QSL Squasher: A Fast Quasi-separatrix Layer Map Calculator

Abstract

Quasi-Separatrix Layers (QSLs) are a useful proxy for the locations where current sheets can develop in the solar corona, and give valuable information about the connectivity in complicated magnetic field configurations. However, calculating QSL maps even for 2-dimensional slices through 3-dimensional models of coronal magnetic fields is a non-trivial task as it usually involves tracing out millions of magnetic field lines with immense precision. Thus, extending QSL calculations to three dimensions has rarely been done until now. In order to address this challenge, we present QSL Squasher -a public, open-source code, which is optimized for calculating QSL maps in both two and three dimensions on GPUs. The code achieves large processing speeds for three reasons, each of which results in an orderof-magnitude speed-up. 1) The code is parallelized using OpenCL. 2) The precision requirements for the QSL calculation are drastically reduced by using perturbation theory. 3) A new boundary detection criterion between quasi-connectivity domains is used, which quickly identifies possible QSL locations which need to be finely sampled by the code. That boundary detection criterion relies on finding the locations of abrupt field-line length changes, which we do by introducing a new Field-line Length Edge (FLEDGE) map. We find FLEDGE maps useful on their own as a quick-and-dirty substitute for QSL maps. QSL Squasher allows constructing high-resolution 3D FLEDGE maps in a matter of minutes, which is two orders of magnitude faster than calculating the corresponding 3D QSL maps. We include a sample of calculations done using QSL Squasher to demonstrate its capabilities as a QSL calculator, as well as to compare QSL and FLEDGE maps.

Magnetic Nulls and Super-radial Expansion in the Solar Corona

“…The method is based on integrating a field line and calculating the field line deviation along it, δ r, from the local variations of the magnetic field vector as obtained from its local interpolation (Longcope & Strauss 1994;Titov et al 2003;Tassev & Savcheva 2017). Once δ r has been integrated along a field line, we can compute δ r ⊥ , the component of δ r perpendicular to the field line.…”

“…To evaluate the LP F , we build upon methodology developed to compute the squashing factor of magnetic flux tubes (Pariat & Démoulin 2012;Tassev & Savcheva 2017). The squashing factor is a measure of the distortion of magnetic flux tubes that provides a means of identifying quasi-separatrix layers (QSLs) in a 3D magnetic field (Demoulin et al 1996;Titov et al 2002), and has been extensively used in solar flare analysis to relate photospheric flare ribbons to the topology of the coronal magnetic field (Schmieder et al 1997;Masson et al 2009;Savcheva et al 2012a;Dalmasse et al 2015).…”

On the Magnetic Squashing Factor and the Lie Transport of Tangents

“…Yet, while the method of Tassev & Savcheva (2017) is computationally efficient, its formulation is based on a perturbative representation of the magnetic field, so it is not entirely clear what we should expect from this method in terms of accuracy. On the one hand, because the field line mapping is never stated explicitly, their method avoids the certain complications that can arise in situations where adjacent field lines are traced to different boundary surfaces.…”

“…This reduces the computational load by 40% from the Pariat method-where the latter must independently trace five 3D field line trajectories, for a total of 15 scalar elements, the former only traces one field line, plus a pair of additional tangent vectors for a total of nine scalar elements. Furthermore, Tassev & Savcheva (2017) claim that their method allows for significant relaxation of the precision requirements for field line integration, leading to further reduction in computing time.…”

“…In an attempt to alleviate this computationally intensive task, Tassev & Savcheva (2017) developed an alternate method, which is based on the construction in Pariat & Démoulin (2012), but differs in its approach to calculating the Jacobian elements, employing a transport technique similar to that of Longcope & Strauss (1994). This reduces the computational load by 40% from the Pariat method-where the latter must independently trace five 3D field line trajectories, for a total of 15 scalar elements, the former only traces one field line, plus a pair of additional tangent vectors for a total of nine scalar elements.…”