arXiv subjects

D. I. Pontin

Publications and source records attributed to D. I. Pontin.

33 records · Page 2Linked to original sources

arXiv2012

Theory of magnetic reconnection in solar and astrophysical plasmas

Magnetic reconnection is a fundamental process in a plasma that facilitates the release of energy stored in the magnetic field by permitting a change in the magnetic topology. In this article we present a review of the current state of understanding of magnetic reconnection. We discuss theoretical results regarding the formation of current sheets in complex 3D magnetic fields, and describe the fundamental differences between reconnection in two and three dimensions. We go on to outline recent developments in modelling of reconnection with kinetic theory, as well as in the MHD framework where a number of new 3D reconnection regimes have been identified. We discuss evidence from observations and simulations of solar system plasmas that support this theory, and summarise some prominent locations in which this new reconnection theory is relevant in astrophysical plasmas.

astro-ph.SR↗

arXiv2011

Heating of braided coronal loops

We investigate the relaxation of braided magnetic loops in order to find out how the type of braiding via footpoint motions affects resultant heating of the loop. Two magnetic loops, braided in different ways, are used as initial conditions in resistive MHD simulations and their subsequent evolution is studied. The fields both undergo a resistive relaxation in which current sheets form and fragment and the system evolves towards a state of lower energy. In one case this relaxation is very efficient with current sheets filling the volume and homogeneous heating of the loop occurring. In the other case fewer current sheets develop, less magnetic energy is released in the process and a patchy heating of the loop results. The two cases, although very similar in their setup, can be distinguished by the mixing properties of the photospheric driver. The mixing can be measured by the topological entropy of the plasma flow, an observable quantity.

astro-ph.SR↗

arXiv2011

Generalised models for torsional spine and fan magnetic reconnection

Three-dimensional null points are present in abundance in the solar corona, and the same is likely to be true in other astrophysical environments. Recent studies suggest that reconnection at such 3D nulls may play an important role in the coronal dynamics. In this paper the properties of the torsional spine and torsional fan modes of magnetic reconnection at 3D nulls are investigated. New analytical models are developed, which for the first time include a current layer that is spatially localised around the null, extending along either the spine or the fan of the null. These are complemented with numerical simulations. The principal aim is to investigate the effect of varying the degree of asymmetry of the null point magnetic field on the resulting reconnection process - where previous studies always considered a non-generic radially symmetric null. The geometry of the current layers within which torsional spine and torsional fan reconnection occur is found to be strongly dependent on the symmetry of the magnetic field. Torsional spine reconnection still occurs in a narrow tube around the spine, but with elliptical cross-section when the fan eigenvalues are different, and with the short axis of the ellipse being along the strong field direction. The spatiotemporal peak current, and the peak reconnection rate attained, are found not to depend strongly on the degree of asymmetry. For torsional fan reconnection, the reconnection occurs in a planar disk in the fan surface, which is again elliptical when the symmetry of the magnetic field is broken. The short axis of the ellipse is along the weak field direction, with the current being peaked in these weak field regions. The peak current and peak reconnection rate in this case are clearly dependent on the asymmetry, with the peak current increasing but the reconnection rate decreasing as the degree of asymmetry is increased.

astro-ph.SR↗

arXiv2011

Steady state reconnection at a single 3D magnetic null point

To systematically stress a rotationally symmetric 3D magnetic null point by advecting the opposite footpoints of the spine axis in opposite directions. This stress eventually concentrates in the vicinity of the null point forming a local current sheet through which magnetic reconnection takes place. The aim is to look for a steady state evolution of the current sheet dynamics which may provide scaling relations for various characteristic parameters of the system. The evolution is followed by solving numerically the non-ideal MHD equations in a Cartesian domain. The null point is embedded in an initially constant density and temperature plasma. It is shown that a quasi-steady reconnection process can be set up at a 3D null by continuous shear driving. It appears that a true steady state in unlikely to be realised as the current layer tends to grow until restricted by the geometry of the computational domain and imposed driving profile. However, ratios between characteristic quantities clearly settle after some time to stable values -- so that the evolution is quasi-steady. The experiments show a number of scaling relations, but they do not provide a clear consensus for extending to lower magnetic resistivity or faster driving velocities. More investigations are needed to fully clarify the properties of current sheets at magnetic null points.

astro-ph.SR↗

arXiv2011

Three-dimensional magnetic reconnection regimes: A review

The magnetic field in many astrophysical plasmas -- such as the Solar corona and Earth's magnetosphere -- has been shown to have a highly complex, three-dimensional structure. Recent advances in theory and computational simulations have shown that reconnection in these fields also has a three-dimensional nature, in contrast to the widely used two-dimensional (or 2.5-dimensional) models. Here we discuss the underlying theory of three-dimensional magnetic reconnection. We also review a selection of new models that illustrate the current state of the art, as well as highlighting the complexity of energy release processes mediated by reconnection in complicated three-dimensional magnetic fields.

