pontin

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Author name code: pontin
ADS astronomy entries on 2022-09-14
author:"Pontin, David I."

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Title: Magnetic reconnection: MHD theory and modelling
Authors: Pontin, David I.; Priest, Eric R.
2022LRSP...19....1P Altcode:
In this review we focus on the fundamental theory of magnetohydrodynamic
reconnection, together with applications to understanding a wide range
of dynamic processes in the solar corona, such as flares, jets, coronal
mass ejections, the solar wind and coronal heating. We summarise
only briefly the related topics of collisionless reconnection,
non-thermal particle acceleration, and reconnection in systems
other than the corona. We introduce several preliminary topics
that are necessary before the subtleties of reconnection can be
fully described: these include null points (Sects. 2.1-2.2), other
topological and geometrical features such as separatrices, separators
and quasi-separatrix layers (Sects. 2.3, 2.6), the conservation
of magnetic flux and field lines (Sect. 3), and magnetic helicity
(Sect. 4.6). Formation of current sheets in two- and three-dimensional
fields is reviewed in Sect. 5. These set the scene for a discussion of
the definition and properties of reconnection in three dimensions that
covers the conditions for reconnection, the failure of the concept of
a flux velocity, the nature of diffusion, and the differences between
two-dimensional and three-dimensional reconnection (Sect. 4). Classical
2D models are briefly presented, including magnetic annihilation
(Sect. 6), slow and fast regimes of steady reconnection (Sect. 7),
and non-steady reconnection such as the tearing mode (Sect. 8). Then
three routes to fast reconnection in a collisional or collisionless
medium are described (Sect. 9). The remainder of the review is
dedicated to our current understanding of how magnetic reconnection
operates in three dimensions and in complex magnetic fields such as
that of the Sun's corona. In Sects. 10-12, 14.1 the different regimes
of reconnection that are possible in three dimensions are summarised,
including at a null point, separator, quasi-separator or a braid. The
role of 3D reconnection in solar flares (Sect. 13) is reviewed, as
well as in coronal heating (Sect. 14), and the release of the solar
wind (Sect. 15.2). Extensions including the role of reconnection in the
magnetosphere (Sect. 15.3), the link between reconnection and turbulence
(Sect. 16), and the role of reconnection in particle acceleration
(Sect. 17) are briefly mentioned.

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Title: Quantifying magnetic reconnection in the Solar corona
Authors: Aslanyan, Valentin; Pontin, David; Wyper, Peter; Antiochos,
Spiro; Scott, Roger; Higginson, Aleida
2022cosp...44.1495A Altcode:
Magnetic reconnection is understood to have important effects on
the dynamics of the Solar atmosphere, including those that lead
to the formation of the slow Solar wind. Of particular importance
is interchange reconnection between very long "open" field lines
emerging from coronal holes into the heliosphere and shorter "closed"
field lines between two points on the photosphere. We have used the
Adaptively Refined Magnetohydrodynamic Solver to perform a number of
simulations of the global corona with varying magnetic geometries,
from which we subsequently determine regions where reconnection has
taken place. Energy is injected into the magnetic field by plasma
flows at the photosphere which transport the footpoints of field
lines. We find that the total reconnected magnetic flux of numerous
localized vortices representing supergranules exceeds that of a global
differential rotation profile. We also find systematic differences in
the interchange reconnection rates based on the length of the closed
field lines involved. Our simulations show that shorter closed field
lines of pseudostreamers reconnect more readily than the longer field
lines of helmet streamers. Consequently, we predict smoother coronal
hole boundaries in the vicinity of pseudostreamers than other coronal
structures. We have identified signatures of these processes which
may be detected both remotely and in-situ by spacecraft such as the
Solar Dynamics Observatory, Parker Solar Probe, and Solar Orbiter.

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Title: Parallel Plasma Loops and the Energization of the Solar Corona
Authors: Peter, Hardi; Chitta, Lakshmi Pradeep; Chen, Feng; Pontin,
David I.; Winebarger, Amy R.; Golub, Leon; Savage, Sabrina L.;
Rachmeler, Laurel A.; Kobayashi, Ken; Brooks, David H.; Cirtain,
Jonathan W.; De Pontieu, Bart; McKenzie, David E.; Morton, Richard J.;
Testa, Paola; Tiwari, Sanjiv K.; Walsh, Robert W.; Warren, Harry P.
2022ApJ...933..153P Altcode: 2022arXiv220515919P
The outer atmosphere of the Sun is composed of plasma heated to
temperatures well in excess of the visible surface. We investigate
short cool and warm (&lt;1 MK) loops seen in the core of an active
region to address the role of field-line braiding in energizing these
structures. We report observations from the High-resolution Coronal
imager (Hi-C) that have been acquired in a coordinated campaign with
the Interface Region Imaging Spectrograph (IRIS). In the core of the
active region, the 172 Å band of Hi-C and the 1400 Å channel of IRIS
show plasma loops at different temperatures that run in parallel. There
is a small but detectable spatial offset of less than 1″ between
the loops seen in the two bands. Most importantly, we do not see
observational signatures that these loops might be twisted around each
other. Considering the scenario of magnetic braiding, our observations
of parallel loops imply that the stresses put into the magnetic field
have to relax while the braiding is applied: the magnetic field never
reaches a highly braided state on these length scales comparable to
the separation of the loops. This supports recent numerical 3D models
of loop braiding in which the effective dissipation is sufficiently
large that it keeps the magnetic field from getting highly twisted
within a loop.

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Title: The Dynamic Structure of Coronal Hole Boundaries
Authors: Aslanyan, V.; Pontin, D. I.; Scott, R. B.; Higginson, A. K.;
Wyper, P. F.; Antiochos, S. K.
2022ApJ...931...96A Altcode:
The boundaries of solar coronal holes are difficult to uniquely
define observationally but are sites of interest in part because the
slow solar wind appears to originate there. The aim of this article
is to explore the dynamics of interchange magnetic reconnection
at different types of coronal hole boundaries-namely streamers and
pseudostreamers-and their implications for the coronal structure. We
describe synthetic observables derived from three-dimensional
magnetohydrodynamic simulations of the atmosphere of the Sun in which
coronal hole boundaries are disturbed by flows that mimic the solar
supergranulation. Our analysis shows that interchange reconnection takes
place much more readily at the pseudostreamer boundary of the coronal
hole. As a result, the portion of the coronal hole boundary formed by
the pseudostreamer remains much smoother, in contrast to the highly
distorted helmet-streamer portion of the coronal hole boundary. Our
results yield important new insights on coronal hole boundary regions,
which are critical in coupling the corona to the heliosphere as the
formation regions of the slow solar wind.

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Title: The Dynamic Coupling of Streamers and Pseudostreamers to
the Heliosphere
Authors: Aslanyan, V.; Pontin, D. I.; Higginson, A. K.; Wyper, P. F.;
Scott, R. B.; Antiochos, S. K.
2022ApJ...929..185A Altcode: 2022arXiv220102388A
The slow solar wind is generally believed to result from the
interaction of open and closed coronal magnetic flux at streamers
and pseudostreamers. We use three-dimensional magnetohydrodynamic
simulations to determine the detailed structure and dynamics of
open-closed interactions that are driven by photospheric convective
flows. The photospheric magnetic field model includes a global dipole
giving rise to a streamer together with a large parasitic polarity
region giving rise to a pseudostreamer that separates a satellite
coronal hole from the main polar hole. Our numerical domain extends
out to 30R ⊙ and includes an isothermal solar wind,
so that the coupling between the corona and heliosphere can be
calculated rigorously. This system is driven by imposing a large set
of quasi-random surface flows that capture the driving of coronal
flux in the vicinity of streamer and pseudostreamer boundaries by
the supergranular motions. We describe the resulting structures and
dynamics. Interchange reconnection dominates the evolution at both
streamer and pseudostreamer boundaries, but the details of the resulting
structures are clearly different from one another. Additionally,
we calculate in situ signatures of the reconnection and determine
the dynamic mapping from the inner heliosphere back to the Sun for a
test spacecraft orbit. We discuss the implications of our results for
interpreting observations from inner heliospheric missions, such as
Parker Solar Probe and Solar Orbiter, and for space weather modeling
of the slow solar wind.

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Title: Spatially Separated Electron and Proton Beams in a Simulated
Solar Coronal Jet
Authors: Pallister, Ross; Wyper, Peter F.; Pontin, David I.; DeVore,
C. Richard; Chiti, Federica
2021ApJ...923..163P Altcode:
Magnetic reconnection is widely accepted to be a major contributor to
nonthermal particle acceleration in the solar atmosphere. In this paper
we investigate particle acceleration during the impulsive phase of a
coronal jet, which involves bursty reconnection at a magnetic null
point. A test-particle approach is employed, using electromagnetic
fields from a magnetohydrodynamic simulation of such a jet. Protons
and electrons are found to be accelerated nonthermally both downwards
toward the domain's lower boundary and the solar photosphere, and
outwards along the axis of the coronal jet and into the heliosphere. A
key finding is that a circular ribbon of particle deposition on the
photosphere is predicted, with the protons and electrons concentrated
in different parts of the ribbon. Furthermore, the outgoing protons
and electrons form two spatially separated beams parallel to the axis
of the jet, signatures that may be observable in in-situ observations
of the heliosphere.

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Title: Magnetic reconnection and the Kelvin-Helmholtz instability
in the solar corona
Authors: Howson, T. A.; De Moortel, I.; Pontin, D. I.
2021A&A...656A.112H Altcode: 2021arXiv210915019H
Context. The magnetic Kelvin-Helmholtz instability (KHI) has been
proposed as a means of generating magnetohydrodynamic turbulence
and encouraging wave energy dissipation in the solar corona,
particularly within transversely oscillating loops. Aims:
Our goal is to determine whether the KHI encourages magnetic
reconnection in oscillating flux tubes in the solar corona. This will
establish whether the instability enhances the dissipation rate of
energy stored in the magnetic field. Methods: We conducted a
series of three-dimensional magnetohydrodynamic simulations of the
KHI excited by an oscillating velocity shear. We investigated the
effects of numerical resolution, field line length, and background
currents on the growth rate of the KHI and on the subsequent rate
of magnetic reconnection. Results: The KHI is able to trigger
magnetic reconnection in all cases, with the highest rates occurring
during the initial growth phase. Reconnection is found to occur
preferentially along the boundaries of Kelvin-Helmholtz vortices,
where the shear in the velocity and magnetic fields is greatest. The
estimated rate of reconnection is found to be lowest in simulations
where the KHI growth rate is reduced. For example, this is the case
for shorter field lines or due to shear in the background field. 
Conclusions: In non-ideal regimes, the onset of the instability causes
the local reconnection of magnetic field lines and enhances the rate
of coronal wave heating. However, we found that if the equilibrium
magnetic field is sheared across the Kelvin-Helmholtz mixing layer,
the instability does not significantly enhance the rate of reconnection
of the background field, despite the free energy associated with the
non-potential field.

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Title: Is Flare Ribbon Fine Structure Related to Tearing in the
Flare Current Sheet?
Authors: Wyper, P. F.; Pontin, D. I.
2021ApJ...920..102W Altcode: 2021arXiv210810966W
Observations of solar flare ribbons show significant fine structure in
the form of breaking wavelike perturbations and spirals. The origin of
this structure is not well understood, but one possibility is that it
is related to the tearing instability in the flare current sheet. Here
we study this connection by constructing an analytical 3D magnetic
field representative of an erupting flux rope with a flare current
sheet below it. We introduce small-scale flux ropes representative of
those formed during a tearing instability in the current layer, and
use the squashing factor on the solar surface to identify the shape of
the presumed flare ribbons and fine structure. Our analysis suggests
there is a direct link between flare ribbon fine structure and flare
current sheet tearing, with the majority of the ribbon fine structure
related to oblique tearing modes. Depending upon the size, location,
and twist of the small-scale flux ropes, breaking wavelike and spiral
features within the hooks and straight sections of the flare ribbon
can be formed that are qualitatively similar to observations. We also
show that the handedness of the spirals/waves must be the same as the
handedness of the hooks of the main ribbon. We conclude that tearing
in the flare current layer is a likely explanation for spirals and
wavelike features in flare ribbons.

