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 $10^{26}$--$10^{28}{\rm ergs}$ of available free magnetic energy, more than sufficient for a large nanoflare.Comment: To appear in ApJ. 20 pages, 10 figure

A generalized Poloidal-Toroidal decomposition and an absolute measure of helicity

This is the final version. Available on open access from IOP Publishing via the DOI in this recordIn fluid mechanics and magneto-hydrodynamics it is often useful to decompose a vector field into poloidal and toroidal components. In a spherical geometry, the poloidal component contains all of the radial part of the field, while the curl of the toroidal component contains all of the radial current. This paper explores how they work in more general geometries, where space is foliated by nested simply connected surfaces. Vector fields can still be divided into poloidal and toroidal components, but in geometries lacking spherical symmetry it makes sense to further divide the poloidal field into a standard part and a 'shape' term, which in itself behaves like a toroidal field and arises from variations in curvature. The generalised P–T decomposition leads to a simple definition of helicity which does not rely on subtracting the helicity of a potential reference field. Instead, the helicity measures the net linking of the standard poloidal field with the toroidal field as well as the new shape field. This helicity is consistent with the relative helicity in spherical and planar geometries. Its time derivative due to motion of field lines in a surface has a simple and intuitively pleasing form.MB acknowledges STFC grant ST/R000891/1. GH acknowledges support from STFC grant ST/N000714/1

The global distribution of magnetic helicity in the solar corona

By defining an appropriate field line helicity, we apply the powerful concept of magnetic helicity to the problem of global magnetic field evolution in the Sun's corona. As an ideal-magnetohydrodynamic invariant, the field line helicity is a meaningful measure of how magnetic helicity is distributed within the coronal volume. It may be interpreted, for each magnetic field line, as a magnetic flux linking with that field line. Using magneto-frictional simulations, we investigate how field line helicity evolves in the non-potential corona as a result of shearing by large-scale motions on the solar surface. On open magnetic field lines, the helicity injected by the Sun is largely output to the solar wind, provided that the coronal relaxation is sufficiently fast. But on closed magnetic field lines, helicity is able to build up. We find that the field line helicity is non-uniformly distributed, and is highly concentrated in twisted magnetic flux ropes. Eruption of these flux ropes is shown to lead to sudden bursts of helicity output, in contrast to the steady flux along the open magnetic field lines.</p

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

Observation of thermal acoustic modes of a droplet coupled to an optomechanical sensor

The bulk acoustic modes of liquid droplets, well understood from a theoretical perspective, have rarely been observed experimentally. Here, we report the direct observation of acoustic vibrational modes in a picoliter-scale droplet, extending up to ~ 40 MHz. This was achieved by coupling the droplet to an ultra-sensitive optomechanical sensor, which operates in a thermal-noise limited regime and with a substantial contribution from acoustic noise in the ambient medium. The droplet vibrational modes manifest as Fano resonances in the thermal noise spectrum of the sensor. This is amongst the few reported observations of droplet acoustic modes, and of Fano interactions in a coupled mechanical oscillator system driven only by thermal Brownian motion.Comment: 11 pages, 3 figure

Topological constraints in the reconnection of vortex braids

We study the relaxation of a topologically nontrivial vortex braid with zero net helicity in a barotropic fluid. The aim is to investigate the extent to which the topology of the vorticity field—characterized by braided vorticity field lines—determines the dynamics, particularly the asymptotic behavior under vortex reconnection in evolution at high Reynolds numbers (25 000). Analogous to the evolution of braided magnetic fields in plasma, we find that the relaxation of our vortex braid leads to a simplification of the topology into large-scale regions of opposite swirl, consistent with an inverse cascade of the helicity. The change of topology is facilitated by a cascade of vortex reconnection events. During this process, the existence of regions of positive and negative kinetic helicities imposes a lower bound for the kinetic energy. For the enstrophy, we derive analytically a lower bound given by the presence of unsigned kinetic helicity, which we confirm in our numerical experiments

Evolution of field line helicity in magnetic relaxation

This work was facilitated by Leverhulme Trust under Grant No. PRG-2017–169, with additional support from Science and Technology Facilities Council (UK) under consortium Grants Nos. ST/N000714, ST/N000781, and ST/S000321.Plasma relaxation in the presence of an initially braided magnetic field can lead to self-organization into relaxed states that retain non-trivial magnetic structure. These relaxed states may be in conflict with the linear force-free fields predicted by the classical Taylor theory, and remain to be fully understood. Here, we study how the individual field line helicities evolve during such a relaxation, and show that they provide new insights into the relaxation process. The line helicities are computed for numerical resistive-magnetohydrodynamic simulations of a relaxing braided magnetic field with line-tied boundary conditions, where the relaxed state is known to be non-Taylor. First, our computations confirm recent analytical predictions that line helicity will be predominantly redistributed within the domain, rather than annihilated. Second, we show that self-organization into a relaxed state with two discrete flux tubes may be predicted from the initial line helicity distribution. Third, for this set of line-tied simulations we observe that the sub-structure within each of the final tubes is a state of uniform line helicity. This uniformization of line helicity is consistent with Taylor theory applied to each tube individually. However, it is striking that the line helicity becomes significantly more uniform than the force-free parameter.Publisher PDFPeer reviewe

The Dependence of Coronal Loop Heating on the Characteristics of Slow Photospheric Motions

The Parker hypothesis (Parker (1972)) assumes that heating of coronal loops occurs due to reconnection, induced when photospheric motions braid field lines to the point of current sheet formation. In this contribution we address the question of how the nature of photospheric motions affects heating of braided coronal loops. We design a series of boundary drivers and quantify their properties in terms of complexity and helicity injection. We examine a series of long-duration full resistive MHD simulations in which a simulated coronal loop, consisting of initially uniform field lines, is subject to these photospheric flows. Braiding of the loop is continually driven until differences in behaviour induced by the drivers can be characterised. It is shown that heating is crucially dependent on the nature of the photospheric driver - coherent motions typically lead to fewer large energy release events, while more complex motions result in more frequent but less energetic heating events