astro-ph.SR↗

arXiv2010

Dynamics of braided coronal loops II: Cascade to multiple small-scale reconnection events

Aims: Our aim is to investigate the resistive relaxation of a magnetic loop that contains braided magnetic flux but no net current or helicity. The loop is subject to line-tied boundary conditions. We investigate the dynamical processes that occur during this relaxation, in particular the magnetic reconnection that occurs, and discuss the nature of the final equilibrium. Methods: The three-dimensional evolution of a braided magnetic field is followed in a series of resistive MHD simulations. Results: It is found that, following an instability within the loop, a myriad of thin current layers forms, via a cascade-like process. This cascade becomes more developed and continues for a longer period of time for higher magnetic Reynolds number. During the cascade, magnetic flux is reconnected multiple times, with the level of this `multiple reconnection' positively correlated with the magnetic Reynolds number. Eventually the system evolves into a state with no more small-scale current layers. This final state is found to approximate a non-linear force-free field consisting of two flux tubes of oppositely-signed twist embedded in a uniform background field.

astro-ph.SR↗

arXiv2010

Dynamics of braided coronal loops - I. Onset of magnetic reconnection

The response of the solar coronal magnetic field to small-scale photospheric boundary motions including the possible formation of current sheets via the Parker scenario is one of open questions of solar physics. Here we address the problem via a numerical simulation. The three-dimensional evolution of a braided magnetic field which is initially close to a force-free state is followed using a resistive MHD code. A long-wavelength instability takes place and leads to the formation of two thin current layers. Magnetic reconnection occurs across the current sheets with three-dimensional features shown, including an elliptic magnetic field structure about the reconnection site, and results in an untwisting of the global field structure.

astro-ph.SR↗

arXiv2010

Magnetic reconnection at 3D null points: effect of magnetic field asymmetry

The aim of this paper is to investigate the properties of magnetic reconnection at a 3D null point, with respect to their dependence on the symmetry of the magnetic field around the null. In particular we examine the rate of flux transport across the null point with symmetric/asymmetric diffusion regions, as well as how the current sheet forms in time, and its properties. Mathematical modelling and finite difference resistive MHD simulations are used. It is found that the basic structure of the mode of magnetic reconnection considered is unaffected by varying the magnetic field symmetry, that is, the plasma flow is found cross both the spine and fan of the null. However, the peak intensity and dimensions of the current sheet are dependent on the symmetry/ asymmetry of the field lines. As a result, the reconnection rate is also found to be strongly dependent on the field asymmetry.

astro-ph.SR↗

arXiv2009

3D Null Point Reconnection Regimes

Recent advances in theory and computational experiments have shown the need to refine the previous categorisation of magnetic reconnection at three-dimensional null points -- points at which the magnetic field vanishes. We propose here a division into three different types, depending on the nature of the flow near the spine and fan of the null. The spine is an isolated field line which approaches the null (or recedes from it), while the fan is a surface of field lines which recede from it (or approach it). So-called "torsional spine reconnection" occurs when field lines in the vicinity of the fan rotate, with current becoming concentrated along the spine, so that nearby field lines undergo rotational slippage. In "torsional fan reconnection" field lines near the spine rotate and create a current that is concentrated in the fan with a rotational flux mismatch and rotational slippage. In both of these regimes, the spine and fan are perpendicular and there is no flux transfer across spine or fan. The third regime, called "spine-fan reconnection", is the most common in practice and combines elements of the previous spine and fan models. In this case, in response to a generic shearing motion, the null point collapses to form a current sheet that is focused at the null itself, in a sheet that locally spans both the spine and fan. In this regime the spine and fan are no longer perpendicular and there is flux transfer across both of them.

astro-ph.SR↗

arXiv2009

Magnetic Braiding and Quasi-Separatrix Layers

The squashing factor Q (Titov et al. 2002), a property of the magnetic field line mapping, has been suggested as an indicator for the formation of current sheets, and subsequently magnetic reconnection, in astrophysical plasmas. Here we test this hypothesis for a particular class of braided magnetic fields which serve as a model for solar coronal loops. We explore the relationship between Quasi-Separatrix Layers (QSLs), that is, layer-like structures with high Q value, electric currents and integrated parallel currents, the latter being a quantity closely related to the reconnection rate. It is found that as the degree of braiding of the magnetic field is increased the maximum values of Q increase exponentially. At the same time, the distribution of Q becomes increasingly filamentary, with the width of the high-Q layers exponentially decreasing. This is accompanied by an increase in the number of layers so that as the field is increasingly braided the volume becomes occupied by a myriad of thin QSLs. QSLs are not found to be good predictors of current features in this class of braided fields. Indeed, despite the presence of multiple QSLs, the current associated with the field remains smooth and large-scale under ideal relaxation; the field dynamically adjusts to a smooth equilibrium. Regions of high Q are found to be better related to regions of high integrated parallel current than to actual current sheets.