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Title: GLEMuR: GPU-based Lagrangian mimEtic Magnetic Relaxation
Authors: Candelaresi, Simon; Pontin, David; Hornig, Gunnar
2021ascl.soft06019C Altcode:
GLEMuR (Gpu-based Lagrangian mimEtic Magnetic Relaxation) is a finite
difference Lagrangian code which uses mimetic differential operators
and runs on Nvidia GPUs. Its main purpose is to study the relaxation of
magnetic relaxation in environments of zero resistivity and viscosity;
it preserves the magnetic flux and the topology of magnetic field
lines. The use of mimetic operators for the spatial derivatives improve
accuracy for high distortions of the grid, and the final state of the
simulation approximates a force-free state with a significantly higher
accuracy. Note, however, that GLEMuR is not a general purpose equation
solver and the full magnetohydrodynamics equations are not implemented.

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Title: The Dynamic Formation of Pseudostreamers
Authors: Scott, R. B.; Pontin, D. I.; Antiochos, S. K.; DeVore, C. R.;
Wyper, P. F.
2021AAS...23832818S Altcode:
Streamers and pseudostreamers structure the corona at the largest
scales, as seen in both eclipse and coronagraph white-light
images. Their inverted-goblet appearance encloses broad coronal
loops at the Sun and tapers to a narrow radial stalk away from the
star. The streamer associated with the global solar dipole magnetic
field is long-lived, predominantly contains a single arcade of nested
loops within it, and separates opposite-polarity interplanetary
magnetic fields with the heliospheric current sheet anchored at
its apex. Pseudostreamers, on the other hand, are transient, enclose
double arcades of nested loops, and separate like-polarity fields with
a dense plasma sheet. We use numerical magnetohydrodynamic simulations
to calculate, for the first time, the formation of pseudostreamers in
response to photospheric magnetic-field evolution. Convective transport
of a minority-polarity flux concentration, initially positioned under
one side of a streamer, through the streamer boundary into the adjacent,
pre-existing coronal hole forms the pseudostreamer. Interchange
magnetic reconnection at the overlying coronal null point(s)
governs the development of the pseudostreamer above - and of a new,
satellite coronal hole behind - the moving minority polarity. The
reconnection dynamics liberate coronal-loop plasma that can escape
into the heliosphere along so-called separatrix-web ("S-Web") arcs,
which reach far from the heliospheric current sheet and the solar
equatorial plane, and can explain the origin of high-latitude slow
solar wind. We describe the implications of our results for in-situ and
remote-sensing observations of the corona and heliosphere as obtained,
most recently, by Parker Solar Probe and Solar Orbiter.

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Title: The Dynamic Formation of Pseudostreamers
Authors: Scott, Roger B.; Pontin, David I.; Antiochos, Spiro K.;
DeVore, C. Richard; Wyper, Peter F.
2021ApJ...913...64S Altcode:
Streamers and pseudostreamers structure the corona at the largest
scales, as seen in both eclipse and coronagraph white-light
images. Their inverted-goblet appearance encloses broad coronal loops
at the Sun and tapers to a narrow radial stalk away from the star. The
streamer associated with the global solar dipole magnetic field is
long-lived, predominantly contains a single arcade of nested loops
within it, and separates opposite-polarity interplanetary magnetic
fields with the heliospheric current sheet (HCS) anchored at its
apex. Pseudostreamers, on the other hand, are transient, enclose double
arcades of nested loops, and separate like-polarity fields with a
dense plasma sheet. We use numerical magnetohydrodynamic simulations
to calculate, for the first time, the formation of pseudostreamers in
response to photospheric magnetic-field evolution. Convective transport
of a minority-polarity flux concentration, initially positioned
under one side of a streamer, through the streamer boundary into the
adjacent preexisting coronal hole forms the pseudostreamer. Interchange
magnetic reconnection at the overlying coronal null point(s) governs the
development of the pseudostreamer above—and of a new satellite coronal
hole behind—the moving minority polarity. The reconnection dynamics
liberate coronal-loop plasma that can escape into the heliosphere
along so-called separatrix-web ("S-Web") arcs, which reach far from
the HCS and the solar equatorial plane, and can explain the origin
of high-latitude slow solar wind. We describe the implications of
our results for in situ and remote-sensing observations of the corona
and heliosphere as obtained, most recently, by Parker Solar Probe and
Solar Orbiter.

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Title: Effects of Pseudostreamer Boundary Dynamics on Heliospheric
Field and Wind
Authors: Aslanyan, V.; Pontin, D. I.; Wyper, P. F.; Scott, R. B.;
Antiochos, S. K.; DeVore, C. R.
2021ApJ...909...10A Altcode:
Interchange reconnection has been proposed as a mechanism for the
generation of the slow solar wind, and a key contributor to determining
its characteristic qualities. In this paper we study the implications
of interchange reconnection for the structure of the plasma and field
in the heliosphere. We use the Adaptively Refined Magnetohydrodynamic
Solver to simulate the coronal magnetic evolution in a coronal topology
containing both a pseudostreamer and helmet streamer. We begin with
a geometry containing a low-latitude coronal hole that is separated
from the main polar coronal hole by a pseudostreamer. We drive the
system by imposing rotating flows at the solar surface within and
around the low-latitude coronal hole, which leads to a corrugation
(at low altitudes) of the separatrix surfaces that separate open from
closed magnetic flux. Interchange reconnection is induced both at the
null points and separators of the pseudostreamer, and at the global
helmet streamer. We demonstrate that a preferential occurrence of
interchange reconnection in the "lanes" between our driving cells leads
to a filamentary pattern of newly opened flux in the heliosphere. These
flux bundles connect to but extend far from the separatrix-web (S-Web)
arcs at the source surface. We propose that the pattern of granular
and supergranular flows on the photosphere should leave an observable
imprint in the heliosphere.

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Title: A constellation of nanosatellites for geodesy, space weather
and radio occultation experiment: An Australian example from Spire
Global CubeSats
Authors: Han, Shin-Chan; Waters, Colin; Pontin, David; McClusky,
Simon; Tao, Li; Papanikolaou, Thomas
2021cosp...43E..54H Altcode:
The recent paradigm shift in space technology (miniaturized sensors,
smaller spacecrafts, affordable launches) opens accessibility
to space at unprecedented levels. Many ground-breakings ways of
utilizing space-borne platforms will be sought after in order to enable
space-based solutions to many national and global problems in the Earth
system change. One of the important issues for the Australian space
and radio science and defence is to monitor and forecast space weather
events. Space weather influences performance, efficiency and reliability
of technological infrastructure. Irregularities in ionospheric plasma
density, particularly at lower latitudes, may produce adversary
effects on navigation, communications and surveillance systems in
Australia. Spire Global has been pioneering small satellite technology
for maritime, aviation and weather forecasting applications. With their
successful launch and operation of a constellation of 3U CubeSats
equipped with dual frequency GNSS receivers as one of the payloads,
Spire Global has demonstrated its leadership in the space-borne
Earth Observation industry. Unprecedentedly massive sampling of GNSS
measurements over the globe for improved weather forecasting became
feasible. In this paper, we will present the results of analyzing
sample dual frequency GNSS tracking data from the CubeSat constellation
provided by Spire Global, with the focus on retrieving and validating
Total Electron Content (TEC) over the Australian continent and precise
kinematic trajectory for gravity and geodesy experiment. We will share
what we have learned from analysing Spire Global data to demonstrate
the feasibility of using a small, low-powered, dual frequency GNSS
receivers for Earth Observation.

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Title: New observational support for the role of magnetic field line
braiding in solar coronal heating
Authors: Pontin, David; Peter, Hardi; Yeates, Anthony; Pradeep Chitta,
L.; Candelaresi, Simon; Hornig, Gunnar; Bushby, Paul
2021cosp...43E1796P Altcode:
We present here new work that links models of magnetic field line
braiding in coronal loops to observations of the photosphere and
corona. We describe analysis of photospheric flows that quantifies the
rate at which coronal magnetic field lines are braided. The results
suggest that the photospheric motions induce complex tangling of the
coronal field on a timescale of minutes to hours. New data from DKIST
promises to further improve such estimates. Theoretical models show that
this persistent tangling inevitably leads to the onset of reconnection
and a turbulent heating of the plasma in the corona. We go on to
describe synthetic emissions in a 3D magnetohydrodynamic model of the
turbulent decay of an initially-braided magnetic field. We discuss how
previously unexplained key features of observed emission line profiles
in coronal loops - such as non-thermal widths and non-Gaussian profiles
- are reproduced in the synthesised spectra.

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Title: Interchange reconnection and the structure of the boundary
between open and closed magnetic flux in the corona
Authors: Pontin, David; Wyper, Peter; Scott, Roger
2021cosp...43E1804P Altcode:
The boundary between open and closed magnetic flux in the corona is one
proposed source region for the slow solar wind. The magnetic topology
there is thought to be important in determining the dynamics, for
example in the "S-web" slow wind model. Here we describe an algorithm
to analyse the magnetic structures that form the boundary between
open and closed magnetic flux on the Sun, and describe the results of
implementing that algorithm on a set of coronal field extrapolations. We
discuss the consequences of interchange reconnection at this boundary
in a fragmented current layer, showing that it leads to efficient mixing
of plasma from open and closed field regions. The associated separatrix
arc of the S-web in the high corona becomes a highly-structured mixture
of open and previously-closed-field-plasma, with implications for in
situ measurements by Parker Solar Probe and Solar Orbiter.

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Title: A comparison of methods for finding magnetic nulls in
simulations and in situ observations of space plasmas
Authors: Olshevsky, V.; Pontin, D. I.; Williams, B.; Parnell, C. E.;
Fu, H. S.; Liu, Y.; Yao, S.; Khotyaintsev, Y. V.
2020A&A...644A.150O Altcode: 2021arXiv210102014O
Context. Magnetic nulls are ubiquitous in space plasmas, and are
of interest as sites of localised energy dissipation or magnetic
reconnection. As such, a number of methods have been proposed for
detecting nulls in both simulation data and in situ spacecraft data
from Earth's magnetosphere. The same methods can be applied to detect
stagnation points in flow fields. Aims: In this paper we describe
a systematic comparison of different methods for finding magnetic
nulls. The Poincaré index method, the first-order Taylor expansion
(FOTE) method, and the trilinear method are considered. Methods:
We define a magnetic field containing fourteen magnetic nulls whose
positions and types are known to arbitrary precision. Furthermore,
we applied the selected techniques in order to find and classify
those nulls. Two situations are considered: one in which the magnetic
field is discretised on a rectangular grid, and the second in which the
magnetic field is discretised along synthetic "spacecraft trajectories"
within the domain. Results: At present, FOTE and trilinear are
the most reliable methods for finding nulls in the spacecraft data
and in numerical simulations on Cartesian grids, respectively. The
Poincaré index method is suitable for simulations on both tetrahedral
and hexahedral meshes. Conclusions: The proposed magnetic field
configuration can be used for grading and benchmarking the new and
existing tools for finding magnetic nulls and flow stagnation points.

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Title: The Parker problem: existence of smooth force-free fields
and coronal heating
Authors: Pontin, David I.; Hornig, Gunnar
2020LRSP...17....5P Altcode:
Parker (Astrophys J 174:499, 1972) put forward a hypothesis regarding
the fundamental nature of equilibrium magnetic fields in astrophysical
plasmas. He proposed that if an equilibrium magnetic field is subjected
to an arbitrary, small perturbation, then—under ideal plasma
dynamics—the resulting magnetic field will in general not relax
towards a smooth equilibrium, but rather, towards a state containing
tangential magnetic field discontinuities. Even at astrophysical plasma
parameters, as the singular state is approached dissipation must
eventually become important, leading to the onset of rapid magnetic
reconnection and energy dissipation. This topological dissipation
mechanism remains a matter of debate, and is a key ingredient in the
nanoflare model for coronal heating. We review the various theoretical
and computational approaches that have sought to prove or disprove
Parker's hypothesis. We describe the hypothesis in the context of
coronal heating, and discuss different approaches that have been taken
to investigating whether braiding of magnetic field lines is responsible
for maintaining the observed coronal temperatures. We discuss the many
advances that have been made, and highlight outstanding open questions.

