Three-dimensional simulations of magnetic reconnection in slab geometry

Abstract

Magnetic reconnection in an incompressible plasma in three-dimensional slab geometry has been studied through magnetohydrodynamics numerical simulations. Particular attention has been paid to the case in which several unstable modes that correspond to resonant surfaces in different positions of the simulation domain, are excited at the beginning of the simulation. The dynamical evolution of such a system leads to a behavior different than what is expected from the linear theory. In particular the effects of the equilibrium field dissipation and the fact that several resonant surfaces are initially excited both concur in modifying the initial growth rates of the instability. In the nonlinear phase two basic phenomena are observed: first, the rapid transfer of energy to large wave numbers, corresponding to a direct cascade of the energy in the spectrum, which approaches, with increasing time, a power law; second, an energy transfer towards smaller wave numbers, which corresponds in the physical space to a coalescence of magnetic islands. Finally, the spectra in the periodic directions exhibit a strongly anisotropic behavior.

Three-dimensional simulations of compressible tearing instability

“…The outer region of the wave-vector space results is deprived of magnetic energy. A similar behavior was also observed by Onofri et al, 27 although in their simulations, an enlargement was observed of the anisotropy angle, which has not been observed in our simulations. One reason could be the fact that our simulations stop earlier than those of Onofri and collaborators.…”

“…As observed also by Onofri et al, 27 most of the energy is confined along a given direction, highlighted with the dashed line. The slope of this line is given by the condition k z = ±k x and corresponds to the resonance condition k · B 0 =0.…”

“…This seems to contradict Squire's theorem, 39,40 which states that for any three-dimensional eigenmode there is a related two-dimensional eigenmode that is more unstable. A similar observation was made by Onofri et al 27 in their incompressible simulations, and they suggest that this behavior can be due to nonlinear effects, namely the coupling of the initially excited Fourier harmonics. A twodimensional contour plot of the magnetic energy spectrum in the ͑k x , k z ͒ plane during the linear phase for all three cases considered here ͑Fig.…”

“…As conjectured by Dahlburg and Einaudi 18 and shown numerically by Onofri et al, 27 the presence of a guide field, i.e., of a homogeneous magnetic field aligned with the current density vector, has a stabilizing effect for the developing of the secondary instability. Our numerical simulations confirm that this is true also in the compressible case, independently of the plasma beta adopted: the nonlinear evolution of such a configuration leads to the formation of magnetic islands that coalesce afterward.…”

“…18 3D incompressible MHD simulations of the tear-ing instability have shown that the presence of a guide field makes the evolution more similar to that observed in the 2D configuration. 27 The simulations show a 2D behavior at large scales ͑formation of magnetic island with increasing size͒ and 3D structuring with current filamentation at smaller scale. More recently, Dahlburg et al 28 studied the linear and nonlinear evolution of a current sheet where a guide field is present.…”