Reconnection events in two-dimensional Hall magnetohydrodynamic turbulence

Abstract

The statistical study of magnetic reconnection events in two-dimensional turbulence has been performed by comparing numerical simulations of magnetohydrodynamics (MHD) and Hall magnetohydrodynamics (HMHD). The analysis reveals that the Hall term plays an important role in turbulence, in which magnetic islands simultaneously reconnect in a complex way. In particular, an increase of the Hall parameter, the ratio of ion skin depth to system size, broadens the distribution of reconnection rates relative to the MHD case. Moreover, in HMHD the local geometry of the reconnection region changes, manifesting bifurcated current sheets and quadrupolar magnetic field structures in analogy to laminar studies, leading locally to faster reconnection processes in this case of reconnection embedded in turbulence. This study supports the idea that the global rate of energy dissipation is controlled by the large scale turbulence, but suggests that the distribution of the reconnection rates within the turbulent system is sensitive to the microphysics at the reconnection sites. V

Small-scale behavior of Hall magnetohydrodynamic turbulence

“…It is found that at small to moderate wave numbers, which can extend to scales below the ion inertial length, E M (k)/E V (k) is in near equipartition. Unlike MHD, at large wave numbers the ratio becomes magnetically dominated and scales as ǫ Current structures in HMHD are found to be narrower and more intense than in MHD, as has been noted by various other authors [46,49,51]. In particular, it is found that while current and vorticity structures have nearly equal sizes on average in MHD, in HMHD current structures become narrower and vorticity structures become broader.…”

“…Two dimensional (2D) simulations have found reconnection sites in the turbulence become similar in structure to laminar studies of HMHD reconnection which exhibit bifurcated current sheets and quadrupolar magnetic fields [51]. Dmitruk and Matthaeus [52] found that while the magnetic field was largely unchanged by the addition of the Hall effect, the electric field was more intermittent.…”

Statistical and Scaling Features of Fluctuations in the Dissipation Range During a Reconnection Event

“…A value of the connectivity index d > 0 (d = 0for a compact non-fractal set) indicates that there are topological obstacles for the current flow, so that a highly structured irregular pattern for the current is formed. These obstacles can be associated with the formation of coherent magnetic structures as observed in numerical simulations (Wu & Chang 2000;Servidio et al 2011;Donato et al 2012). We underline that the above scenario is in agreement with a coarse-grained nature of plasma media due to the formation of multiscale coherent structure as suggested by Chang (1999).…”

“…We underline that the above scenario is in agreement with a coarse-grained nature of plasma media due to the formation of multiscale coherent structure as suggested by Chang (1999). Furthermore, the above considerations support the view of a not space-filling nature of the reconnection region, which can also be relevant to overcome the inherent difficulties of the Sweet-Parker model as described in Materassi & Consolini (2007) and Donato et al (2012).…”

“…This finding supports the idea of a notspace-filling structure of the current in the dissipation region. We note that in numerous MHD and Hall-MHD simulations (see, e.g., Wu & Chang 2000;Servidio et al 2011;Donato et al 2012) there is a wide evidence for the formation of filamentary current structures from MHD scales down to scales below the ion inertial length. Furthermore, making use of the Alexander-Orbach conjecture (Alexander & Orbach 1982), which relates the fractal dimension d s of a percolating network to the connectivity exponent d˜via the fracton dimension = D 4 3, i.e.,…”