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Title: Non-thermal line broadening due to braiding-induced turbulence
in solar coronal loops
Authors: Pontin, D. I.; Peter, H.; Chitta, L. P.
2020A&A...639A..21P Altcode: 2020arXiv200811915P
 Aims: Emission line profiles from solar coronal loops exhibit
properties that are unexplained by current models. We investigate
the non-thermal broadening associated with plasma heating in coronal
loops that is induced by magnetic field line braiding. Methods:
We describe the coronal loop by a 3D magnetohydrodynamic model of
the turbulent decay of an initially-braided magnetic field. From
this, we synthesised the Fe XII line at 193 Å that forms around
1.5 MK. Results: The key features of current observations of
extreme ultraviolet (UV) lines from the corona are reproduced in the
synthesised spectra: (i) Typical non-thermal widths range from 15 to
20 km s-1. (ii) The widths are approximately independent
of the size of the field of view. (iii) There is a correlation between
the line intensity and non-thermal broadening. (iv) Spectra are found
to be non-Gaussian, with enhanced power in the wings of the order
of 10-20%. Conclusions: Our model provides an explanation
that self-consistently connects the heating process to the observed
non-thermal line broadening. The non-Gaussian nature of the spectra
is a consequence of the non-Gaussian nature of the underlying velocity
fluctuations, which is interpreted as a signature of intermittency in
the turbulence.

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Title: SOTE: A Nonlinear Method for Magnetic Topology Reconstruction
in Space Plasmas
Authors: Liu, Y. Y.; Fu, H. S.; Olshevsky, V.; Pontin, D. I.; Liu,
C. M.; Wang, Z.; Chen, G.; Dai, L.; Retino, A.
2019ApJS..244...31L Altcode:
Complex magnetic structures are ubiquitous in turbulent astrophysical
plasmas. Such structures can be host to many dynamic processes,
such as magnetic reconnection and energy dissipation. Thus,
revealing the 3D topologies of these structures is necessary. In
this study, we propose a new method to reconstruct complex magnetic
topologies in quasi-steady space plasmas, by utilizing eight-point
measurements of magnetic fields and particles. Such a method, based
on the Second-Order Taylor Expansion (SOTE) of a magnetic field, is
nonlinear; it is constrained by {{\nabla }}\cdot {\boldsymbol{B}}=0 and
{{\nabla }}× {\boldsymbol{B}}={μ }0{\boldsymbol{J}}, where
{\boldsymbol{J}}={ne}({{\boldsymbol{V}}}{\boldsymbol{i}}-{{\boldsymbol{V}}}{\boldsymbol{e}})
is from particle moments. A benchmark test of this method,
using the simulation data, shows that the method can give accurate
reconstruction results within an area about three times the size of a
spacecraft tetrahedron. By comparing to the previous First-Order Taylor
Expansion (FOTE) method, this method (SOTE) gives similar results for
reconstructing quasilinear structures but exhibits better accuracy in
reconstructing nonlinear structures. Such a method will be useful to
the multi-scale missions, such as the future European Space Agency's
“cross-scale” mission and China's “self-adaptive” mission. Also,
it can be applied to four-point missions, such as Cluster and the
Magnetospheric Multiscale Mission. We demonstrated how to apply this
method to the four-point missions. In principle, this method will
be useful to study shocks, magnetic holes, dipolarization fronts,
and other nonlinear structures in space plasmas.

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Title: Do Current and Magnetic Helicities Have the Same Sign?
Authors: Russell, A. J. B.; Demoulin, P.; Hornig, G.; Pontin, D. I.;
Candelaresi, S.
2019ApJ...884...55R Altcode:
Current helicity, H c , and magnetic helicity, H 
m , are two main quantities used to characterize magnetic
fields. For example, such quantities have been widely used
to characterize solar active regions and their ejecta (magnetic
clouds). It is commonly assumed that H c and H m
 have the same sign, but this has not been rigorously addressed
beyond the simple case of linear force-free fields. We aim to answer
whether H m H c ≥ 0 in general, and whether
it is true over some useful set of magnetic fields. This question is
addressed analytically and with numerical examples. The main focus is on
cylindrically symmetric straight flux tubes, referred to as flux ropes
(FRs), using the relative magnetic helicity with respect to a straight
(untwisted) reference field. Counterexamples with H m H
 c &lt; 0 have been found for cylindrically symmetric FRs
with finite plasma pressure, and for force-free cylindrically symmetric
FRs in which the poloidal field component changes direction. Our main
result is a proof that H m H c ≥ 0 is true
for force-free cylindrically symmetric FRs where the toroidal field and
poloidal field components are each of a single sign, and the poloidal
component does not exceed the toroidal component. We conclude that the
conjecture that current and magnetic helicities have the same sign is
not true in general, but it is true for a set of FRs of importance to
coronal and heliospheric physics.

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Title: Magnetic Structures at the Boundary of the Closed Corona:
A Semi-automated Study of S-Web Morphology
Authors: Scott, Roger B.; Pontin, David I.; Wyper, Peter F.
2019ApJ...882..125S Altcode:
Interchange reconnection is thought to play an important role in driving
the dynamics of the slow solar wind. To understand the details of this
process, it is important to catalog the various magnetic structures that
are present at the boundary between open and closed magnetic flux. To
this end we have developed a numerical method for partitioning the
coronal volume into individual flux domains using volume segmentation
along layers of high magnetic squashing degree (Q). Our publicly
available implementation of this method is able to identify the
different magnetic structures within a coronal magnetic field model
that define the open-closed boundary and comprise the so-called
Separatrix-Web (S-Web). With this we test previous predictions of how
different configurations of high-Q arcs within the S-Web are related
to coronal magnetic field structures. Here we present our findings
from a survey of 11 different potential field source surface models,
spanning from 2008 to 2017, which offer a representative sample of the
coronal magnetic field across nearly a complete solar cycle. Two key
findings of our analysis are that (i) “vertex” structures—where
arcs of the S-Web meet away from the heliospheric current sheet—are
associated with underlying magnetic dome structures, and (ii) that
any given arc of the S-Web is almost equally as likely to be formed
by a narrow corridor of open flux (corresponding to a hyperbolic
flux tube) as by the separatrix surface of a magnetic null. Together,
these findings highlight the importance of a variety of topological
configurations for future studies of interchange reconnection and the
acceleration of the solar wind.

---------------------------------------------------------
Title: Magnetic Structures at the Boundary of the Closed Corona:
A Semi-Automated Study of S-Web Morphology
Authors: Scott, Roger B.; Pontin, David I.; Wyper, Peter F.
2019shin.confE.169S Altcode:
Interchange reconnection at the open closed boundary (OCB) is thought
to play an important role in driving the dynamics of the slow solar
wind. In order to catalog the various magnetic structures that
are present along the OCB we have developed a numerical method for
partitioning the coronal volume into magnetic flux domains, using volume
segmentation along layers of high magnetic squashing degree. Using
our publicly available implementation of this method we are able
to identify structures within coronal models in order to test our
previous predictions regarding high-Q arcs in the so-called Separatrix
Web (S-Web) and topological features in the solar corona. Here we
present our findings from a survey of eleven different PFSS models,
spanning from 2008 to 2017, which offer a representative sample of
the types and rates of occurrence of various coronal structures. Two
key findings of our analysis are that (i) “vertex” lines - where
arcs of the S-web meet away from the heliospheric current sheet -
are associated with the spines of underlying magnetic nulls, and (ii)
that any given arc of the S-web is approximately equally likely to
be formed by the separatrix surface of a magnetic null or a narrow
corridor of open flux corresponding to a hyperbolic flux tube (HFT),
indicating the importance of both types of structures for studies of
interchange reconnection and the acceleration of the solar wind.

---------------------------------------------------------
Title: Interchange reconnection at different topological structures
of the Sun's open-closed-flux boundary
Authors: Pontin, David; Scott, Roger B.; Wyper, Peter F.
2019shin.confE.170P Altcode:
Interchange reconnection can occur at different topological structures
that separate open and closed magnetic flux in the corona. Here we
examine the different topological features that make up the separatrix
web (S-web) and their occurrence in global field models. We go on to
discuss the implications of interchange reconnection at these different
structures for the plasma properties in the slow solar wind observable
by Parker Solar Probe.

---------------------------------------------------------
Title: Proton acceleration at tearing coronal null-point current
sheets
Authors: Pallister, R.; Pontin, D. I.; Wyper, P. F.
2019A&A...622A.207P Altcode:
Context. Non-thermal particle acceleration in the solar corona is
thought to constitute a substantial part of the energy budget of
explosive events such as solar flares. One well-established mechanism of
non-thermal acceleration is directly via fields in current sheets. Aims: In this paper we study proton acceleration during "spine-fan
reconnection" at a 3D magnetic null point. This type of reconnection
has recently been implicated in some flares known as circular-ribbon
flares. It has also recently been discovered that the reconnecting
current sheet may undergo a non-linear tearing-type instability. This
tearing leads to the formation of flux ropes and quasi-turbulent
dynamics. Methods: A predictor-corrector test particle code is
used to model the trajectories of protons at different stages of sheet
tearing: when the sheet is intact, just after the formation of the first
major flux rope, and once the non-linear phase of the instability has
become more fully developed. The fields for these proton trajectories
were taken from snapshots of a 3D magnetohydrodynamics simulation
treated as three static field geometries represented by interpolated
grids. Acceleration in the intact current sheet is compared to earlier
simulations of infinite static current sheets and then used as a
control case with which to compare the later snapshots. Results:
Protons are found to be predominantly accelerated along the fan surface,
especially in the absence of current sheet tearing. Most of the highest
energy protons are accelerated in the main body of the current sheet,
along the direction of strongest parallel electric field. A high
energy tail is present in the kinetic energy distribution. After
tearing commences, this direct acceleration no longer dominates and
acceleration in the outflow regions makes a proportionally greater
contribution. Sheet tearing appears overall to hinder the acceleration
of protons in the fan plane, at least in the absence of time-dependent
acceleration mechanisms. Some correlation is found between high energy
protons and locations of flux ropes formed by the instability, but
the nature of the link remains at present unclear.

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Title: On the periodicity of linear and nonlinear oscillatory
reconnection
Authors: Thurgood, J. O.; Pontin, D. I.; McLaughlin, J. A.
2019A&A...621A.106T Altcode: 2018arXiv181108831T
Context. An injection of energy towards a magnetic null point can
drive reversals of current-sheet polarity leading to time-dependent,
oscillatory reconnection (OR), which may explain periodic phenomena
generated when reconnection occurs in the solar atmosphere. However, the
details of what controls the period of these current-sheet oscillations
in realistic systems is poorly understood, despite being of crucial
importance in assessing whether a specific model of OR can account for
observed periodic behaviour. Aims: This paper aims to highlight
that different types of reconnection reversal are supported about
null points, and that these can be distinct from the oscillation
in the closed-boundary, linear systems considered by a number of
authors in the 1990s. In particular, we explore the features of a
nonlinear oscillation local to the null point, and examine the effect
of resistivity and perturbation energy on the period, contrasting it to
the linear, closed-boundary case. Methods: Numerical simulations
of the single-fluid, resistive MHD equations are used to investigate the
effects of plasma resistivity and perturbation energy upon the resulting
OR. Results: It is found that for small perturbations that behave
linearly, the inverse Lundquist number dictates the period, provided
the perturbation energy (i.e. the free energy) is small relative to
the inverse Lundquist number defined on the boundary, regardless of
the broadband structure of the initial perturbation. However, when the
perturbation energy exceeds the threshold required for "nonlinear"
null collapse to occur, a complex oscillation of the magnetic
field is produced which is, at most, only weakly-dependent on the
resistivity. The resultant periodicity is instead strongly influenced
by the amount of free energy, with more energetic perturbations
producing higher-frequency oscillations. Conclusions: Crucially,
with regards to typical solar-based and astrophysical-based input
energies, we demonstrate that the majority far exceed the threshold
for nonlinearity to develop. This substantially alters the properties
and periodicity of both null collapse and subsequent OR. Therefore,
nonlinear regimes of OR should be considered in solar and astrophysical
contexts. The movie associated to Fig. 3 is available at <A
href="https://www.aanda.org/10.1051/0004-6361/201834369/olm">https://www.aanda.org</A>

---------------------------------------------------------
Title: Magnetic Structures at the Boundary of the Closed Corona:
Interpretation of S-Web Arcs
Authors: Scott, Roger B.; Pontin, David I.; Yeates, Anthony R.; Wyper,
Peter F.; Higginson, Aleida K.
2018ApJ...869...60S Altcode: 2018arXiv180504459S
The topology of coronal magnetic fields near the open-closed
magnetic flux boundary is important to the the process of interchange
reconnection, whereby plasma is exchanged between open and closed
flux domains. Maps of the magnetic squashing factor in coronal field
models reveal the presence of the Separatrix-Web (S-Web), a network of
separatrix surfaces and quasi-separatrix layers, along which interchange
reconnection is highly likely. Under certain configurations, interchange
reconnection within the S-Web could potentially release coronal material
from the closed magnetic field regions to high-latitude regions far
from the heliospheric current sheet, where it is observed as slow solar
wind. It has also been suggested that transport along the S-Web may be
a possible cause for the observed large longitudinal spreads of some
impulsive, 3He-rich solar energetic particle events. Here,
we demonstrate that certain features of the S-Web reveal structural
aspects of the underlying magnetic field, specifically regarding the
arcing bands of highly squashed magnetic flux observed at the outer
boundary of global magnetic field models. In order for these S-Web
arcs to terminate or intersect away from the helmet streamer apex,
there must be a null spine line that maps a finite segment of the
photospheric open-closed boundary up to a singular point in the open
flux domain. We propose that this association between null spine lines
and arc termination points may be used to identify locations in the
heliosphere that are preferential for the appearance of solar energetic
particles and plasma from the closed corona, with characteristics
that may inform our understanding of interchange reconnection and the
acceleration of the slow solar wind.

