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.
Bibcode: 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.

Title: Quantifying magnetic reconnection in the Solar corona
Authors: Aslanyan, Valentin; Pontin, David; Wyper, Peter; Antiochos,
   Spiro; Scott, Roger; Higginson, Aleida
Bibcode: 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.

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.
Bibcode: 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.

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.
Bibcode: 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.

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.
Bibcode: 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 <SUB>⊙</SUB> 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.

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
Bibcode: 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.

Title: Magnetic reconnection and the Kelvin-Helmholtz instability
    in the solar corona
Authors: Howson, T. A.; De Moortel, I.; Pontin, D. I.
Bibcode: 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. <BR /> 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. <BR /> 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. <BR /> 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. <BR />
  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.

Title: Is Flare Ribbon Fine Structure Related to Tearing in the
    Flare Current Sheet?
Authors: Wyper, P. F.; Pontin, D. I.
Bibcode: 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.

Title: GLEMuR: GPU-based Lagrangian mimEtic Magnetic Relaxation
Authors: Candelaresi, Simon; Pontin, David; Hornig, Gunnar
Bibcode: 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.

Title: The Dynamic Formation of Pseudostreamers
Authors: Scott, R. B.; Pontin, D. I.; Antiochos, S. K.; DeVore, C. R.;
   Wyper, P. F.
Bibcode: 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.

Title: The Dynamic Formation of Pseudostreamers
Authors: Scott, Roger B.; Pontin, David I.; Antiochos, Spiro K.;
   DeVore, C. Richard; Wyper, Peter F.
Bibcode: 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.

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.
Bibcode: 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.

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
Bibcode: 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.

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
Bibcode: 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.

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
Bibcode: 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.

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.
Bibcode: 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. <BR /> 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. <BR /> 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. <BR /> 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. <BR /> 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.

Title: The Parker problem: existence of smooth force-free fields
    and coronal heating
Authors: Pontin, David I.; Hornig, Gunnar
Bibcode: 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.

Title: Non-thermal line broadening due to braiding-induced turbulence
    in solar coronal loops
Authors: Pontin, D. I.; Peter, H.; Chitta, L. P.
Bibcode: 2020A&A...639A..21P
Altcode: 2020arXiv200811915P
  <BR /> 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. <BR /> 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. <BR /> 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<SUP>-1</SUP>. (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%. <BR /> 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.

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.
Bibcode: 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 }<SUB>0</SUB>{\boldsymbol{J}}, where
  {\boldsymbol{J}}={ne}({{\boldsymbol{V}}}<SUB>{\boldsymbol{i</SUB>}}-{{\boldsymbol{V}}}<SUB>{\boldsymbol{e</SUB>}})
  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.

Title: Do Current and Magnetic Helicities Have the Same Sign?
Authors: Russell, A. J. B.; Demoulin, P.; Hornig, G.; Pontin, D. I.;
   Candelaresi, S.
Bibcode: 2019ApJ...884...55R
Altcode:
  Current helicity, H <SUB> c </SUB>, and magnetic helicity, H <SUB>
  m </SUB>, 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 <SUB> c </SUB> and H <SUB> m
  </SUB> 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 <SUB> m </SUB> H <SUB> c </SUB> ≥ 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 <SUB> m </SUB> H
  <SUB> c </SUB> &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 <SUB> m </SUB> H <SUB> c </SUB> ≥ 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.

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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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. <BR
  /> 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. <BR /> 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. <BR /> 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.

Title: On the periodicity of linear and nonlinear oscillatory
    reconnection
Authors: Thurgood, J. O.; Pontin, D. I.; McLaughlin, J. A.
Bibcode: 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. <BR /> 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. <BR /> 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. <BR /> 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. <BR /> 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. <P />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.
Bibcode: 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, <SUP>3</SUP>He-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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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
Bibcode: 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.

Title: Magnetic field line braiding in the solar atmosphere
Authors: Candelaresi, S.; Pontin, D. I.; Hornig, G.
Bibcode: 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
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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
Bibcode: 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
Bibcode: 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.
Bibcode: 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
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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
  10<SUP>26</SUP>-{{10}<SUP>28</SUP>} 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
Bibcode: 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 10<SUP>26</SUP>-10<SUP>28</SUP>ergs
  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
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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
Bibcode: 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
Bibcode: 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
Bibcode: 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.
Bibcode: 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.
Bibcode: 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 x<SUP>n</SUP> as the position of
  a null, U≡dx<SUP>n</SUP>/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
  x<SUP>n</SUP> with velocity U, the velocity of the null is given by
  U=M<SUB>-1</SUB>▽×E. This expression is independent of Ohm's law. For
  resistive magnetohydrodynamics with uniform resistivity η, this
  reduces to U=V(x<SUP>n</SUP>)-ηM<SUB>-1</SUB>▽<SUB>2</SUB>B. 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
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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. <BR /> 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. <BR /> 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. <BR
  /> 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. <BR />
  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.
Bibcode: 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.
Bibcode: 2011A&A...536A..67W
Altcode: 2011arXiv1111.1100W
  <BR /> 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. <BR /> Methods: Two magnetic
  loops, braided in different ways, are used as initial conditions in
  resistive MHD simulations and their subsequent evolution is studied. <BR
  /> 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.
Bibcode: 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. <BR /> 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. <BR /> 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. <BR /> 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. <BR /> 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.
Bibcode: 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. <BR /> 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. <BR /> 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. <BR /> 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.
Bibcode: 2011A&A...529A..20G
Altcode: 2011arXiv1102.2351G
  <BR /> 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. <BR /> 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. <BR
  /> 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.
Bibcode: 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.
Bibcode: 2011A&A...525A..57P
Altcode: 2010arXiv1003.5784P
  <BR /> 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. <BR /> Methods: The three-dimensional
  evolution of a braided magnetic field is followed in a series of
  resistive MHD simulations. <BR /> 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.
Bibcode: 2010A&A...516A...5W
Altcode: 2010arXiv1001.1717W
  <BR /> 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. <BR /> 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. <BR /> 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.
Bibcode: 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. <BR /> 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. <BR /> Methods: We use mathematical modelling and
  finite difference resistive MHD simulations. <BR /> 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. <BR /> 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
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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. <P />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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 2004ESASP.575..507P
Altcode: 2004soho...15..507P
  No abstract at ADS

Title: Magnetic Reconnection
Authors: Priest, E. R.; Pontin, D. I.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.

