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The non-modal onset of the tearing instability  

David MacTaggart   Submitted: 2018-09-03 02:01

We investigate the onset of the classical magnetohydrodynamic (MHD) tearing instability (TI) and focus on non-modal (transient) growth rather than the tearing mode. With the help of pseudospectral theory, the operators of the linear equations are shown to be highly non-normal, resulting in the possibility of significant transient growth at the onset of the TI. This possibility increases as the Lundquist number S increases. In particular, we find evidence, numerically, that the maximum possible transient growth, measured in the L2-norm, for the classical setup of current sheets unstable to the TI, scales as O(S1/4) on time scales of O(S1/4) for S\gg 1. This behaviour is much faster than the time scale O(S1/2) when the solution behaviour is dominated by the tearing mode. The size of transient growth obtained is dependent on the form of the initial perturbation. Optimal initial conditions for the maximum possible transient growth are determined, which take the form of wave packets and can be thought of as noise concentrated at the current sheet. We also examine how the structure of the eigenvalue spectrum relates to physical quantities.

Authors: David MacTaggart
Projects: None

Publication Status: accepted for Journal of Plasma Phsyics
Last Modified: 2018-09-04 09:19
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Optimal Energy Growth in Current Sheets  

David MacTaggart   Submitted: 2017-09-14 08:21

In this paper, we investigate the possibility of transient growth in the linear perturbation of current sheets. The resistive magnetohydrodynamic (MHD) operator for a background field consisting of a current sheet is non-normal, meaning that associated eigenvalues and eigenmodes can be very sensitive to perturbation. In a linear stability analysis of a tearing current sheet, we show that modes that are damped as t\rightarrow\infty can produce transient energy growth, contributing faster growth rates and higher energy attainment (within a fixed finite time) than the unstable tearing mode found from normal-mode analysis. We determine the transient growth for tearing-stable and tearing-unstable regimes and discuss the consequences of our results for processes in the solar atmosphere, such as flares and coronal heating. Our results have significant potential impact on how fast current sheets can be disrupted. In particular, transient energy growth due to (asymptotically) damped modes may lead to accelerated current sheet thinning and, hence, a faster onset of the plasmoid instability, compared to the rate determined by the tearing mode alone.

Authors: David MacTaggart, Peter Stewart
Projects: None

Publication Status: Accepted for Solar Physics
Last Modified: 2017-09-15 10:13
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The pre-penumbral magnetic canopy in the solar atmosphere  

David MacTaggart   Submitted: 2016-10-19 02:51

Penumbrae are the manifestation of magnetoconvection in highly inclined (to the vertical direction) magnetic field. The penumbra of a sunspot tends to form, initially, along the arc of the umbra antipodal to the main region of flux emergence. The question of how highly inclined magnetic field can concentrate along the antipodal curves of umbrae, at least initially, remains to be answered. Previous observational studies have suggested the existence of some form of overlying magnetic canopy which acts as the progenitor for penumbrae. We propose that such overlying magnetic canopies are a consequence of how the magnetic field emerges into the atmosphere and are, therefore, part of the emerging region. We show, through simulations of twisted flux tube emergence, that canopies of highly inclined magnetic field form preferentially at the required locations above the photosphere.

Authors: MacTaggart, D., Guglielmino, S.L., Zuccarello, F.
Projects: None

Publication Status: Accepted by ApJL
Last Modified: 2016-10-19 13:08
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The emergence of braided magnetic fields  

David MacTaggart   Submitted: 2016-08-08 02:57

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.

Authors: Prior, C., MacTaggart, D.
Projects: None

Publication Status: accepted by GAFD
Last Modified: 2016-08-10 16:04
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The magnetic structure of surges in small-scale emerging flux regions  

David MacTaggart   Submitted: 2015-02-05 09:03

Aims. To investigate the relationship between surges and magnetic reconnection during the emergence of small-scale active regions. In particular, to examine how the large-scale geometry of the magnetic field, shaped by different phases of reconnection, guides the flowing of surges. Methods. We present three flux emergence models. The first model, and the simplest, consists of a region emerging into a horizontal ambient field that is initially parallel to the top of the emerging region. The second model is the same as the first but with an extra smaller emerging region which perturbs the main region. This is added to create a more complex magnetic topology and to test how this complicates the development of surges compared to the first model. The last model has a non-uniform ambient magnetic field to model the effects of emergence near a sunspot field and impose asymmetry on the system through the ambient magnetic field. At each stage, we trace the magnetic topology to identify the locations of reconnection. This allows for field lines to be plotted from different topological regions, highlighting how their geometry affects the development of surges. Results. In the first model, we identify distinct phases of reconnection. Each phase is associated with a particular geometry for the magnetic field and this determines the paths of the surges. The second model follows a similar pattern to the first but with a more complex magnetic topology and extra eruptions. The third model highlights how an asymmetric ambient field can result in preferred locations for reconnection, subsequently guiding the direction of surges. Conclusions. Each of the identified phases highlights the close connection between magnetic field geometry, reconnection and the flow of surges. These phases can now be detected observationally and may prove to be key signatures in determining whether or not an emerging region will produce a large-scale (CME-type) eruption.