---------------------------------------------------------
Title: Estimating the Rate of Field Line Braiding in the Solar Corona
by Photospheric Flows
Authors: Candelaresi, S.; Pontin, D. I.; Yeates, A. R.; Bushby, P. J.;
Hornig, G.
2018ApJ...864..157C Altcode: 2018arXiv180503010C
In this paper, we seek to understand the timescale in which
the photospheric motions on the Sun braid coronal magnetic field
lines. This is a crucial ingredient for determining the viability of
the braiding mechanism for explaining the high temperatures observed
in the corona. We study the topological complexity induced in the
coronal magnetic field, primarily using plasma motions extracted
from magneto-convection simulations. This topological complexity is
quantified using the field line winding, finite time topological entropy
(FTTE), and passive scalar mixing. With these measures, we contrast
mixing efficiencies of the magneto-convection simulation, a benchmark
flow known as a “blinking vortex”, and finally photospheric
flows inferred from sequences of observed magnetograms using local
correlation tracking. While the highly resolved magneto-convection
simulations induce a strong degree of field line winding and FTTE, the
values obtained from the observations from the plage region are around
an order of magnitude smaller. This behavior is carried over to the
FTTE. Nevertheless, the results suggest that the photospheric motions
induce complex tangling of the coronal field on a timescale of hours.

---------------------------------------------------------
Title: Interchange reconnection and the 'blurring' of the Sun's
open-closed-flux boundary
Authors: Pontin, David Iain; Scott, Roger B.; Wyper, Peter F.
2018shin.confE..53P Altcode:
We describe a new computational approach for 'segmentation' of the
coronal magnetic field into distinct flux domains based on global
renderings of the squashing factor Q. The boundaries of these domains
constitute the S-web: the web of high Q structures thought to play
an important role in the generation of the slow solar wind. We then
use static models to demonstrate the consequences of interchange
reconnection at the open-closed-flux boundary (OCB) in a fragmented
current layer. We show that it leads to efficient mixing of magnetic
flux (and therefore plasma) from open and closed field regions. This
corresponds to an increase in the length and complexity of the
OCB. Thus, whenever reconnection occurs at a null point or separator
of this OCB, the associated separatrix arc of the S-web in the high
corona becomes not a single line but a band of finite thickness within
which the OCB is highly structured. This suggests that around the
high-Q arcs of the S-web a structured mixture of open and previously
closed-field plasma is present that could be detectable by the upcoming
Parker Solar Probe mission.

---------------------------------------------------------
Title: Resistively-limited current sheet implosions in planar
anti-parallel (1D) and null-point containing (2D) magnetic field
geometries
Authors: Thurgood, Jonathan O.; Pontin, David I.; McLaughlin, James A.
2018PhPl...25g2105T Altcode: 2018arXiv180608157T
Implosive formation of current sheets is a fundamental plasma
process. Previous studies focused on the early time evolution, while
here our primary aim is to explore the longer-term evolution, which
may be critical for determining the efficiency of energy release. To
address this problem, we investigate two closely related problems,
namely: (i) 1D, pinched anti-parallel magnetic fields and (ii) 2D, null
point containing fields which are locally imbalanced ("null-collapse"
or "X-point collapse"). Within the framework of resistive MHD, we
simulate the full nonlinear evolution through three distinct phases:
the initial implosion, its eventual halting mechanism, and subsequent
evolution post-halting. In a parameter study, we find that the scaling
with resistivity of current sheet properties at the halting time is in
good agreement—in both geometries—with that inferred from a known 1D
similarity solution. We find that the halting of the implosions occurs
rapidly after reaching the diffusion scale by sudden Ohmic heating of
the dense plasma within the current sheet, which provides a pressure
gradient sufficient to oppose further collapse and decelerate the
converging flow. This back-pressure grows to exceed that required for
force balance and so the post-implosion evolution is characterised by
the consequences of the current sheet "bouncing" outwards. These are:
(i) the launching of propagating fast MHD waves (shocks) outwards and
(ii) the width-wise expansion of the current sheet itself. The expansion
is only observed to stall in the 2D case, where the pressurisation
is relieved by outflow in the reconnection jets. In the 2D case, we
quantify the maximum amount of current sheet expansion as it scales
with resistivity and analyse the structure of the reconnection region,
which forms post-expansion, replete with Petschek-type slow shocks
and fast termination shocks.

---------------------------------------------------------
Title: Magnetic Structures at the Boundary of the Closed Corona
Authors: Scott, Roger B.; Pontin, David I.; Yeates, Anthony R.; Wyper,
Peter F.; Higginson, Aleida K.
2018shin.confE..73S Altcode:
The topology of magnetic fields near the open-closed flux boundary in
the Sun's corona is an important influencing factor in the process of
interchange reconnection, whereby plasma is exchanged between open
and closed flux domains. Maps of the magnetic squashing factor at
the radial outer boundary in coronal field models reveal the presence
of the so-called 'S-web', and suggest that interchange reconnection
could potentially deposit closed coronal material into high-latitude
regions far from the heliospheric current sheet. Here we demonstrate
that certain features of the S-web reveal the underlying topological
structure of the magnetic field. Specifically, in order for the arcing
bands of highly squashed magnetic flux of the S-web to terminate or
intersect away from the helmet streamer apex, there must be a null
spine line that maps a finite segment of the photospheric open-closed
boundary up to a singular point in the open flux domain. We propose
that this association between null spine lines and arc termination
points may be used to identify locations in the heliosphere that are
preferential for the appearance of solar energetic particles or slow
solar wind plasma with certain characteristics.

---------------------------------------------------------
Title: Implosive Collapse about Magnetic Null Points: A Quantitative
Comparison between 2D and 3D Nulls
Authors: Thurgood, Jonathan O.; Pontin, David I.; McLaughlin, James A.
2018ApJ...855...50T Altcode: 2018arXiv180207076T
Null collapse is an implosive process whereby MHD waves focus their
energy in the vicinity of a null point, forming a current sheet and
initiating magnetic reconnection. We consider, for the first time,
the case of collapsing 3D magnetic null points in nonlinear, resistive
MHD using numerical simulation, exploring key physical aspects of the
system as well as performing a detailed parameter study. We find that
within a particular plane containing the 3D null, the plasma and current
density enhancements resulting from the collapse are quantitatively
and qualitatively as per the 2D case in both the linear and nonlinear
collapse regimes. However, the scaling with resistivity of the 3D
reconnection rate—which is a global quantity—is found to be less
favorable when the magnetic null point is more rotationally symmetric,
due to the action of increased magnetic back-pressure. Furthermore,
we find that, with increasing ambient plasma pressure, the collapse
can be throttled, as is the case for 2D nulls. We discuss this
pressure-limiting in the context of fast reconnection in the solar
atmosphere and suggest mechanisms by which it may be overcome. We
also discuss the implications of the results in the context of
null collapse as a trigger mechanism of Oscillatory Reconnection,
a time-dependent reconnection mechanism, and also within the wider
subject of wave-null point interactions. We conclude that, in general,
increasingly rotationally asymmetric nulls will be more favorable in
terms of magnetic energy release via null collapse than their more
symmetric counterparts.

---------------------------------------------------------
Title: On the Magnetic Squashing Factor and the Lie Transport
of Tangents
Authors: Scott, Roger B.; Pontin, David I.; Hornig, Gunnar
2017ApJ...848..117S Altcode:
The squashing factor (or squashing degree) of a vector field is a
quantitative measure of the deformation of the field line mapping
between two surfaces. In the context of solar magnetic fields, it is
often used to identify gradients in the mapping of elementary magnetic
flux tubes between various flux domains. Regions where these gradients
in the mapping are large are referred to as quasi-separatrix layers
(QSLs), and are a continuous extension of separators and separatrix
surfaces. These QSLs are observed to be potential sites for the
formation of strong electric currents, and are therefore important
for the study of magnetic reconnection in three dimensions. Since the
squashing factor, Q, is defined in terms of the Jacobian of the field
line mapping, it is most often calculated by first determining the
mapping between two surfaces (or some approximation of it) and then
numerically differentiating. Tassev &amp; Savcheva have introduced an
alternative method, in which they parameterize the change in separation
between adjacent field lines, and then integrate along individual field
lines to get an estimate of the Jacobian without the need to numerically
differentiate the mapping itself. But while their method offers
certain computational advantages, it is formulated on a perturbative
description of the field line trajectory, and the accuracy of this
method is not entirely clear. Here we show, through an alternative
derivation, that this integral formulation is, in principle, exact. We
then demonstrate the result in the case of a linear, 3D magnetic null,
which allows for an exact analytical description and direct comparison
to numerical estimates.

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Title: Magnetic field line braiding in the solar atmosphere
Authors: Candelaresi, S.; Pontin, D. I.; Hornig, G.
2017IAUS..327...77C Altcode:
Using a magnetic carpet as model for the near surface solar magnetic
field we study its effects on the propagation of energy injectected
by photospheric footpoint motions. Such a magnetic carpet structure is
topologically highly non-trivial and with its magnetic nulls exhibits
qualitatively different behavior than simpler magnetic fields. We
show that the presence of magnetic fields connecting back to the
photosphere inhibits the propagation of energy into higher layers of
the solar atmosphere, like the solar corona. By applying certain types
of footpoint motions the magnetic field topology is is greatly reduced
through magnetic field reconnection which facilitates the propagation
of energy and disturbances from the photosphere.

---------------------------------------------------------
Title: Three-dimensional Oscillatory Reconnection
Authors: Thurgood, Jonathan; Pontin, David; McLaughlin, James
2017shin.confE..88T Altcode:
Here we detail the dynamic evolution of localised reconnection regions
about three-dimensional (3D) magnetic null points by using numerical
simulation. We demonstrate for the first time that reconnection
triggered by the localised collapse of a 3D null point due to an
external MHD wave involves a self-generated oscillation, whereby the
current sheet and outflow jets undergo a reconnection reversal process
during which back-pressure formation at the jet heads acts to prise
open the collapsed field before overshooting the equilibrium into an
opposite-polarity configuration. The discovery that reconnection at
fully 3D nulls can proceed naturally in a time-dependent and periodic
fashion is suggestive that oscillatory reconnection mechanisms may play
a role in explaining periodicity in astrophysical phenomena associated
with magnetic reconnection, such as the observed quasi-periodicity of
solar and stellar flare emission. Furthermore, we find a consequence
of oscillatory reconnection is the generation of a plethora of
freely-propagating MHD waves which escape the vicinity of the
reconnection region.

