115 research outputs found
On magnetic reconnection and flux rope topology in solar flux emergence
We present an analysis of the formation of atmospheric flux ropes in a magnetohydrodynamic solar flux emergence simulation. The simulation domain ranges from the top of the solar interior to the low corona. A twisted magnetic flux tube emerges from the solar interior and into the atmosphere where it interacts with the ambient magnetic field. By studying the connectivity of the evolving magnetic field, we are able to better understand the process of flux rope formation in the solar atmosphere. In the simulation, two flux ropes are produced as a result of flux emergence. Each has a different evolution resulting in different topological structures. These are determined by plasma flows and magnetic reconnection. As the flux rope is the basic structure of the coronal mass ejection, we discuss the implications of our findings for solar eruptions
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
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
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
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From: Douglas L. MacTaggart
To: Kevin EERC Dalsted; Mary Jo Benton EERC Lee; Dan Swets; Donald Ohlen; Hank Lehre
On Signatures of Twisted Magnetic Flux Tube Emergence
Recent studies of NOAA active region 10953, by Okamoto {\it et al.} ({\it
Astrophys. J. Lett.} {\bf 673}, 215, 2008; {\it Astrophys. J.} {\bf 697}, 913,
2009), have interpreted photospheric observations of changing widths of the
polarities and reversal of the horizontal magnetic field component as
signatures of the emergence of a twisted flux tube within the active region and
along its internal polarity inversion line (PIL). A filament is observed along
the PIL and the active region is assumed to have an arcade structure. To
investigate this scenario, MacTaggart and Hood ({\it Astrophys. J. Lett.} {\bf
716}, 219, 2010) constructed a dynamic flux emergence model of a twisted
cylinder emerging into an overlying arcade. The photospheric signatures
observed by Okamoto {\it et al.} (2008, 2009) are present in the model although
their underlying physical mechanisms differ. The model also produces two
additional signatures that can be verified by the observations. The first is an
increase in the unsigned magnetic flux in the photosphere at either side of the
PIL. The second is the behaviour of characteristic photospheric flow profiles
associated with twisted flux tube emergence. We look for these two signatures
in AR 10953 and find negative results for the emergence of a twisted flux tube
along the PIL. Instead, we interpret the photospheric behaviour along the PIL
to be indicative of photospheric magnetic cancellation driven by flows from the
dominant sunspot. Although we argue against flux emergence within this
particular region, the work demonstrates the important relationship between
theory and observations for the successful discovery and interpretation of
signatures of flux emergence.Comment: 14 pages, 8 figures, accepted for publication in Solar Physic
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
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
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
3D MHD Flux Emergence Experiments: Idealized models and coronal interactions
This paper reviews some of the many 3D numerical experiments of the emergence
of magnetic fields from the solar interior and the subsequent interaction with
the pre-existing coronal magnetic field. The models described here are
idealized, in the sense that the internal energy equation only involves the
adiabatic, Ohmic and viscous shock heating terms. However, provided the main
aim is to investigate the dynamical evolution, this is adequate. Many
interesting observational phenomena are explained by these models in a
self-consistent manner.Comment: Review article, accepted for publication in Solar Physic
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