Very Fast Opening of a Three-dimensional Twisted Magnetic Flux Tube

Abstract

This Letter is devoted to the still open problem of the evolution of a three-dimensional coronal flux tube embedded in a low-beta ideal plasma and having its footpoints twisted by slow photospheric motions. Such a process has been simulated with a recently developed magnetohydrodynamic code. In the particular calculation reported here, the system occupies a large cubic box. The field is initially potential, being generated by an underlying horizontal dipole, and it is twisted by two vortices located on the lower face { z ϭ 0} of the box, on both sides of the neutral line. In a first phase, the field roughly evolves quasi-statically through a sequence of force-free configurations. Thus, it enters a dynamical phase during which it suffers a very fast expansion, closely approaching after some finite time a semiopen configuration. The energy increases monotonically during all the evolution, and it tends to a limit, which is equal to about 80% of the energy of the totally open field associated with B z .

The role of magnetic reconnection in solar activity

“…Sturrock (1991) independently presented similar arguments. Although their arguments do not constitute a rigorous proof, they are quite convincing and appear to be in good agreement with every numerical simulation performed to date [e.g., Roumeliotis, Antiochos, and Sturrock, 1994;Mikic and Linker, 1994;Amari et al, 1996], (but see Wolfson and Low (1992) for a possible counter example). The Aly-Sturrock energy limit also seems physically intuitive.…”

Global budget for an eruptive active region

“…During the process of computing α one can interpolate α from its nearest neighbors already computed in the domain Ω. The existence of solutions (Boulmezaoud & Amari 2000) being ensured, the numerical procedure used to solve BVP (1)-(4) is explained in detail in Amari et al (1996.…”

“…We note that field lines make approximately one turn about the axis between the two ends of the flux tube. Because of the large scale of this flux rope, a twist of about 2π may be considered as large enough to be close to disruption (Amari & Aly 1996; for unconfined disruption or Raadu 1972, Hood & Priest 1979, Amari & Luciani 1999, Baty 2001; for confined disruptions). One may notice that there exists another S-shaped, sheared flux tube located at a higher level in the corona which corresponds to a positive mean value of α (0.02845 Mm −1 ).…”

Simple analytical examples of boundary driven evolution of a two-dimensional magnetohydrostatic equilibrium

“…Analytical studies (Aly 1985(Aly , 1990(Aly , 1994 have shown that one of the most significant feature of such an evolution in the ideal MHD case is an indefinite expansion of the field leading asymptotically (for t → ∞) to its partial or full opening, with the formation of an infinitely thin current-sheet, a transition by reconnection to a lower energy state becoming however energetically favorable at some stage if resistivity is introduced in the model. Numerical simulations based on both dynamical and static schemes (Amari et al 1996;Choe & Lee 1996) have lead to similar conclusions, and have also provided valuable descriptions of the nonideal reconnection phase.…”