---------------------------------------------------------
Title: Three-dimensional Oscillatory Magnetic Reconnection
Authors: Thurgood, Jonathan O.; Pontin, David I.; McLaughlin, James A.
2017ApJ...844....2T Altcode: 2017arXiv170609662T
Here we detail the dynamic evolution of localized reconnection regions
about 3D magnetic null points using numerical simulation. We demonstrate
for the first time that reconnection triggered by the localized collapse
of a 3D null point that is due to an external magnetohydrodynamic
(MHD) wave involves a self-generated oscillation, whereby the current
sheet and outflow jets undergo a reconnection reversal process
during which back-pressure formation at the jet heads acts to prise
open the collapsed field before overshooting the equilibrium into an
opposite-polarity configuration. The discovery that reconnection at
fully 3D nulls can proceed naturally in a time-dependent and periodic
fashion suggests that oscillatory reconnection mechanisms may play a
role in explaining periodicity in astrophysical phenomena associated
with magnetic reconnection, such as the observed quasi-periodicity
of solar and stellar flare emission. Furthermore, we find that
a consequence of oscillatory reconnection is the generation of a
plethora of freely propagating MHD waves that escape the vicinity of
the reconnection region.

---------------------------------------------------------
Title: Observable Signatures of Energy Release in Braided Coronal
Loops
Authors: Pontin, D. I.; Janvier, M.; Tiwari, S. K.; Galsgaard, K.;
Winebarger, A. R.; Cirtain, J. W.
2017ApJ...837..108P Altcode:
We examine the turbulent relaxation of solar coronal loops containing
non-trivial field line braiding. Such field line tangling in the
corona has long been postulated in the context of coronal heating
models. We focus on the observational signatures of energy release
in such braided magnetic structures using MHD simulations and forward
modeling tools. The aim is to answer the following question: if energy
release occurs in a coronal loop containing braided magnetic flux,
should we expect a clearly observable signature in emissions? We
demonstrate that the presence of braided magnetic field lines does not
guarantee a braided appearance to the observed intensities. Observed
intensities may—but need not necessarily—reveal the underlying
braided nature of the magnetic field, depending on the degree and
pattern of the field line tangling within the loop. However, in all
cases considered, the evolution of the braided loop is accompanied
by localized heating regions as the loop relaxes. Factors that
may influence the observational signatures are discussed. Recent
high-resolution observations from Hi-C have claimed the first direct
evidence of braided magnetic fields in the corona. Here we show that
both the Hi-C data and some of our simulations give the appearance of
braiding at a range of scales.

---------------------------------------------------------
Title: Effects of Field-line Topology on Energy Propagation in
the Corona
Authors: Candelaresi, S.; Pontin, D. I.; Hornig, G.
2016ApJ...832..150C Altcode: 2016arXiv161103325C
We study the effect of photospheric footpoint motions on magnetic
field structures containing magnetic nulls. The footpoint motions
are prescribed on the photospheric boundary as a velocity field that
entangles the magnetic field. We investigate the propagation of the
injected energy, the conversion of energy, emergence of current layers,
and other consequences of the nontrivial magnetic field topology in
this situation. These boundary motions lead initially to an increase in
magnetic and kinetic energy. Following this, the energy input from the
photosphere is partially dissipated and partially transported out of the
domain through the Poynting flux. The presence of separatrix layers and
magnetic null points fundamentally alters the propagation behavior of
disturbances from the photosphere into the corona. Depending on the
field-line topology close to the photosphere, the energy is either
trapped or free to propagate into the corona.

---------------------------------------------------------
Title: Why Are Flare Ribbons Associated with the Spines of Magnetic
Null Points Generically Elongated?
Authors: Pontin, David; Galsgaard, Klaus; Démoulin, Pascal
2016SoPh..291.1739P Altcode: 2016arXiv160505704P; 2016SoPh..tmp..101P
Coronal magnetic null points exist in abundance, as demonstrated by
extrapolations of the coronal field, and have been inferred to be
important for a broad range of energetic events. These null points
and their associated separatrix and spine field lines represent
discontinuities of the field line mapping, making them preferential
locations for reconnection. This field line mapping also exhibits strong
gradients adjacent to the separatrix (fan) and spine field lines, which
can be analysed using the "squashing factor", Q . In this article we
analyse in detail the distribution of Q in the presence of magnetic
nulls. While Q is formally infinite on both the spine and fan of the
null, the decay of Q away from these structures is shown in general to
depend strongly on the null-point structure. For the generic case of a
non-radially-symmetric null, Q decays most slowly away from the spine or
fan in the direction in which |B | increases most slowly. In particular,
this demonstrates that the extended elliptical high-Q halo around the
spine footpoints observed by Masson et al. (Astrophys. J.700, 559,
2009) is a generic feature. This extension of the Q halos around the
spine or fan footpoints is important for diagnosing the regions of the
photosphere that are magnetically connected to any current layer that
forms at the null. In light of this, we discuss how our results can be
used to interpret the geometry of observed flare ribbons in circular
ribbon flares, in which typically a coronal null is implicated. We
conclude that both the physics in the vicinity of the null and how
this is related to the extension of Q away from the spine or fan can be
used in tandem to understand observational signatures of reconnection
at coronal null points.

---------------------------------------------------------
Title: Why are flare ribbons generically elongated in configurations
with magnetic null points?
Authors: Pontin, David Iain; Galsgaard, Klaus; Demoulin, Pascal
2016SPD....47.0625P Altcode:
Coronal magnetic null points exist in abundance as demonstrated by
extrapolations of the coronal field, and have been inferred to be
important for a broad range of energetic events. These null points
and their associated separatrix and spine field lines represent
discontinuities of the field line mapping, making them preferential
locations for reconnection in the corona. In addition, the field line
mapping in the vicinity of these null points exhibits strong gradients
as measured by the “squashing factor”, Q. We demonstrate that
the extension of the Q halos around the spine/fan footpoints is in
general important for diagnosing the regions of the photosphere that are
magnetically connected to any current layer that forms at the null. In
light of this, we discuss the extent to which our results can be used
to interpret the geometry of observed flare ribbons in events in which
a coronal null is implicated. We conclude that together the physics
in the vicinity of the null and how this is related to the extension
of Q away from the spine/fan can be used in tandem to understand
observational signatures of reconnection at coronal null points.

---------------------------------------------------------
Title: Braided magnetic fields: equilibria, relaxation and heating
Authors: Pontin, D. I.; Candelaresi, S.; Russell, A. J. B.; Hornig, G.
2016PPCF...58e4008P Altcode: 2015arXiv151205918P
We examine the dynamics of magnetic flux tubes containing non-trivial
field line braiding (or linkage), using mathematical and computational
modelling, in the context of testable predictions for the laboratory
and their significance for solar coronal heating. We investigate
the existence of braided force-free equilibria, and demonstrate
that for a field anchored at perfectly-conducting plates, these
equilibria exist and contain current sheets whose thickness scales
inversely with the braid complexity—as measured for example by the
topological entropy. By contrast, for a periodic domain braided exact
equilibria typically do not exist, while approximate equilibria contain
thin current sheets. In the presence of resistivity, reconnection is
triggered at the current sheets and a turbulent relaxation ensues. We
finish by discussing the properties of the turbulent relaxation and
the existence of constraints that may mean that the final state is
not the linear force-free field predicted by Taylor’s hypothesis.

---------------------------------------------------------
Title: Braided coronal loops: equilibria, heating, and observational
signatures
Authors: Pontin, David Iain; Hornig, Gunnar; Candelaresi, Simon
2016SPD....47.1010P Altcode:
We examine the dynamics of coronal loops containing non-trivial
magnetic field line braiding. We discuss the existence of braided
force-free equilibria, and demonstrate that these equilibria must
contain current layers whose thickness becomes increasingly small
for increasing field complexity. In practical terms, the implication
is that if one considers a line-tied coronal loop that is driven by
photospheric motions, then the eventual onset of reconnection and
energy release is inevitable. Once the initial reconnection event
is triggered a turbulent relaxation ensues. We discuss the relation
with Parker’s braiding mechanism for coronal heating, and go on to
describe the expected observational signatures of energy release in
such a braided coronal loop.

---------------------------------------------------------
Title: Magnetic Field Relaxation and Current Sheets in an Ideal Plasma
Authors: Candelaresi, S.; Pontin, D. I.; Hornig, G.
2015ApJ...808..134C Altcode: 2015arXiv150503043C
We investigate the existence of magnetohydrostatic equilibria for
topologically complex magnetic fields. The approach employed is
to perform ideal numerical relaxation experiments. We use a newly
developed Lagrangian relaxation scheme that exactly preserves the
magnetic field topology during the relaxation. Our configurations
include both twisted and sheared fields, of which some fall into the
category for which Parker predicted no force-free equilibrium. The
first class of field considered contains no magnetic null points, and
field lines connect between two perfectly conducting plates. In these
cases, we observe only resolved current layers of finite thickness. In
further numerical experiments, we confirm that magnetic null points
are loci of singular currents.

---------------------------------------------------------
Title: The Effect of Reconnection on the Structure of the Sun's
Open-Closed Flux Boundary
Authors: Pontin, D. I.; Wyper, P. F.
2015ApJ...805...39P Altcode: 2015arXiv150201311P
Global magnetic field extrapolations are now revealing the huge
complexity of the Sun's corona, and in particular the structure
of the boundary between open and closed magnetic flux. Moreover,
recent developments indicate that magnetic reconnection in the
corona likely occurs in highly fragmented current layers, and that
this typically leads to a dramatic increase in the topological
complexity beyond that of the equilibrium field. In this paper we
use static models to investigate the consequences of reconnection at
the open-closed flux boundary (“interchange reconnection”) in a
fragmented current layer. We demonstrate that it leads to efficient
mixing of magnetic flux (and therefore plasma) from open and closed
field regions. This corresponds to an increase in the length and
complexity of the open-closed boundary. Thus, whenever reconnection
occurs at a null point or separator of this open-closed boundary, the
associated separatrix arc of the so-called S-web in the high corona
becomes not a single line but a band of finite thickness within which
the open-closed boundary is highly structured. This has significant
implications for the acceleration of the slow solar wind, for which
the interaction of open and closed field is thought to be important,
and may also explain the coronal origins of certain solar energetic
particles. The topological structures examined contain magnetic
null points, separatrices and separators, and include a model for a
pseudo-streamer. The potential for understanding both the large scale
morphology and fine structure observed in flare ribbons associated
with coronal nulls is also discussed.

---------------------------------------------------------
Title: The Structure of Current Layers and Degree of Field-line
Braiding in Coronal Loops
Authors: Pontin, D. I.; Hornig, G.
2015ApJ...805...47P Altcode: 2014arXiv1411.2845P
One proposed resolution to the long-standing problem of solar coronal
heating involves the buildup of magnetic energy in the corona due to
turbulent motions at the photosphere that braid the coronal field, and
the subsequent release of this energy via magnetic reconnection. In
this paper the ideal relaxation of braided magnetic fields modeling
solar coronal loops is followed. A sequence of loops with increasing
braid complexity is considered, with the aim of understanding how this
complexity influences the development of small scales in the magnetic
field, and thus the energy available for heating. It is demonstrated
that the ideally accessible force-free equilibrium for these braided
fields contains current layers of finite thickness. It is further shown
that for any such braided field, if a force-free equilibrium exists
then it should contain current layers whose thickness is determined by
length scales in the field-line mapping. The thickness and intensity
of the current layers follow scaling laws, and this allows us to
extrapolate beyond the numerically accessible parameter regime and
to place an upper bound on the braid complexity possible at coronal
plasma parameters. At this threshold level the braided loop contains
1026-{{10}28} ergs of available free magnetic
energy, more than sufficient for a large nanoflare.

---------------------------------------------------------
Title: The structure of current layers and degree of field line
braiding in coronal loops
Authors: Pontin, David I.; Hornig, Gunnar
2015TESS....131205P Altcode:
One proposed resolution to the long-standing problem of solar coronal
heating involves the buildup of magnetic energy in the corona due to
turbulent motions at the photosphere that braid the coronal field, and
the subsequent release of this energy via magnetic reconnection. We
examine the ideal relaxation of braided magnetic fields modelling
solar coronal loops. It is demonstrated that the ideally accessible
force-free equilibria for these braided fields contain current layers of
finite thickness. It is further shown that for any such braided field,
if a force-free equilibrium exists then it should contain current
layers whose thickness is determined by length scales in the field
line mapping. The thickness and intensity of the current layers follow
scaling laws, and this allows us to extrapolate beyond the numerically
accessible parameter regime and to place an upper bound on the braid
complexity possible at coronal plasma parameters. At this threshold
level the braided loop contains 1026-1028ergs
of available free magnetic energy, more than sufficient for a large
nanoflare.

