[1] Although the analysis of observational data indicates that quasi-separatrix layers (QSLs) of magnetic configurations have to play an important role in solar flares, the corresponding theory is only at an initial stage so far. In particular, there is still a need of a proper definition of QSLs based on a comprehensive mathematical description of magnetic connectivity. Such a definition is given here by analyzing the mapping produced by the field lines which connect photospheric areas of positive and negative magnetic polarities. It is shown that magnetic configurations may have regions, where cross sections of magnetic flux tubes are strongly squashed by this mapping. These are the geometrical features that can be identified as the QSLs. The theory is applied to quadrupole configuration to demonstrate that it may contain two QSLs combined in a special structure called hyperbolic flux tube (HFT). Both theoretical and observational arguments indicate that the HFT is a preferred site for magnetic reconnection processes in solar flares.

[1] Three-dimensional magnetohydrodynamic reconnection in a finite diffusion region is completely different in many respects from two-dimensional reconnection at an X-point. In two dimensions a magnetic flux velocity can always be defined: two flux tubes can break at a single point and rejoin to form two new flux tubes. In three dimensions we demonstrate that a flux tube velocity does not generally exist. The magnetic field lines continually change their connections throughout the diffusion region rather than just at one point. The effect of reconnection on two flux tubes is generally to split them into four flux tubes rather than to rejoin them perfectly. During the process of reconnection each of the four parts flips rapidly in a virtual flow that differs from the plasma velocity in the ideal region beyond the diffusion region.

A realistic notion of magnetic reconnection is essential to understand the dynamics of magnetic fields in plasmas. Therefore a three-dimensional reconnection process is modeled in a region of nonvanishing magnetic field and is analyzed with respect to the way in which the connection of magnetic flux is changed. The process is localized in space in the sense that the diffusion region is limited to a region of finite radius in an otherwise ideal plasma. A kinematic, stationary model is presented, which allows for analytical solutions. Aside from the well-known flipping of magnetic flux in the reconnection process, the localization requires additional features which were not present in previous two- and 2.5-dimensional models. In particular, rotational plasma flows above and below the diffusion region are found, which substantially modify the process.

Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. We investigate the evolution of field line helicity for magnetic fields that connect two boundaries without null points, with emphasis on localized finite-B magnetic reconnection. Total (relative) magnetic helicity is already recognized as an important topological constraint on magnetohydrodynamic processes. Field line helicity offers further advantages because it preserves all topological information and can distinguish between different magnetic fields with the same total helicity. Magnetic reconnection changes field connectivity and field line helicity reflects these changes; the goal of this paper is to characterize that evolution. We start by deriving the evolution equation for field line helicity and examining its terms, also obtaining a simplified form for cases where dynamics are localized within the domain. The main result, which we support using kinematic examples, is that during localized reconnection in a complex magnetic field, the evolution of field line helicity is dominated by a work-like term that is evaluated at the field line endpoints, namely, the scalar product of the generalized field line velocity and the vector potential. Furthermore, the flux integral of this term over certain areas is very small compared to the integral of the unsigned quantity, which indicates that changes of field line helicity happen in a well-organized pairwise manner. It follows that reconnection is very efficient at redistributing helicity in complex magnetic fields despite having little effect on the total helicity. V C 2015 AIP Publishing LLC.

Aims. Our aim is to investigate the resistive relaxation of a magnetic loop that contains braided magnetic flux but no net current or helicity. The loop is subject to line-tied boundary conditions. We investigate the dynamical processes that occur during this relaxation, in particular the magnetic reconnection that occurs, and discuss the nature of the final equilibrium. Methods. The three-dimensional evolution of a braided magnetic field is followed in a series of resistive MHD simulations. Results. It is found that, following an instability within the loop, a myriad of thin current layers forms, via a cascade-like process. This cascade becomes more developed and continues for a longer period of time for higher magnetic Reynolds number. During the cascade, magnetic flux is reconnected multiple times, with the level of this "multiple reconnection" positively correlated with the magnetic Reynolds number. Eventually the system evolves into a state with no more small-scale current layers. This final state is found to approximate a non-linear force-free field consisting of two flux tubes of oppositely-signed twist embedded in a uniform background field.