P. F. Wyper

Non-linear tearing of 3D null point current sheets

The manner in which the rate of magnetic reconnection scales with the Lundquist number in realistic three-dimensional (3D) geometries is still an unsolved problem. It has been demonstrated that in 2D rapid non-linear tearing allows the reconnection rate to become almost independent of the Lundquist number (the “plasmoid instability”). Here, we present the first study of an analogous instability in a fully 3D geometry, defined by a magnetic null point. The 3D null current layer is found to be susceptible to an analogous instability but is marginally more stable than an equivalent 2D Sweet-Parker-like layer. Tearing of the sheet creates a thin boundary layer around the separatrix surface, contained within a flux envelope with a hyperbolic structure that mimics a spine-fan topology. Efficient mixing of flux between the two topological domains occurs as the flux rope structures created during the tearing process evolve within this envelope. This leads to a substantial increase in the rate of reconnection between the two domains.

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 (3D) 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 MHD waves and dynamic braiding of magnetic fields. The implications of these results to several areas of heliophysics are discussed.

Torsional magnetic reconnection at three dimensional null points: A phenomenological study

Magnetic reconnection around three dimensional (3D) magnetic null points is the natural progression from X-point reconnection in two dimensions. In 3D the separator field lines of the X-point are replaced with the spine line and fan plane (the field lines which asymptotically approach or recede from the null). In this work analytical models are developed for the newly classified torsional spine and torsional fan reconnection regimes by solving the steady state, kinematic, resistive magnetohydrodynamic equations. Reconnection is localized to around the null through the use of a localized field perturbation leading to a localized current while a constant resistivity is assumed. For the torsional spine case current is found to localize around the spine leading to a spiraling slippage of the field around the spine and out along the fan. For the torsional fan case current is found to be localized to the fan plane leading again to a spiraling slippage of the field. In each case no flux is transported across eit...

Simulations of solar jets confined by coronal loops.

Coronal jets are collimated, dynamic events that occur over a broad range of spatial scales in the solar corona. In the open magnetic field of coronal holes, jets form quasi-radial spires that can extend far out into the heliosphere, while in closed-field regions the jet outflows are confined to the corona. We explore the application of the embedded-bipole model to jets occurring in closed coronal loops. In this model, magnetic free energy is injected slowly by footpoint motions that introduce twist within the closed dome of the jet source region, and is released rapidly by the onset of an ideal kink-like instability. Two length scales characterize the system: the width (N) of the jet source region and the footpoint separation (L) of the coronal loop that envelops the jet source. We find that the jet characteristics are highly sensitive to the ratio L/N, in both the conditions for initiation and the subsequent dynamics. The longest-lasting and most energetic jets occur along long coronal loops with large L/N ratios, and share many features of open-field jets, while smaller L/N ratios produce shorter-duration, less energetic jets that are affected by reflections from the far-loop footpoint. We quantify the transition between these behaviours and show that our model replicates key qualitative and quantitative aspects of both quiet-Sun and active-region loop jets. We also find that the reconnection between the closed dome and surrounding coronal loop is very extensive: the cumulative reconnected flux at least matches the total flux beneath the dome for small L/N, and is more than double that value for large L/N.

Kelvin-Helmholtz instability in a current-vortex sheet at a 3D magnetic null

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.

Dynamics of Coronal Hole Boundaries

Remote and in-situ observations strongly imply that the slow solar wind consists of plasma from the hot, closed-field corona that is released onto open magnetic field lines. The Separatrix Web (S-Web) theory for the slow wind proposes that photospheric motions, at the scale of supergranules, are responsible for generating dynamics at coronal-hole boundaries, which result in the closed plasma release. We use three-dimensional magnetohydrodynamic (3D MHD) simulations to determine the effect of photospheric flows on the open and closed magnetic flux of a model corona with a dipole magnetic field and an isothermal solar wind. A rotational surface motion is used to approximate photospheric supergranular driving and is applied at the boundary between the coronal hole and helmet streamer. The resulting dynamics consist primarily of prolific and efficient interchange reconnection between open and closed flux. Magnetic flux near the coronal-hole boundary experiences multiple interchange events, with some flux interchanging over fifty times in one day. Additionally, we find that the interchange reconnection occurs all along the coronal-hole boundary, even producing a lasting change in magnetic-field connectivity in regions that were not driven by the applied motions. Our results show that these dynamics should be ubiquitous in the Sun and heliosphere. We discuss the implications of our simulations for understanding the observed properties of the slow solar wind, with particular focus on the global-scale consequences of interchange reconnection.

Reconnection at three dimensional magnetic null points: Effect of current sheet asymmetry

Asymmetric current sheets are likely to be prevalent in both astrophysical and laboratory plasmas with complex three dimensional (3D) magnetic topologies. This work presents kinematic analytical models for spine and fan reconnection at a radially symmetric 3D null (i.e., a null where the eigenvalues associated with the fan plane are equal) with asymmetric current sheets. Asymmetric fan reconnection is characterized by an asymmetric reconnection of flux past each spine line and a bulk flow of plasma across the null point. In contrast, asymmetric spine reconnection is characterized by the reconnection of an equal quantity of flux across the fan plane in both directions. The higher modes of spine reconnection also include localized wedges of vortical flux transport in each half of the fan. In this situation, two definitions for reconnection rate become appropriate: a local reconnection rate quantifying how much flux is genuinely reconnected across the fan plane and a global rate associated with the net flux driven across each semi-plane. Through a scaling analysis, it is shown that when the ohmic dissipation in the layer is assumed to be constant, the increase in the local rate bleeds from the global rate as the sheet deformation is increased. Both models suggest that asymmetry in the current sheet dimensions will have a profound effect on the reconnection rate and manner of flux transport in reconnection involving 3D nulls.

Spine-fan reconnection. The influence of temporal and spatial variation in the driver.

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

Quantifying three dimensional reconnection in fragmented current layers

There is growing evidence that when magnetic reconnection occurs in high Lundquist number plasmas such as in the Solar Corona or the Earths Magnetosphere it does so within a fragmented, rather than a smooth current layer. Within the extent of these fragmented current regions, the associated magnetic flux transfer and energy release occur simultaneously in many different places. This investigation focusses on how best to quantify the rate at which reconnection occurs in such layers. An analytical theory is developed which describes the manner in which new connections form within fragmented current layers in the absence of magnetic nulls. It is shown that the collective rate at which new connections form can be characterized by two measures; a total rate which measures the true rate at which new connections are formed and a net rate which measures the net change of connection associated with the largest value of the integral of E|| through all of the non-ideal regions. Two simple analytical models are pres...

Torsional magnetic reconnection: The effects of localizing the non-ideal (ηJ) term

Magnetic reconnection in three dimensions (3D) is a natural extension from X-point reconnection in two dimensions. Of central importance in the 3D process is a localized non-ideal region within which the plasma and magnetic field decouple allowing for field line connectivity change. In practice, localized current structures provide this localization; however, mathematically a similar effect can be achieved with the localization of plasma resistivity instead. Physically though, such approaches are unrealistic, as anomalous resistivity requires very localized currents. Therefore, we wish to know how much information is lost in localizing η instead of current? In this work we develop kinematic models for torsional spine and fan reconnection using both localized η and localized current and compare the non-ideal flows predicted by each. We find that the flow characteristics are dictated almost exclusively by the form taken for the current profile with η acting only to scale the flow. We do, however, note that the reconnection mechanism is the same in each case. Therefore, from an understanding point of view, localized η models are still important first steps into exploring the role of non-ideal effects.