| Magnetic reconnection,a topological rearrangement of magnetic field lines,is a fundamental process in plasmas.During magnetic reconnection,a conversion of magnetic energy to plasma kinetic energy occurs by way of acceleration or heating of plasma particles.Magnetic reconnection is seen in the dynamics of the Earth’s magnetosphere,in the evolution of solar flares,and is considered to occur in the formation process of stars.The typical time scales of reconnection in solar dynamic events demonstrate the existence of fast reconnection.In recent years,there have been significant new developments in reconnection theory that provide alternative and more convincing mechanisms for fast reconnection.One of them is the plasmoid instability.This super-Alfvenic instability occurs in an extended current sheet,when the Lundquist number S exceeds a critical value.The large-aspect-ratio current sheet is fragmented by birth,growing,coalescing and ejection of plasmoids.This phenomenon has been proposed as a possible mechanism for fast reconnection scenario.In the past two decades a wide variety of plasmoids observations have been presented,ranging from space and astrophysical phenomenon to magnetically confined laboratory plasmas,where there are many evidences of observational plasmoid-like features supported by direct numerical simulations.However,most previous numerical studies in plasmoid dominated reconnection,have been limited in single current sheet systems where the reconnection rate usually decreases with increasing S or is independent of S.In fact,in most real applications of reconnection,multiple current systems are mainly generated in space plasma and tokamaks.It is well known that such systems are subject to double or even triple tearing modes(DTM,or TTM).Interestingly,the interplay of adjacent current layers makes new physical regimes with different temporal and spatial scales in the whole system,which has different features from those characterized by single current sheet systems.For instance,it is shown that DTM weakly depends on the Lundquist number with a much faster reconnection rate.In this study,DTM with high Lundquist numbers has been investigated in the linear and nonlinear regimes.Indeed,the surprising scalings of the double tearing mode have been presented,within the framework of a reduced magnetohydrodynamic model in the linear regime for a high Lundquist number(S≥105),leading to onset of fast reconnection.Analytical analysis shows that if the separation of double current sheets is sufficiently small[kxs<<k2/9 SL1/3],the growth rate of DTM scales as k2/3SL0 in the non-constant-Ψ regime,where k=kLcs/2is the wave vector measured by the half length of the system Lcs/2,2xs is the separation between two resonant surfaces,and SL=LCSVA/2η is Lundquist number with VA and ηbeing Alfven velocity and resistivity,respectively.If the separation is very large[kx2>>K2/9SL1/3],the growth rate scales as K-2/5SL2/5 in the constant-Ψ regime.Furthermore,it is also analytically found that the maximum wave number scales as xs-9/7SL3/7 at the transition position between these two regimes,and the corresponding maximum growth rate scales as xs-6/7SL2/7 there.The analytically predicted scalings are verified in some limits through direct numerical calculations.Furthermore,in the fully nonlinear regime,a new physical process for the formation of plasmoids in a double current system has been reported based on a set of 2D resistive magnetohydrodynamics(MHD)simulations.This new physical process is essentially different from the result obtained directly from a single large-aspect-ratio SP current sheet.The nonlinear simulations show that due to the interaction of adjacent current layers,the DTM reconnection current layer can self-consistently change into the elongated current sheet,which is unstable to the plasmoid instability.Interestingly,it is observed that as the flux drive on the current sheet becomes very strong,the resultant growth rate of the dominant plasmoid increases with increasing Lundquist number S,thus leading to a very fast reconnection.Moreover,the continuous growth of the dominant plasmoid squeezes the DTM island so significantly that a new SP current sheet forms on the separatrix of the island,which is also unstable to plasmoid instability.Also,a fundamcental destabilization process in the nonlinear phase of double tearing mode,for different lengths of the system has been found.The primary current sheet in double current systems with large size becomes thinner and longer and breaks into multiple plasmoids.It is shown that as the system size is increased,the secondary current sheets become so long as to produce more plasmoids.It is demonstrated that dependence of the number of plasmoids on resistivity η is changed from no clear scaling for small system size to the scaling～η-1 for large system size.Moreover,increasing the current length of the system weakens the negative dependence of early growth rate of the monster plasmoid on η.This is qualitatively different from the reconnection rate for a single current sheet,where it usually has a positive dependence on η or is independent of η.In addition,increasing the current length significantly increases the maximum width of the monster plasmoid in the low-η regime,manifesting a scaling～η-0.4.Finally,the linear properties of DTMs for high Lundquist number in the presence of symmetric and anti-symmetric shear flow between the two current sheets in slab geometry have been studied.It is shown that with increasing anti-symmetric shear flow amplitude,both even and odd eigenstates of the DTM are excited dramatically.Interestingly,their corresponding growth rates γ(ky)coalesce with each other,when the wave vector ky exceeds a critical value kyc.The critical pointkyc is located in the constant-Ψ regime for the low value of shear amplitude and gradually moves into the non-constant-Ψ regime as the shear amplitude is raised.It is demonstrated thatkyc decreases with decreasing η for xs = 0.5,while decreasing x,raises the value of kyc for a fix shear velocity. |
