Magnetic pinching of hyperbolic flux tubes. II. Dynamic numerical model

In this paper we present the results of a series of numerical experiments that extend and supplement the recent analytical investigations by Titov et al. of the formation of strong current layers in coronal magnetic fields containing hyperbolic flux tubes (HFTs). The term "hyperbolic'' refers to the special geometrical properties of the magnetic field, whereas the topology of the field is simple; i.e., there are no magnetic null points and separatrix lines or surfaces associated with them inside the coronal volume. However, the field lines passing through a hyperbolic flux tube show a large variation in the mapping between their photospheric endpoints. On the basis of analytical estimates, it has been suggested by Titov et al. that HFTs are preferred locations for the formation of strong current layers in coronal magnetic fields with trivial topologies, provided the driving motions on the photospheric boundary are of a special type. Such motions must have shearing components that are applied across narrow HFT feet as if trying to twist it. This system of motions is then capable of causing a pinching deformation of the HFT by a sustained stagnation point flow inside the HFT. The numerical experiments presented in this paper clearly confirm this suggestion. HFTs are generic features of geometrically complex but topologically trivial magnetic fields, and therefore our results are very important for understanding magnetic reconnection in such fields, since reconnection is occurring preferentially at locations with strong current densities.