---------------------------------------------------------
Title: The effect of reconnection on the structure of the Sun's
open-closed-flux boundary, and implications for the structure of
the solar wind
Authors: Pontin, David I.; Wyper, Peter Fraser
2015TESS....110801P Altcode:
Global magnetic field extrapolations are now revealing the huge
complexity of the Sun's corona, and in particular the structure of
the boundary between open and closed magnetic flux. Moreover, recent
developments indicate that magnetic reconnection in the corona likely
occurs in highly fragmented current layers, and that this typically
leads to a dramatic increase in the topological complexity beyond
that of the equilibrium field. Here we investigate the consequences
of reconnection at the open-closed flux boundary ("interchange
reconnection") in a fragmented current layer. We demonstrate that
it leads to a situation in which magnetic flux (and therefore
plasma) from open and closed field regions is efficiently mixed
together. This corresponds to an increase in the length and complexity
of the open-closed boundary. Thus, whenever reconnection occurs at a
null point or separator of the open-closed boundary, the associated
separatrix arc of the so-called S-web in the high corona becomes not a
single line but a band of finite thickness within which the open-closed
flux boundary is highly structured. This has significant implications
for the structuring of the solar wind.

---------------------------------------------------------
Title: Non-linear Tearing and Flux rope Formation in 3D Null Current
Sheets
Authors: Wyper, P. F.; Pontin, D. I.
2014AGUFMSH23A4152W Altcode:
The manner in which small scale structure affects the large scale
reconnection process in realistic 3D geometries is still an unsolved
problem. With the increase in computational resources and improvements
in satellite instrumentation, signatures of flux ropes or "plasmoids"
are now observed with increasing regularity, yet their formation and
dynamics are poorly understood. It has been demonstrated that even
at MHD scales, in 2D rapid non-linear tearing of Sweet-Parker-like
layers forms multiple magnetic islands ("plasmoids") and allows the
reconnection rate to become almost independent of the Lundquist number
(the "plasmoid instability"). This work presents some of our recent
theoretical work focussing on an analogous instability in a fully
3D geometry. Using results from a series of 3D high resolution MHD
simulations, the formation and evolution of fully three dimensional
"flux rope" structures following the 3D plasmoid instability will be
presented, and their effects on the manner of the reconnection process
as a whole discussed.

---------------------------------------------------------
Title: Dynamic topology and flux rope evolution during non-linear
tearing of 3D null point current sheets
Authors: Wyper, P. F.; Pontin, D. I.
2014PhPl...21j2102W Altcode: 2014arXiv1406.6120W
In this work, the dynamic magnetic field within a tearing-unstable
three-dimensional current sheet about a magnetic null point is described
in detail. We focus on the evolution of the magnetic null points and
flux ropes that are formed during the tearing process. Generally, we
find that both magnetic structures are created prolifically within
the layer and are non-trivially related. We examine how nulls are
created and annihilated during bifurcation processes, and describe
how they evolve within the current layer. The type of null bifurcation
first observed is associated with the formation of pairs of flux ropes
within the current layer. We also find that new nulls form within these
flux ropes, both following internal reconnection and as adjacent flux
ropes interact. The flux ropes exhibit a complex evolution, driven by
a combination of ideal kinking and their interaction with the outflow
jets from the main layer. The finite size of the unstable layer also
allows us to consider the wider effects of flux rope generation. We
find that the unstable current layer acts as a source of torsional
magnetohydrodynamic waves and dynamic braiding of magnetic fields. The
implications of these results to several areas of heliophysics are
discussed.

---------------------------------------------------------
Title: Current Singularities in Line-tied Three-dimensional Magnetic
Fields
Authors: Craig, I. J. D.; Pontin, D. I.
2014ApJ...788..177C Altcode: 2014arXiv1406.1364C
This paper considers the current distributions that derive
from finite amplitude perturbations of line-tied magnetic fields
comprising hyperbolic field structures. The initial equilibrium on
which we principally focus is a planar magnetic X-point threaded by
a uniform axial field. This field is line-tied on all surfaces but
subject to three-dimensional (3D) disturbances that alter the initial
topology. Results of ideal relaxation simulations are presented which
illustrate how intense current structures form that can be related,
through the influence of line-tying, to the quasi-separatrix layers
(QSLs) of the initial configuration. It is demonstrated that the
location within the QSL that attracts the current, and its scaling
properties, are strongly dependent on the relative dimensions of the QSL
with respect to the line-tied boundaries. These results are contrasted
with the behavior of a line-tied 3D field containing an isolated null
point. In this case, it is found that the dominant current always
forms at the null, but that the collapse is inhibited when the null
is closer to a line-tied boundary.

---------------------------------------------------------
Title: A new relaxation technique for determining the structure of
coronal magnetic fields
Authors: Pontin, David; Candelaresi, Simon; Hornig, Gunnar
2014AAS...22440206P Altcode:
The existence of force-free equilibria for arbitrary field
topology is a long-standing and unresolved problem (c.f. the 'Parker
problem'). We introduce a new numerical method for obtaining force-free
equilibria. From an initial non-equilibrium field, an evolution
towards a force-free field is followed that strictly preserves the
magnetic topology (i.e. connectivity and linkage of all magnetic field
lines). The method is based on a Lagrangian formulation, and employs
a so-called mimetic method for calculating finite differences on the
computational mesh. We demonstrate that this provides a significant
improvement in the accuracy of the force-free equilibrium obtained,
compared with the traditional finite difference approach previously
employed. The method is a powerful tool to understand the properties
of coronal loops, which are typically modelled as consisting of ideal
plasma threaded by a force-free magnetic field. We present some examples
of equilibria representative of coronal loops.

---------------------------------------------------------
Title: Magnetic reconnection and tearing in a 3D current sheet about
a solar coronal null
Authors: Pontin, David; Wyper, Peter
2014AAS...22432346P Altcode:
Three-dimensional magnetic null points are ubiquitous in the solar
corona and in any generic mixed-polarity magnetic field. We discuss
the nature of flux transfer during reconnection an isolated coronal
null point, that occurs across the fan plane when a current sheet
forms about the null. We then go on to discuss the breakup of the
current sheet via a non-linear tearing-type instability and show that
the instability threshold corresponds to a Lundquist number comparable
to the 2D case. We also discuss the resulting topology of the magnetic
field, which involves a layer in which open and closed magnetic fields
are effectively mixed, with implications for particle transport.

---------------------------------------------------------
Title: Mimetic Methods for Lagrangian Relaxation of Magnetic Fields
Authors: Candelaresi, Simon; Pontin, David; Hornig, Gunnar
2014arXiv1405.0942C Altcode:
We present a new code that performs a relaxation of a magnetic
field towards a force-free state (Beltrami field) using a Lagrangian
numerical scheme. Beltrami fields are of interest for the dynamics of
many technical and astrophysical plasmas as they are the lowest energy
states that the magnetic field can reach. The numerical method strictly
preserves the magnetic flux and the topology of magnetic field lines. In
contrast to other implementations we use mimetic operators for the
spatial derivatives in order to improve accuracy for high distortions
of the grid. Compared with schemes using direct derivatives we find
that the final state of the simulation approximates a force-free state
with a significantly higher accuracy. We implement the scheme in a
code which runs on graphical processing units (GPU), which leads to
an enhanced computing speed compared to previous relaxation codes.

---------------------------------------------------------
Title: On the Nature of Reconnection at a Solar Coronal Null Point
above a Separatrix Dome
Authors: Pontin, D. I.; Priest, E. R.; Galsgaard, K.
2013ApJ...774..154P Altcode: 2013arXiv1307.6874P
Three-dimensional magnetic null points are ubiquitous in the solar
corona and in any generic mixed-polarity magnetic field. We consider
magnetic reconnection at an isolated coronal null point whose fan
field lines form a dome structure. Using analytical and computational
models, we demonstrate several features of spine-fan reconnection
at such a null, including the fact that substantial magnetic flux
transfer from one region of field line connectivity to another can
occur. The flux transfer occurs across the current sheet that forms
around the null point during spine-fan reconnection, and there is no
separator present. Also, flipping of magnetic field lines takes place
in a manner similar to that observed in the quasi-separatrix layer or
slip-running reconnection.

---------------------------------------------------------
Title: The Emergence, Motion, and Disappearance of Magnetic Null
Points
Authors: Murphy, Nicholas A.; Parnell, C.; Haynes, A. L.; Pontin, D.
2013SPD....44..103M Altcode:
Magnetic reconnection frequently occurs at and around magnetic nulls:
locations where the magnetic field strength equals zero. While
theoretical models and simulations of magnetic reconnection often
assume that the magnetic field null is co-located with a flow
stagnation point, the introduction of asymmetry typically leads to
flow across the magnetic null. We derive an exact expression for
the three dimensional motion of a magnetic null point in a smoothly
varying magnetic field. We define xn as the position of
a null, U≡dxn/dt as the null's velocity, and M as the
Jacobian matrix of the magnetic field at the null. By using Faraday's
law and evaluating the convective derivative of the magnetic field at
xn with velocity U, the velocity of the null is given by
U=M-1▽×E. This expression is independent of Ohm's law. For
resistive magnetohydrodynamics with uniform resistivity η, this
reduces to U=V(xn)-ηM-1▽2B. This
indicates that any difference between the plasma flow velocity at
the null and the velocity of the null itself is due to resistive
diffusion of the magnetic field. Null points must diffuse in and out
of existence. Null-null pairs first appear (or disappear) as a single
degenerate null with singular M, and then instantaneously move apart
(or together) infinitely fast. However, the motion of separators cannot
be described using solely local parameters because the identification
of a particular magnetic field line as a separator may change due to
non-ideal behavior at another location.

---------------------------------------------------------
Title: The Emergence, Motion, and Disappearance of Magnetic Null
Points
Authors: Murphy, Nicholas A.; Parnell, Clare; Haynes, Andrew L.;
Pontin, David
2013shin.confE.118M Altcode:
Magnetic reconnection frequently occurs at and around magnetic
nulls: locations where the magnetic field strength equals zero. While
theoretical models and simulations of laminar, non-turbulent magnetic
reconnection often assume that the magnetic field null is co-located
with a flow stagnation point, the introduction of asymmetry typically
leads to flows across the magnetic null. We derive an exact expression
for the three dimensional motion of a magnetic null point in a
smoothly varying magnetic field by using Faraday's law and evaluating
the convective derivative of the magnetic field at the null using the
null's velocity. In resistive magnetohydrodynamics, any difference
between the plasma flow velocity at the null and the velocity of
the null itself must be due to resistive diffusion of the magnetic
field. Null points must diffuse in and out of existence. Null-null
pairs first appear (disappear) as a single degenerate null with
a singular Jacobian matrix, and then instantaneously move apart
(together) infinitely fast. However, the motion of separators cannot
be described using solely local parameters because the identification
of a particular magnetic field line as a separator may change due to
non-ideal behavior at another location.

---------------------------------------------------------
Title: Kelvin-Helmholtz instability in a current-vortex sheet at a
3D magnetic null
Authors: Wyper, P. F.; Pontin, D. I.
2013PhPl...20c2117W Altcode: 2013arXiv1303.6215W
We report here, for the first time, an observed instability of a
Kelvin-Helmholtz nature occurring in a fully three-dimensional (3D)
current-vortex sheet at the fan plane of a 3D magnetic null point. The
current-vortex layer forms self-consistently in response to foot point
driving around the spine lines of the null. The layer first becomes
unstable at an intermediate distance from the null point, with the
instability being characterized by a rippling of the fan surface and
a filamentation of the current density and vorticity in the shear
layer. Owing to the 3D geometry of the shear layer, a branching of the
current filaments and vortices is observed. The instability results in
a mixing of plasma between the two topologically distinct regions of
magnetic flux on either side of the fan separatrix surface, as flux is
reconnected across this surface. We make a preliminary investigation of
the scaling of the system with the dissipation parameters. Our results
indicate that the fan plane separatrix surface is an ideal candidate
for the formation of current-vortex sheets in complex magnetic fields
and, therefore, the enhanced heating and connectivity change associated
with the instabilities of such layers.

