Quasi-separatrix layers and three-dimensional reconnection diagnostics for line-tied tearing modes

In three-dimensional magnetic configurations for a plasma in which no closed field line or magnetic null exists, no magnetic reconnection can occur, by the strictest definition of reconnection. A finitely long pinch with line-tied boundary conditions, in which all the magnetic field lines start at one end of the system and proceed to the opposite end, is an example of such a system. Nevertheless, for a long system of this type, the physical behavior in resistive magnetohydrodynamics (MHD) essentially involves reconnection. This has been explained in terms comparing the geometric and tearing widths [1] and [2]. The concept of a quasi-separatrix layer [3] and [4] was developed for such systems. In this paper we study a model for a line-tied system in which the corresponding periodic system has an unstable tearing mode. We analyze this system in terms of two magnetic field line diagnostics, the squashing factor [5], [6] and [7] and the electrostatic potential difference [8] and [9] which has been used in kinematic reconnection studies. We discuss the physical and geometric significance of these two diagnostics and compare them in the context of discerning tearing-like (reconnection-like) behavior in line-tied modes.

► We study a model of line-tied MHD modes, with no nulls or closed field lines.
► We analyze quasi-separatrix layers, the squashing factor, and two scalar potentials.
► Comparing the potentials distinguishes cases with and without magnetic reconnection.
► These cases are distinguished in terms of the tearing width and the geometric width.
► The squashing degree detects magnetic configurations with potential for reconnection.