
Jeffrey, A. and Taniuti, T.: 1964, Non-linear Wave Propagation, Academic Press, London, p. 256.
Levy, R. H., Petschek, H. E., and Siscoe, G. L.: 1964, AIAA J. 2, 2065.
Malherbe, J. M. and Priest, E. R.: 1983, Astron. Astrophys. 123, 80.
Martin, S. and Harvey, K.: 1973, Solar Phys. 32, 389.
Martres, M. J., Michard, R., Soru-Iscovici, I., and Tsap, T.: 1968, in K. O. Kiepenheuer (ed.), ‘Structure and Development of Solar Active Regions’, IAU Symp. 35, 318.
Matthaeus, W. H.: 1982, Geophys. Res. Letters 9, 660.
Matthaeus, W. H. and Montgomery, P.: 1981, J. Plasma Phys. 25, 11.
Milne, A. M. and Priest, E. R.: 1981, Solar Phys. 73, 157.
Nakagawa, Y.: 1981a, Astrophys. J. 247, 707.
Nakagawa, Y.: 1981b, Astrophys. J. 247, 719.
Nakagawa, Y. and Steinolfson, R. S.: 1976, Astrophys. J. 207, 296.
Neidig, D. F.: 1979, Solar Phys. 61, 121.
Orlanski, I.: 1976, J. Comp. Phys. 21, 251.
Petschek, H. E.: 1964, AAS-NASA Symp. on Solar Flares, NASA SP-50, p. 344.
Priest, E. R.: 1984, in E. W. Hones, Jr. (ed.), AGU Chapman Conference on Magnetic Reconnection, Los Alamos National Laboratory, New Mexico.
Priest, E. R. and Sonnerup, B. U. Ö.: 1975, Geophys. J. Roy. Astron. Soc. 41, 405.
Rust, D. M.: 1972, Solar Phys. 25, 141.
Sato, T.: 1979, J. Geophys. Res. 84, 7177.
Sheeley, N. R. and Harvey, J. W.: 1975, Solar Phys. 45, 275.
Sonnerup, B. U. Ö.: 1970, J. Plasma Phys. 4, 161.
Sonnerup, B. U. Ö: 1973, NASA-BSFC Doc. X-639-73-193, p. 357.
Sonnerup, B. U. Ö: 1979, in L. T. Lanzerotti, C. F. Kennel, and E. N. Parker (eds.), Solar System Plasma Physics, Volume III, p. 46.
Soward, A. M. and Priest, E. R.: 1982, J. Plasma Phys. 28, 335.
Steinolfson, R. S.: 1981, J. Geophys. Res. 86, 535.
Steinolfson, R. S. and Nakagawa, Y.: 1976, Astrophys. J. 207, 300.
Sweet, P. A.: 1958, Nuovo Cimento Suppl. 8X, 188.
Tur, T. J. and Priest, E. R.: 1976, Solar Phys. 48, 89.
Tur, T. J. and Priest, E. R.: 1978, Solar Phys. 58, 181.
Vasyliunas, V. M.: 1975, Rev. Geophys. Space Phys. 13, 303.
Vorpahl, J. A.: 1973, Solar Phys. 28, 115.
Weber, W. J., Boris, J. P., and Gardner, J. J.: 1979, Computer Phys. Commun. 16, 243.
Yang, C. K. and Sonnerup, B. U. Ö.: 1976, J. Geophys. Res. 82, 4.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Forbes, T.G., Priest, E.R. Numerical simulation of reconnection in an emerging magnetic flux region. Sol Phys 94, 315–340 (1984). https://doi.org/10.1007/BF00151321
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00151321