---------------------------------------------------------
Title: On the Formation of Current Sheets in Response to the
Compression or Expansion of a Potential Magnetic Field
Authors: Pontin, D. I.; Huang, Y. -M.
2012ApJ...756....7P Altcode: 2012arXiv1207.1127P
The compression or expansion of a magnetic field that is initially
potential is considered. It was recently suggested by Janse &amp; Low
that, following the volumetric deformation, the relevant lowest energy
state for the magnetic field is another potential magnetic field that
in general contains tangential discontinuities (current sheets). Here,
we examine this scenario directly using a numerical relaxation method
that exactly preserves the topology of the magnetic field. It is found
that, of the magnetic fields discussed by Janse &amp; Low, only those
containing magnetic null points develop current singularities during
an ideal relaxation, while the magnetic fields without null points
relax toward smooth force-free equilibria with finite nonzero current.

---------------------------------------------------------
Title: Spine-fan reconnection. The influence of temporal and spatial
variation in the driver
Authors: Wyper, P. F.; Jain, R.; Pontin, D. I.
2012A&A...545A..78W Altcode:
Context. From observations, the atmosphere of the Sun has been shown to
be highly dynamic with perturbations of the magnetic field often lacking
temporal or spatial symmetry. Despite this, studies of the spine-fan
reconnection mode at 3D nulls have so far focused on the very idealised
case with symmetric driving of a fixed spatial extent. Aims:
We investigate the spine-fan reconnection process for less idealised
cases, focusing on asymmetric driving and drivers with different
length scales. We look at the initial current sheet formation and
whether the scalings developed in the idealised models are robust
in more realistic situations. Methods: The investigation
was carried out by numerically solving the resistive compressible
3D magnetohydrodynamic equations in a Cartesian box containing a
linear null point. The spine-fan collapse was driven at the null
through tangential boundary driving of the spine foot points. Results: We find significant differences in the initial current
sheet formation with asymmetric driving. Notable is the displacement
of the null point position as a function of driving velocity and
resistivity (η). However, the scaling relations developed in the
idealised case are found to be robust (albeit at reduced amplitudes)
despite this extra complexity. Lastly, the spatial variation is also
shown to play an important role in the initial current sheet formation
through controlling the displacement of the spine foot points. 
Conclusions: We conclude that during the early stages of spine-fan
reconnection both the temporal and spatial nature of the driving play
important roles, with the idealised symmetrically driven case giving
a "best case" for the rate of current development and connectivity
change. As the most interesting eruptive events occur in relatively
short time frames this work clearly shows the need for high temporal
and spatial knowledge of the flows for accurate interpretation of
the reconnection scenario. Lastly, since the scalings developed in
the idealised case remain robust with more complex driving we can be
more confident of their use in interpreting reconnection in complex
magnetic field structures.

---------------------------------------------------------
Title: Theory of magnetic reconnection in solar and astrophysical
plasmas
Authors: Pontin, D. I.
2012RSPTA.370.3169P Altcode: 2012arXiv1202.4013P
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.

---------------------------------------------------------
Title: Heating of braided coronal loops
Authors: Wilmot-Smith, A. L.; Pontin, D. I.; Yeates, A. R.; Hornig, G.
2011A&A...536A..67W Altcode: 2011arXiv1111.1100W
 Aims: 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. Methods: Two magnetic
loops, braided in different ways, are used as initial conditions in
resistive MHD simulations and their subsequent evolution is studied. Results: 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.

---------------------------------------------------------
Title: Current accumulation at an asymmetric 3D null point caused
by generic shearing motions
Authors: Galsgaard, K.; Pontin, D. I.
2011A&A...534A...2G Altcode: 2011arXiv1108.3304G
Context. Here we investigate the dynamical evolution of the reconnection
process at an initially linear 3D null point that is stressed by a
localised shear motion across the spine axis. The difference to previous
investigations is that the fan plane is not rotationally symmetric and
this allows for different behaviours depending on the alignment of the
fan plane relative to the imposed driver direction. Aims: The aim
is to show how the current accumulation and the associated reconnection
process at the non-axisymmetric null depends on the relative orientation
between the driver imposed stress across the spine axis of the null
and the main eigenvector direction in the fan plane. Methods:
The time evolution of the 3D null point is investigated solving
the 3D non-ideal MHD equations numerically in a Cartesian box. The
magnetic field is frozen to the boundaries and the boundary velocity
is only non-zero where the imposed driving for stressing the system is
applied. Results: The current accumulation is found to be along
the direction of the fan eigenvector associated with the smallest
eigenvalue until the direction of the driver is almost parallel to
this eigenvector. When the driving velocity is parallel to the weak
eigenvector and has an impulsive temporal profile the null only has
a weak collapse forming only a weak current layer. However, when the
null point is stressed continuously boundary effects dominates the
current accumulation. Conclusions: There is a clear relation
between the orientation of the current concentration and the direction
of the fan eigenvector corresponding to the small eigenvalue. This
shows that the structure of the magnetic field is the most important in
determining where current is going to accumulate when a single 3D null
point is perturbed by a simple shear motion across the spine axis. As
the angle between the driving direction and the strong eigenvector
direction increases, the current that accumulates at the null becomes
progressively weaker.

---------------------------------------------------------
Title: Generalised models for torsional spine and fan magnetic
reconnection
Authors: Pontin, D. I.; Al-Hachami, A. K.; Galsgaard, K.
2011A&A...533A..78P Altcode: 2011arXiv1105.2684P
Context. Three-dimensional (3D) null points are present in abundance
in the solar corona, and the same is likely to be true in other
astrophysical environments. Recent results from solar observations and
from simulations suggest that reconnection at such 3D nulls may play an
important role in the coronal dynamics. Aims: 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. 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. Methods:
Analytical solutions are derived for the steady kinematic equations,
and are compared with the results of numerical simulations in which
the full set of resistive MHD equations is solved. Results:
The geometry of the current layers within which torsional spine and
torsional fan reconnection occur is strongly dependent on the symmetry
of the magnetic field. Torsional spine reconnection occurs in a narrow
tube around the spine, with elliptical cross-section when the fan
eigenvalues are different. The eccentricity of the ellipse increases as
the degree of asymmetry increases, 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.

---------------------------------------------------------
Title: Steady state reconnection at a single 3D magnetic null point
Authors: Galsgaard, K.; Pontin, D. I.
2011A&A...529A..20G Altcode: 2011arXiv1102.2351G
 Aims: We 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, thereby 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. Methods: 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. Results: 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 is unlikely to be realised because the current
layer tends to grow until it is restricted by the geometry of the
computational domain and the 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.

---------------------------------------------------------
Title: Three-dimensional magnetic reconnection regimes: A review
Authors: Pontin, D. I.
2011AdSpR..47.1508P Altcode: 2011arXiv1101.0924P
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.

---------------------------------------------------------
Title: Dynamics of braided coronal loops. II. Cascade to multiple
small-scale reconnection events
Authors: Pontin, D. I.; Wilmot-Smith, A. L.; Hornig, G.; Galsgaard, K.
2011A&A...525A..57P Altcode: 2010arXiv1003.5784P
 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.

---------------------------------------------------------
Title: Dynamics of braided coronal loops. I. Onset of magnetic
reconnection
Authors: Wilmot-Smith, A. L.; Pontin, D. I.; Hornig, G.
2010A&A...516A...5W Altcode: 2010arXiv1001.1717W
 Aims: 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. Methods: 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. Results: 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.

---------------------------------------------------------
Title: Magnetic reconnection at 3D null points: effect of magnetic
field asymmetry
Authors: Al-Hachami, A. K.; Pontin, D. I.
2010A&A...512A..84A Altcode: 2009arXiv0908.4507A
Context. The magnetic field in many astrophysical plasmas, for example
in the solar corona, is known to have a highly complex - and clearly
three-dimensional - structure. Turbulent plasma motions in high-β
regions where field lines are anchored, such as the solar interior,
can store large amounts of energy in the magnetic field. This energy
can only be released when magnetic reconnection occurs. Reconnection
may only occur in locations where huge gradients of the magnetic field
develop, and one candidate for such locations are magnetic null points,
known to be abundant for example in the solar atmosphere. Reconnection
leads to changes in the topology of the magnetic field, and energy being
released as heat, kinetic energy and acceleration of particles. Thus
reconnection is responsible for many dynamic processes, for instance
flares and jets. Aims: 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 reconnection of magnetic
flux at the null point, as well as how the current sheet forms and
its properties. Methods: We use mathematical modelling and
finite difference resistive MHD simulations. Results: 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 to 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. Conclusions: The symmetry/asymmetry
of the magnetic field in the vicinity of a magnetic null can have a
profound effect on the geometry of any associated reconnection region,
and the rate at which the reconnection process proceeds.

---------------------------------------------------------
Title: Three-dimensional magnetic reconnection regimes
Authors: Pontin, David
2010cosp...38.1934P Altcode: 2010cosp.meet.1934P
The magnetic field in many astrophysical plasmas -such as the Solar
corona and Earth's magnetosphere -has been shown to have a highly
complex structure that is clearly three-dimensional (3D). Recent
advances in theory and computational experiments have shown that
the nature of reconnection in 3D is fundamentally different from
2D models. Here we discuss the underlying theory of 3D magnetic
reconnection. We also review a selection of new 3D reconnection models
that illustrate the current state of the art, as well as highlighting
the complexity of energy release processes mediated by reconnection
in complicated 3D magnetic fields.

---------------------------------------------------------
Title: Three-dimensional null point reconnection regimes
Authors: Priest, E. R.; Pontin, D. I.
2009PhPl...16l2101P Altcode: 2009arXiv0910.3043P
Recent advances in theory and computational experiments have shown the
need to refine the previous categorization 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.

---------------------------------------------------------
Title: Magnetic Braiding and Quasi-Separatrix Layers
Authors: Wilmot-Smith, A. L.; Hornig, G.; Pontin, D. I.
2009ApJ...704.1288W Altcode: 2009arXiv0907.3820W
The squashing factor Q, 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.

---------------------------------------------------------
Title: Lagrangian Relaxation Schemes for Calculating Force-free
Magnetic Fields, and Their Limitations
Authors: Pontin, D. I.; Hornig, G.; Wilmot-Smith, A. L.; Craig,
I. J. D.
2009ApJ...700.1449P Altcode: 2009arXiv0903.1226P
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. In the present work we discuss a serious limitation
on the computation of force-free fields, within the context of a
Lagrangian relaxation scheme that conserves magnetic flux and ∇ ·
B identically. This issue 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. Error estimates are introduced to assess the quality
of the calculated equilibrium. We go on to present an algorithm, based
on rewriting the curl operation via Stokes' theorem, for calculating
the current which holds great promise for improving dramatically the
accuracy of the Lagrangian relaxation procedure.

---------------------------------------------------------
Title: Dynamics and waves near multiple magnetic null points in
reconnection diffusion region
Authors: Deng, X. H.; Zhou, M.; Li, S. Y.; Baumjohann, W.; Andre, M.;
Cornilleau, N.; Santolík, O.; Pontin, D. I.; Reme, H.; Lucek, E.;
Fazakerley, A. N.; Decreau, P.; Daly, P.; Nakamura, R.; Tang, R. X.;
Hu, Y. H.; Pang, Y.; Büchner, J.; Zhao, H.; Vaivads, A.; Pickett,
J. S.; Ng, C. S.; Lin, X.; Fu, S.; Yuan, Z. G.; Su, Z. W.; Wang, J. F.
2009JGRA..114.7216D Altcode: 2009JGRA..11407216D
Identifying the magnetic structure in the region where the magnetic
field lines break and how reconnection happens is crucial to improving
our understanding of three-dimensional reconnection. Here we show the in
situ observation of magnetic null structures in the diffusion region,
the dynamics, and the associated waves. Possible spiral null pair has
been identified near the diffusion region. There is a close relation
among the null points, the bipolar signature of the Z component of the
magnetic field, and enhancement of the flux of energetic electrons up to
100 keV. Near the null structures, whistler-mode waves were identified
by both the polarity and the power law of the spectrum of electric and
magnetic fields. It is found that the angle between the fans of the
nulls is quite close to the theoretically estimated maximum value of the
group-velocity cone angle for the whistler wave regime of reconnection.