astro-ph.SR↗

arXiv2009

Lagrangian relaxation schemes for calculating force-free magnetic fields, and their limitations

Force-free magnetic fields are important in many astrophysical settings. Determining the properties of such force-free fields -- especially smoothness and stability properties -- is crucial to understanding many key phenomena in astrophysical plasmas, for example energy release processes that heat the plasma and lead to dynamic or explosive events. Here we report on a serious limitation on the computation of force-free fields that has the potential to invalidate the results produced by numerical force-free field solvers even for cases in which they appear to converge (at fixed grid resolution) to an equilibrium magnetic field. In the present work we discuss this problem within the context of a Lagrangian relaxation scheme that conserves magnetic flux and div(B) identically. Error estimates are introduced to assess the quality of the calculated equilibrium. We go on to present an algorithm, based on re-writing the curl operation via Stokes' theorem, for calculating the current which holds great promise for improving dramatically the accuracy of the Lagrangian relaxation procedure.

astro-ph.SR↗

arXiv2008

Magnetic Braiding and Parallel Electric Fields

The braiding of the solar coronal magnetic field via photospheric motions - with subsequent relaxation and magnetic reconnection -- is one of the most widely debated ideas of solar physics. We readdress the theory in the light of developments in three-dimensional magnetic reconnection theory. It is known that the integrated parallel electric field along field lines is the key quantity determining the rate of reconnection, in contrast with the two-dimensional case where the electric field itself is the important quantity. We demonstrate that this difference becomes crucial for sufficiently complex magnetic field structures. A numerical method is used to relax a braided magnetic field to an ideal force-free equilibrium; that equilibrium is found to be smooth, with only large- scale current structures. However, the equilibrium is shown to have a highly filamentary integrated parallel current structure with extremely short length- scales. An analytical model is developed to show that, in a coronal situation, the length scales associated with the integrated parallel current structures will rapidly decrease with increasing complexity, or degree of braiding, of the magnetic field. Analysis shows the decrease in these length scales will, for any finite resistivity, eventually become inconsistent with the stability of a force- free field. Thus the inevitable consequence of the magnetic braiding process is shown to be a loss of equilibrium of the coronal field, probably via magnetic reconnection events.

astro-ph↗

arXiv2007

Current sheets at three-dimensional magnetic nulls: Effect of compressibility

The nature of current sheet formation in the vicinity of three-dimensional (3D) magnetic null points is investigated. The particular focus is upon the effect of the compressibility of the plasma on the qualitative and quantitative properties of the current sheet. An initially potential 3D null is subjected to shearing perturbations, as in a previous paper [Pontin et al., Phys. Plasmas, in press (2007)]. It is found that as the incompressible limit is approached, the collapse of the null point is suppressed, and an approximately planar current sheet aligned to the fan plane is present instead. This is the case regardless of whether the spine or fan of the null is sheared. Both the peak current and peak reconnection rate are reduced. The results have a bearing on previous analytical solutions for steady-state reconnection in incompressible plasmas, implying that fan current sheet solutions are dynamically accessible, while spine current sheet solutions are not.

physics.plasm-ph↗

arXiv2007

Current sheet formation and non-ideal behaviour at three-dimensional magnetic null points

The nature of the evolution of the magnetic field, and of current sheet formation, at three-dimensional (3D) magnetic null points is investigated. A kinematic example is presented which demonstrates that for certain evolutions of a 3D null (specifically those for which the ratios of the null point eigenvalues are time-dependent) there is no possible choice of boundary conditions which renders the evolution of the field at the null ideal. Resistive MHD simulations are described which demonstrate that such evolutions are generic. A 3D null is subjected to boundary driving by shearing motions, and it is shown that a current sheet localised at the null is formed. The qualitative and quantitative properties of the current sheet are discussed. Accompanying the sheet development is the growth of a localised parallel electric field, one of the signatures of magnetic reconnection. Finally, the relevance of the results to a recent theory of turbulent reconnection is discussed.

astro-ph↗

arXiv2007

Current amplification and magnetic reconnection at a 3D null point. I - Physical characteristics

The behaviour of magnetic perturbations of an initially potential three-dimensional equilibrium magnetic null point are investigated. The basic components which constitute a typical disturbance are taken to be rotations and shears, in line with previous work. The spine and fan of the null point (the field lines which asymptotically approach or recede from the null) are subjected to such rotational and shear perturbations, using three-dimensional magnetohydrodynamic simulations. It is found that rotations of the fan plane and about the spine lead to current sheets which are spatially diffuse in at least one direction, and form in the locations of the spine and fan. However, shearing perturbations lead to 3D-localised current sheets focused at the null point itself. In addition, rotations are associated with a growth of current parallel to the spine, driving rotational flows and a type of rotational reconnection. Shears, on the other hand, cause a current through the null which is parallel to the fan plane, and are associated with stagnation-type flows and field line reconnection across both the spine and fan. The importance of the parallel electric field, and its meaning as a reconnection rate, are discussed.

astro-ph↗