Braginskii magnetohydrodynamics for arbitrary magnetic topologies: coronal applications

We investigate single-fluid magnetohydrodynamics (MHD) with anisotropic viscosity, often referred to as Braginskii MHD, with a particular eye to solar coronal applications. First, we examine the full Braginskii viscous tensor in the single-fluid limit. We pay particular attention to how the Braginskii tensor behaves as the magnetic field strength vanishes. The solar corona contains a magnetic field with a complex and evolving topology, so the viscosity must revert to its isotropic form when the field strength is zero, e.g. at null points. We highlight that the standard form in which the Braginskii tensor is written is not suitable for inclusion in simulations as singularities in the individual terms can develop. Instead, an altered form, where the parallel and perpendicular tensors are combined, provides the required asymptotic behaviour in the weak-field limit. We implement this combined form of the tensor into the Lare3D code, which is widely used for coronal simulations. Since our main focus is the viscous heating of the solar corona, we drop the drift terms of the Braginskii tensor. In a stressed null point simulation, we discover that small-scale structures, which develop very close to the null, lead to anisotropic viscous heating at the null itself (that is, heating due to the anisotropic terms in the viscosity tensor). The null point simulation we present has a much higher resolution than many other simulations containing null points so this excess heating is a practical concern in coronal simulations. To remedy this unwanted heating at the null point, we develop a model for the viscosity tensor that captures the most important physics of viscosity in the corona: parallel viscosity for strong field and isotropic viscosity at null points. We derive a continuum model of viscosity where momentum transport, described by this viscosity model, has the magnetic field as its preferred orientation. When the field strength is zero, there is no preferred direction for momentum transport and viscosity reverts to the standard isotropic form. The most general viscous stress tensor of a (single-fluid) plasma satisfying these conditions is found. It is shown that the Braginskii model, without the drift terms, is a specialization of the general model. Performing the stressed null point simulation with this simplified model of viscosity reveals very similar heating profiles compared to the full Braginskii model. The new model, however, does not produce anisotropic heating at the null point, as required. Since the vast majority of coronal simulations use only isotropic viscosity, we perform the stressed null point simulation with isotropic viscosity and compare the heating profiles to those of the anisotropic models. It is shown than the fully isotropic viscosity can over-estimate the viscous heating by an order of magnitude

The emergence of braided magnetic fields

We study the emergence of braided magnetic fields from the top of the solar interior through to the corona. It is widely believed that emerging regions smaller than active regions are formed in the upper convection zone near the photosphere. Here, bundles of braided, rather than twisted, magnetic field can be formed, which then rise upward to emerge into the atmosphere. To test this theory, we investigate the behaviour of braided magnetic fields as they emerge into the solar atmosphere. We compare and contrast our models to previous studies of twisted flux tube emergence and discuss results that can be tested observationally. Although this is just an initial study, our results suggest that the underlying magnetic field structure of small emerging regions need not be twisted and that braided field, formed in the convection zone, could suffice

Pine Ridge Reservation Trip Email

Pine Ridge Reservation Trip Email From: Douglas L. MacTaggart To: Kevin EERC Dalsted; Mary Jo Benton EERC Lee; Dan Swets; Donald Ohlen; Hank Lehre

Magnetic helicity in multiply connected domains

Magnetic helicity is a fundamental quantity of magnetohydrodynamics that carries topological information about the magnetic field. By ‘topological information’, we usually refer to the linkage of magnetic field lines. For domains that are not simply connected, however, helicity also depends on the topology of the domain. In this paper we expand the standard definition of magnetic helicity in simply connected domains to multiply connected domains in of arbitrary topology. We also discuss how using the classic Biot–Savart operator simplifies the expression for helicity and how domain topology affects the physical interpretation of helicity

ARTop: an open-source tool for measuring active region topology at the solar photosphere

The importance of measuring topological quantities, such as magnetic helicity, in solar observations has long been recognized. In particular, topological quantities play an important role in both understanding and predicting solar eruptions. In this paper, we present ARTop (Active Region Topology), an open-source and end-to-end software tool that allows researchers to calculate the fluxes of topological quantities based on solar magnetograms. In addition to this, ARTop also allows for the efficient analysis of these quantities in both 2D maps and time series. ARTop calculates the fluxes of magnetic helicity and magnetic winding, together with particular decompositions of these quantities. To perform these calculations, SHARP magnetograms are downloaded and velocity maps are created using the DAVE4VM method. Visualization tools, written in Python, are provided to aid in the selection of appropriate output variables and for the straightforward creation of maps and time series. Additionally, other analysis functions are included to facilitate and aid solar flare investigations. This software offers researchers a powerful tool for investigating the behaviour of active regions and the origins of space weather

