155 research outputs found
The structure of current layers and degree of field line braiding in coronal loops
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 modelling 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 -- of available free magnetic energy, more
than sufficient for a large nanoflare.Comment: To appear in ApJ. 20 pages, 10 figure
On the formation of current sheets in response to the compression or expansion of a potential magnetic field
The compression or expansion of a magnetic field that is initially potential
is considered. It was recently suggested by Janse & Low [2009, ApJ, 690, 1089]
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 & 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
non-zero current.Comment: Accepted for publication in Ap
Current sheet formation and nonideal behavior at three-dimensional magnetic null points
The nature of the evolution of the magnetic field, and of current sheet
formation, at three-dimensional (3D) magnetic null points is investigated. A
kinematic example is presented which demonstrates that for certain evolutions
of a 3D null (specifically those for which the ratios of the null point
eigenvalues are time-dependent) there is no possible choice of boundary
conditions which renders the evolution of the field at the null ideal.
Resistive MHD simulations are described which demonstrate that such evolutions
are generic. A 3D null is subjected to boundary driving by shearing motions,
and it is shown that a current sheet localised at the null is formed. The
qualitative and quantitative properties of the current sheet are discussed.
Accompanying the sheet development is the growth of a localised parallel
electric field, one of the signatures of magnetic reconnection. Finally, the
relevance of the results to a recent theory of turbulent reconnection is
discussed.Comment: to appear in Phys. Plasmas. A version with higher quality figures can
be found at http://www.maths.dundee.ac.uk/~dpontin/ In this replacement
version, typos have been corrected, and in addition references and some
further discussion adde
On the nature of reconnection at a solar coronal null point above a separatrix dome
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. We demonstrate using analytical and computational models
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 quasi-separatrix layer or slip-running
reconnection.Comment: Accepted for publication in the Astrophysical Journa
Generalised models for torsional spine and fan magnetic reconnection
Three-dimensional null points are present in abundance in the solar corona,
and the same is likely to be true in other astrophysical environments. Recent
studies suggest that reconnection at such 3D nulls may play an important role
in the coronal dynamics. In this paper the properties of the torsional spine
and torsional fan modes of magnetic reconnection at 3D nulls are investigated.
New analytical models are developed, which for the first time include a current
layer that is spatially localised around the null, extending along either the
spine or the fan of the null. These are complemented with numerical
simulations. The principal aim is to investigate the effect of varying the
degree of asymmetry of the null point magnetic field on the resulting
reconnection process - where previous studies always considered a non-generic
radially symmetric null. The geometry of the current layers within which
torsional spine and torsional fan reconnection occur is found to be strongly
dependent on the symmetry of the magnetic field. Torsional spine reconnection
still occurs in a narrow tube around the spine, but with elliptical
cross-section when the fan eigenvalues are different, and with the short axis
of the ellipse being along the strong field direction. The spatiotemporal peak
current, and the peak reconnection rate attained, are found not to depend
strongly on the degree of asymmetry. For torsional fan reconnection, the
reconnection occurs in a planar disk in the fan surface, which is again
elliptical when the symmetry of the magnetic field is broken. The short axis of
the ellipse is along the weak field direction, with the current being peaked in
these weak field regions. The peak current and peak reconnection rate in this
case are clearly dependent on the asymmetry, with the peak current increasing
but the reconnection rate decreasing as the degree of asymmetry is increased
Magnetic field line braiding in the solar atmosphere
AbstractUsing 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.</jats:p
Current sheets at three-dimensional magnetic nulls:effect of compressibility
The nature of current sheet formation in the vicinity of three-dimensional
(3D) magnetic null points is investigated. The particular focus is upon the
effect of the compressibility of the plasma on the qualitative and quantitative
properties of the current sheet. An initially potential 3D null is subjected to
shearing perturbations, as in a previous paper [Pontin et al., Phys. Plasmas,
in press (2007)]. It is found that as the incompressible limit is approached,
the collapse of the null point is suppressed, and an approximately planar
current sheet aligned to the fan plane is present instead. This is the case
regardless of whether the spine or fan of the null is sheared. Both the peak
current and peak reconnection rate are reduced. The results have a bearing on
previous analytical solutions for steady-state reconnection in incompressible
plasmas, implying that fan current sheet solutions are dynamically accessible,
while spine current sheet solutions are not.Comment: to appear in Physics of Plasmas. This version contains updated
figures and references, additional discussion, and typos are fixed. This is
the second in a series of papers - the first of which (by the same authors)
is located at astro-ph/0701462. A version with higher quality figures can be
found at http://www.maths.dundee.ac.uk/~dpontin
Magnetic reconnection at 3D null points: effect of magnetic field asymmetry
The aim of this paper is to investigate the properties of magnetic
reconnection at a 3D null point, with respect to their dependence on the
symmetry of the magnetic field around the null. In particular we examine the
rate of flux transport across the null point with symmetric/asymmetric
diffusion regions, as well as how the current sheet forms in time, and its
properties. Mathematical modelling and finite difference resistive MHD
simulations are used. It is found that the basic structure of the mode of
magnetic reconnection considered is unaffected by varying the magnetic field
symmetry, that is, the plasma flow is found cross both the spine and fan of the
null. However, the peak intensity and dimensions of the current sheet are
dependent on the symmetry/ asymmetry of the field lines. As a result, the
reconnection rate is also found to be strongly dependent on the field
asymmetry.Comment: 23 pages, 9 figure
Non-thermal line broadening due to braiding-induced turbulence in solar coronal loops
Aims. Emission line profiles from solar coronal loops exhibit properties that are unexplained by current models. We investigate the non-thermal broadening associated with plasma heating in coronal loops that is induced by magnetic field line braiding.
Methods. We describe the coronal loop by a 3D magnetohydrodynamic model of the turbulent decay of an initially-braided magnetic field. From this, we synthesised the Fe XI
Dynamic topology and flux rope evolution during non-linear tearing of 3D null point current sheets
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
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