Authors: MacTaggart, D., Guglielmino, S.L., Haynes, A.L., Simitev, R., and Zuccarello, F.
Projects:

Publication Status: Accepted for A&A
Last Modified: 2015-02-28 08:07
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The magnetic structure of surges in small-scale emerging flux regions  

David MacTaggart   Submitted: 2015-02-05 09:03

Aims. To investigate the relationship between surges and magnetic reconnection during the emergence of small-scale active regions. In particular, to examine how the large-scale geometry of the magnetic field, shaped by different phases of reconnection, guides the flowing of surges. Methods. We present three flux emergence models. The first model, and the simplest, consists of a region emerging into a horizontal ambient field that is initially parallel to the top of the emerging region. The second model is the same as the first but with an extra smaller emerging region which perturbs the main region. This is added to create a more complex magnetic topology and to test how this complicates the development of surges compared to the first model. The last model has a non-uniform ambient magnetic field to model the effects of emergence near a sunspot field and impose asymmetry on the system through the ambient magnetic field. At each stage, we trace the magnetic topology to identify the locations of reconnection. This allows for field lines to be plotted from different topological regions, highlighting how their geometry affects the development of surges. Results. In the first model, we identify distinct phases of reconnection. Each phase is associated with a particular geometry for the magnetic field and this determines the paths of the surges. The second model follows a similar pattern to the first but with a more complex magnetic topology and extra eruptions. The third model highlights how an asymmetric ambient field can result in preferred locations for reconnection, subsequently guiding the direction of surges. Conclusions. Each of the identified phases highlights the close connection between magnetic field geometry, reconnection and the flow of surges. These phases can now be detected observationally and may prove to be key signatures in determining whether or not an emerging region will produce a large-scale (CME-type) eruption.

Authors: The magnetic structure of surges in small-scale emerging flux regions MacTaggart, D., Guglielmino, S.L., Haynes, A.L., Simitev, R., and Zuccarello, F.
Projects: None

Publication Status: Accepted for A&A
Last Modified: 2015-02-06 11:50
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On magnetic reconnection and flux rope topology in solar flux emergence  

David MacTaggart   Submitted: 2013-11-26 05:39

We present an analysis of the formation of atmospheric flux ropes in a magnetohydro-dynamic (MHD) 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 fi eld, 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 diff erent evolution resulting in di fferent topological structures. These are determined by plasma flows and magnetic reconnection. As the flux rope is the basic structure of the coronal mass ejection (CME), we discuss the implications of our ndings for solar eruptions.

Authors: D. MacTaggart, A.L. Haynes
Projects: None

Publication Status: MNRAS, Submitted
Last Modified: 2013-11-26 05:41
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Non-symmetric magnetohydrostatic equilibria: a multigrid approach  

David MacTaggart   Submitted: 2013-07-23 08:36

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.

Authors: D. MacTaggart, A. Elsheikh, J. A. McLaughlin and R. D. Simitev
Projects: None

Publication Status: Published
Last Modified: 2013-07-24 11:16
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Finite deformation in Ideal MHD  

David MacTaggart   Submitted: 2012-05-21 05:43

Aims. In this paper we investigate the finite deformation of magnetic fields that can enable one to find complex analytical magnetohydrostatic (MHS) equilibria. These can be used as input to non-linear simulations. Methods. In order to find analytical equilibria, one normally has to consider simplifications or exploit a particular symmetry. Even with these measures, however, the desired equilibrium is often out of analytical reach. Here we describe a method that can work when traditional methods fail. It is based on the smooth deformation of simple magnetic fields into complex ones. Results. Examples are given, to demonstrate the method, that are of practical importance in coronal physics. This technique will prove useful in setting up the initial conditions of non-linear magnetohydrodynamic (MHD) simulations.