Direct evidence that twisted flux tube emergence creates solar active regions

The magnetic nature of the formation of solar active regions lies at the heart of understanding solar activity and, in particular, solar eruptions. A widespread model, used in many theoretical studies, simulations and the interpretation of observations, is that the basic structure of an active region is created by the emergence of a large tube of pre-twisted magnetic field. Despite plausible reasons and the availability of various proxies suggesting the accuracy of this model, there has not yet been a methodology that can clearly and directly identify the emergence of large pre-twisted magnetic flux tubes. Here, we present a clear signature of the emergence of pre-twisted magnetic flux tubes by investigating a robust topological quantity, called magnetic winding, in solar observations. This quantity detects the emerging magnetic topology despite the significant deformation experienced by the emerging magnetic field. Magnetic winding complements existing measures, such as magnetic helicity, by providing distinct information about field line topology, thus allowing for the direct identification of emerging twisted magnetic flux tubes

Homologous Flares and Magnetic Field Topology in Active Region NOAA 10501 on 20 November 2003

We present and interpret observations of two morphologically homologous flares that occurred in active region (AR) NOAA 10501 on 20 November 2003. Both flares displayed four homologous H-alpha ribbons and were both accompanied by coronal mass ejections (CMEs). The central flare ribbons were located at the site of an emerging bipole in the center of the active region. The negative polarity of this bipole fragmented in two main pieces, one rotating around the positive polarity by ~ 110 deg within 32 hours. We model the coronal magnetic field and compute its topology, using as boundary condition the magnetogram closest in time to each flare. In particular, we calculate the location of quasiseparatrix layers (QSLs) in order to understand the connectivity between the flare ribbons. Though several polarities were present in AR 10501, the global magnetic field topology corresponds to a quadrupolar magnetic field distribution without magnetic null points. For both flares, the photospheric traces of QSLs are similar and match well the locations of the four H-alpha ribbons. This globally unchanged topology and the continuous shearing by the rotating bipole are two key factors responsible for the flare homology. However, our analyses also indicate that different magnetic connectivity domains of the quadrupolar configuration become unstable during each flare, so that magnetic reconnection proceeds differently in both events.Comment: 24 pages, 10 figures, Solar Physics (accepted

Kelvin-Helmholtz instability and collapse of a twisted magnetic nullpoint with anisotropic viscosity

Context. Magnetic null points are associated with high-energy coronal phenomena such as solar flares and are often sites of reconnection and particle acceleration. Dynamic twisting of a magnetic null point can generate a Kelvin-Helmholtz instability (KHI) within its fan plane and can instigate spine-fan reconnection and an associated collapse of the null point under continued twisting. Aims. This article aims to compare the effects of isotropic and anisotropic viscosity in simulations of the KHI and collapse in a dynamically twisted magnetic null point. Methods. We performed simulations using the 3D magnetohydrodynamics code Lare3d with a custom anisotropic viscosity module. A pair of high-resolution simulations were performed, one using isotropic viscosity and another using anisotropic viscosity, keeping all other factors identical. We analysed the results in detail. A further parameter study was performed over a range of values for viscosity and resistivity. Results. Both viscosity models permit the growth of the KHI and the eventual collapse of the null point. Over all studied parameters, anisotropic viscosity allows a faster growing instability, while isotropic viscosity damps the instability to the extent of stabilisation in some cases. Although the viscous heating associated with anisotropic viscosity is generally smaller, the ohmic heating dominates and is enhanced by the current sheets generated by the instability. This leads to a greater overall heating rate when using anisotropic viscosity. The collapse of the null point occurs significantly sooner when anisotropic viscosity is employed

The Magnetic Topology of AR13664 Leading to Its First Halo CME

In the first half of May 2024, the solar active region (AR) NOAA 13664 was responsible for generating the strongest geomagnetic storm in over 20 years through an enhanced production of coronal mass ejections (CMEs). A key factor in this production was the complex magnetic topology of AR13664. In this work, we investigate the region's magnetic topology related to the production of its first halo CME on May 8th. This is achieved by combining different observations of magnetic topology based on photospheric magnetic helicity and winding signatures and nonlinear force‐free field extrapolations, together with Atmospheric Imaging Assembly observations at different wavelengths. We present evidence that the first halo CME, and its associated X1.0 flare, was created by an emerging twisted flux tube within AR13664, following the general picture of the standard flare model. The coincidence of the first large magnetic winding signature with the start time of the X1.0 flare provides the onset time for the CME as well as the period of enhanced eruptive activity of the region—04:36 UT on May 8th

Non-symmetric magnetohydrostatic equilibria: a multigrid approach

Aims. Linear magnetohydrostatic (MHS) models of solar magnetic fields balance plasma pressure gradients, gravity and Lorentz forces where the current density is composed of a linear force-free component and a cross-field component that depends on gravitational stratification. In this paper, we investigate an efficient numerical procedure for calculating such equilibria. Methods. The MHS equations are reduced to two scalar elliptic equations – one on the lower boundary and the other within the interior of the computational domain. The normal component of the magnetic field is prescribed on the lower boundary and a multigrid method is applied on both this boundary and within the domain to find the poloidal scalar potential. Once solved to a desired accuracy, the magnetic field, plasma pressure and density are found using a finite difference method. Results. We investigate the effects of the cross-field currents on the linear MHS equilibria. Force-free and non-force-free examples are given to demonstrate the numerical scheme and an analysis of speed-up due to parallelization on a graphics processing unit (GPU) is presented. It is shown that speed-ups of ×30 are readily achievable