---------------------------------------------------------
Title: Magnetic Braiding and Parallel Electric Fields
Authors: Wilmot-Smith, A. L.; Hornig, G.; Pontin, D. I.
2009ApJ...696.1339W Altcode: 2008arXiv0810.1415W
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 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 toward an ideal force-free equilibrium; the field is found to
remain smooth throughout the relaxation, with only large-scale current
structures. However, a highly filamentary integrated parallel current
structure with extremely short length-scales is found in the field,
with the associated gradients intensifying during the relaxation
process. 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 the coronal field. Thus the
inevitable consequence of the magnetic braiding process is a loss of
equilibrium of the magnetic field, probably via magnetic reconnection
events.

---------------------------------------------------------
Title: Observations of 3-D Reconnection and Dynamics of Electron
Scale Thin Current Sheets with Small Satellite Separation
Authors: Deng, X.; Decreau, P.; Ashour-Abdalla, M.; Zhou, M.; Li,
S.; Pang, Y.; Lucek, E.; Andre, M.; Fazakerley, A.; Dandouras, I.;
Pickett, J.; Daly, P.; Cornilleau-Wehrlin, N.; Pontin, D.
2008AGUFMSM22A..06D Altcode:
A variety of spacecraft separation distances, together with different
constellation orientations, are important to fully investigate
neutral sheet dynamics and the complex geophysical phenomena that
occur there. Beginning on June 20, 2007, two of the four Cluster
satellites were in orbit in a formation with only 17km separation. The
new orientation, with two spacecraft very close together, provided an
excellent opportunity to study thin neutral sheets and to investigate
the micro- and meso-scale dynamics of critical magnetospheric
phenomena. In this talk, we will concentrate on several reconnection
events in magnetotail region with small separation distances and high
resolution fields, particles and waves data. We will show the results
from a study of dynamics and structure of thin current sheets and
the structure of the 3-D magnetic null on the electron scale. We also
will investigate the related particle dynamics, the characteristics
of waves and plasma flows in the vicinity of the reconnection site.

---------------------------------------------------------
Title: Magnetic Braiding and the Onset of Reconnection
Authors: Wilmot-Smith, A.; Hornig, G.; Pontin, D.
2008ESPM...12.3.40W Altcode:
The braiding of the solar corona via photospheric motions with
subsequent relaxation and magnetic reconnection is one of the most
widely debated ideas of solar physics. Standard theories in the
area are based on the two-dimensional paradigm for reconnection
- where thin current sheets are needed for rapid reconnection -
and they therefore seek to demonstrate the development, in generic
situations, of the necessary short length-scales in the magnetic
field. However, in realistic three-dimensional situations it is the
integrated parallel electric field along field lines that is the
crucial quantity for reconnection. In resistive MHD this corresponds
to the integrated parallel current and is a key difference from the
2D case. A mixed analytical-numerical model is used to reassess
magnetic braiding in view of recent developments in 3D reconnection
theory. A realistic braided field containing only small amounts of
twist undergoes ideal relaxation to attain a force-free equilibrium;
that equilibrium is found to be smooth, with large-scale field and
current structures. Significantly however, the equilibrium is shown to
have a highly filamentary integrated parallel current structure with
extremely short length-scales. In a resistive solar plasma such fine
scales would lead to the generation of super-Alfvenic flows, causing a
loss of equilibrium. Implications for reconnection and coronal heating
are discussed.

---------------------------------------------------------
Title: Current sheet formation and nonideal behavior at
three-dimensional magnetic null points
Authors: Pontin, D. I.; Bhattacharjee, A.; Galsgaard, K.
2007PhPl...14e2106P Altcode: 2007astro.ph..1462P
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 that 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 that renders the evolution of
the field at the null ideal. Resistive magnetohydrodynamics simulations
are described that 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 localized 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
localized 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.

---------------------------------------------------------
Title: Current sheets at three-dimensional magnetic nulls: Effect
of compressibility
Authors: Pontin, D. I.; Bhattacharjee, A.; Galsgaard, K.
2007PhPl...14e2109P Altcode: 2007physics...1197P
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 14, 052106 (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.

---------------------------------------------------------
Title: Current amplification and magnetic reconnection at a
three-dimensional null point: Physical characteristics
Authors: Pontin, D. I.; Galsgaard, K.
2007JGRA..112.3103P Altcode: 2007astro.ph..1555P; 2007JGRA..11203103P
The behavior of magnetic perturbations of an initially potential
three-dimensional equilibrium magnetic null point is 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 3-D-localized 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.

---------------------------------------------------------
Title: Current Sheet Formation and Magnetic Reconnection at 3D
Null Points
Authors: Pontin, D. I.; Bhattacharjee, A.; Galsgaard, K.
2006AGUFMSH33B0407P Altcode:
The evolution of the magnetic field in the vicinity of a single
isolated three-dimensional magnetic null point is discussed. While
magnetic reconnection at separator lines joining two such nulls is
thought to occur in many situations in the Earth's magnetosphere and
the Solar corona, the importance of the nulls themselves is poorly
understood. Reconnection at an isolated 3D null is also thought to be
important in some solar flares, and is involved in models of magnetic
breakout. We present numerical and analytical results on current sheet
formation at such a 3D null. Under steady boundary driving the current
sheet which forms at the null grows steadily in both intensity and
dimensions, indicating that its nature is that of a Sweet-Parker current
sheet. The qualitative and quantitative properties of the current
sheet with respect to the driving parameters and plasma parameters
are discussed. The nature of current sheet formation turns out to be
strongly dependent on the compressibility of the plasma, which is highly
relevant for comparing to earlier analytical models. Accompanying the
current growth is the development of a component of the electric field
parallel to the magnetic field, a signal of the breakdown of ideal
MHD and of magnetic reconnection. This work is supported by the NSF
and the DOE.

---------------------------------------------------------
Title: Reconnection and Non-Ideal Behaviour at 3D Magnetic Null Points
Authors: Pontin, David; Bhattacharjee, A.; Galsgaard, K.
2006SPD....37.1007P Altcode: 2006BAAS...38R.238P
The evolution of the magnetic field in the vicinity of three-dimensional
magnetic null points---thought to be present in abundance in the
complex field of the Solar corona---is discussed, with reference to
the possibility that reconnection might occur there. It is shown that
in the framework of ideal MHD, certain evolutions of the null point
are prohibited, specifically, evolutions which cause the ratios of
the null point eigenvalues to change in time. Particular analytical
kinematic examples are discussed which demonstrate that in the ideal
limit, physical quantities are not smooth at the null point spine and
fan when such an evolution occurs. Simulations of the full resistive
MHD equations are then presented. The simulations demonstrate that
typical perturbations of a 3D magnetic null point inevitably cause
the null point to evolve in the very way that is excluded under the
ideal evolution. It is demonstrated that the changing eigenvalue ratio
is linked to a growth of electic current, as well as a component of
the electric field parallel to the magnetic field, at the null. This
parallel electric field is a signal of the breakdown of ideal MHD,
and of magnetic reconnection. Implications for coronal heating will
be discussed. This work is supported by the NSF and the DOE.

---------------------------------------------------------
Title: Dynamic Three-dimensional Reconnection in a Separator Geometry
with Two Null Points
Authors: Pontin, D. I.; Craig, I. J. D.
2006ApJ...642..568P Altcode:
The dynamic behavior of disturbances in the vicinity of a
pair of magnetically connected three-dimensional null points is
examined. The aim is to investigate how nonlinear disturbances lead
to strong localized currents that initiate magnetic reconnection
at the separator. The problem is formulated in an incompressible
cylindrical geometry by superposing arbitrary disturbance fields onto
a “background” two-null field. Two different regimes are found for
the dynamic evolution, depending on the relative strengths of the
background magnetic and velocity fields. In one regime, disturbance
pulses split into ingoing and outgoing components, which propagate
along the background field lines. In the other “flux pileup” regime,
a strong driving flow localizes the disturbances toward the null point
pair. Current structures aligned with the spines, fans, and separator
present in the field are found to result, and the structure of these
currents and their scaling with resistivity is investigated.

---------------------------------------------------------
Title: Kinematic reconnection at a magnetic null point: fan-aligned
current
Authors: Pontin, D. I.; Hornig, G.; Priest, E. R.
2005GApFD..99...77P Altcode:
Magnetic reconnection at a three-dimensional null point is a natural
extension of the familiar two-dimensional X-point reconnection. A
model is set up here for reconnection at a null point with current
directed parallel to the fan plane, by solving the kinematic, steady,
resistive magnetohydrodynamic equations in its vicinity. The magnetic
field is assumed to be steady, and a localised diffusion region
surrounding the null point is also assumed, outside which the plasma is
ideal. Particular attention is focussed on the way that the magnetic
flux changes its connections as a result of the reconnection. The
resultant plasma flow is found to cross the spine and fan of the
null, and thus transfer magnetic flux between topologically distinct
regions. Solutions are also found in which the flow crosses either
the spine or fan only.

---------------------------------------------------------
Title: Kinematic Magnetic Reconnection at 3d Null Points
Authors: Pontin, D. I.; Hornig, G.; Priest, E. R.
2004ESASP.575..507P Altcode: 2004soho...15..507P
No abstract at ADS

---------------------------------------------------------
Title: Magnetic Reconnection
Authors: Priest, E. R.; Pontin, D. I.
2004ASSL..317..397P Altcode: 2004shis.conf..397P
No abstract at ADS

---------------------------------------------------------
Title: Kinematic reconnection at a magnetic null point: spine-aligned
current
Authors: Pontin, D. I.; Hornig, G.; Priest, E. R.
2004GApFD..98..407P Altcode:
Magnetic reconnection at a three-dimensional null point is the natural
extension of the familiar two-dimensional X-point reconnection. A model
is set up here for reconnection at a spiral null point, by solving
the kinematic, steady, resistive magnetohydrodynamic equations in its
vicinity. A steady magnetic field is assumed, as well as the existence
of a localised diffusion region surrounding the null point. Outside the
diffusion region the plasma and magnetic field move ideally. Particular
attention is focussed on the way that the magnetic flux changes its
connections as a result of the reconnection. The resultant plasma flows
are found to be rotational in nature, as is the change in connections
of the magnetic field lines.

---------------------------------------------------------
Title: On the nature of three-dimensional magnetic reconnection
Authors: Priest, E. R.; Hornig, G.; Pontin, D. I.
2003JGRA..108.1285P Altcode:
Three-dimensional magnetohydrodynamic reconnection in a finite diffusion
region is completely different in many respects from two-dimensional
reconnection at an X-point. In two dimensions a magnetic flux velocity
can always be defined: two flux tubes can break at a single point and
rejoin to form two new flux tubes. In three dimensions we demonstrate
that a flux tube velocity does not generally exist. The magnetic field
lines continually change their connections throughout the diffusion
region rather than just at one point. The effect of reconnection on
two flux tubes is generally to split them into four flux tubes rather
than to rejoin them perfectly. During the process of reconnection each
of the four parts flips rapidly in a virtual flow that differs from
the plasma velocity in the ideal region beyond the diffusion region.

---------------------------------------------------------
Title: A Framework for Understanding the Topology of Complex Coronal
Structures
Authors: Pontin, D. I.; Priest, E. R.; Longcope, D. W.
2003SoPh..212..319P Altcode:
The Sun's coronal magnetic field is highly complex and provides the
driving force for many dynamical processes. The topology of this
complex field is made up mainly of discrete topological building
blocks produced by small numbers of magnetic fragments. In this work
we develop a method for predicting the possible topologies due to a
potential field produced by three photospheric sources, and describe
how this model accurately predicts the results of Brown and Priest
(1999). We then sketch how this idea may be extended to more general
non-symmetric configurations. It is found that, for the case of positive
total flux, a local separator bifurcation may take place with three
positive sources or with one positive and two negative sources, but
not for two positive sources and one negative.