Authors: MacTaggart, D.
Projects:

Publication Status: accepted by A&A
Last Modified: 2012-05-22 08:56
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Simulating the ''sliding doors'' effect through magnetic flux emergence  

David MacTaggart   Submitted: 2010-05-28 06:42

Recent Hinode photospheric vector magnetogram observations (Okamoto et al. 2008, 2009) have shown the opposite polarities of a long arcade structure move apart and then come together. In addition to this ''sliding doors'' effect, orientations of horizontal magnetic fields along the polarity inversion line (PIL) on the photosphere evolve from a normal-polarity configuration to an inverse one. To explain this behaviour, a simple cartoon model suggested that it is the result of the emergence of a twisted flux rope. Here we model this scenario using a 3D MHD simulation of a twisted flux rope emerging into a pre-existing overlying arcade. We construct magnetograms from the simulation and compare them with the observations. The model produces the two signatures mentioned above. However, the cause of the ''sliding doors'' effect differs from the previous cartoon model.

Authors: David MacTaggart, Alan Hood
Projects: None

Publication Status: Accepted by ApJ Letters
Last Modified: 2010-05-29 05:26
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Multiple eruptions from magnetic flux emergence  

David MacTaggart   Submitted: 2009-10-14 07:07

In this paper we study the effects of a toroidal magnetic flux tube emerging into a magnetized corona, with an emphasis on large-scale eruptions. The orientation of the fields is such that the two flux systems are almost antiparallel when they meet. We follow the dynamic evolution of the system by solving the 3D MHD equations using a Lagrangian remap scheme. Multiple eruptions are found to occur. The physics of the trigger mechanisms are discussed and related to well-known eruption models.

Authors: D. MacTaggart, A.W. Hood
Projects: None

Publication Status: accepted by A&A
Last Modified: 2009-10-14 07:58
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On the emergence of toroidal flux tubes: general dynamics and comparisons with the cylinder model  

David MacTaggart   Submitted: 2009-09-11 12:50

In this paper we study the dynamics of toroidal flux tubes emerging from the solar interior, through the photosphere and into the corona. Many previous theoretical studies of flux emergence use a twisted cylindrical tube in the solar interior as the initial condition. Important insights can be gained from this model, however, it does have shortcomings. The axis of the tube never fully emerges as dense plasma becomes trapped in magnetic dips and restrains its ascent. Also, since the entire tube is buoyant, the main photospheric footpoints (sunspots) continually drift apart. These problems make it difficult to produce a convincing sunspot pair. We aim to address these problems by considering a different initial condition, namely a toroidal flux tube. We perform numerical experiments and solve the 3D MHD equations. The dynamics are investigated through a range of initial field strengths and twists. The experiments demonstrate that the emergence of toroidal flux tubes is highly dynamic and exhibits a rich variety of behaviour. In answer to the aims, however, if the initial field strength is strong enough, the axis of the tube can fully emerge. Also, the sunspot pair does not continually drift apart. Instead, its maximum separation is the diameter of the original toroidal tube.

Authors: David MacTaggart, Alan Hood
Projects: None

Publication Status: accepted (A&A)
Last Modified: 2009-09-14 09:37
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Can magnetic breakout be achieved from multiple flux emergence?  

David MacTaggart   Submitted: 2009-05-15 03:44

We study the breakout model using multiple flux emergence to produce the magnetic configuration and the trigger. We do not impose any artificial motions on the boundaries. Once the original flux tube configuration is chosen the system is left to evolve itself. We perform non-linear simulations in 2.5D by solving the compressible and resistive MHD equations using a Lagrangian remap, shock capturing code (Lare2D). To produce a quadrupolar configuration from flux emergence we build on previous work where the interaction of two flux tubes forms the required quadrupole. Instead of imposing a shearing flow, a third flux tube is then allowed to emerge up through the central arcade. Breakout is not achieved in any of the experiments. This is due to the interaction of the third tube with the quadrupole and the effect of the plasma beta being O(1) at the photosphere and >= O(1) in the solar interior. When beta is of these orders, flows generated in the plasma can influence the magnetic field and so photospheric footpoints do not remain fixed.

Authors: MacTaggart, D., Hood, A.W.
Projects: None

Publication Status: accepted by A&A
Last Modified: 2009-05-17 11:53
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Abstracts by Author
The non-modal onset of the tearing instability
Optimal Energy Growth in Current Sheets
The pre-penumbral magnetic canopy in the solar atmosphere
The emergence of braided magnetic fields
The magnetic structure of surges in small-scale emerging flux regions
The magnetic structure of surges in small-scale emerging flux regions
On magnetic reconnection and flux rope topology in solar flux emergence
Non-symmetric magnetohydrostatic equilibria: a multigrid approach
Finite deformation in Ideal MHD
Simulating the ''sliding doors'' effect through magnetic flux emergence
Multiple eruptions from magnetic flux emergence
On the emergence of toroidal flux tubes: general dynamics and comparisons with the cylinder model
Can magnetic breakout be achieved from multiple flux emergence?

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