Professor David Pontin

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.

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

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.

Current helicity, H c, and magnetic helicity, H m, are two main quantities used to characterize magnetic fields. For example, such quantities have been widely used to characterize solar active regions and their ejecta (magnetic clouds). It is commonly assumed that H c and H m have the same sign, but this has not been rigorously addressed beyond the simple case of linear force-free fields. We aim to answer whether H m H c = 0 in general, and whether it is true over some useful set of magnetic fields. This question is addressed analytically and with numerical examples. The main focus is on cylindrically symmetric straight flux tubes, referred to as flux ropes (FRs), using the relative magnetic helicity with respect to a straight (untwisted) reference field. Counterexamples with H m H c < 0 have been found for cylindrically symmetric FRs with finite plasma pressure, and for force-free cylindrically symmetric FRs in which the poloidal field component changes direction. Our main result is a proof that H m H c = 0 is true for force-free cylindrically symmetric FRs where the toroidal field and poloidal field components are each of a single sign, and the poloidal component does not exceed the toroidal component. We conclude that the conjecture that current and magnetic helicities have the same sign is not true in general, but it is true for a set of FRs of importance to coronal and heliospheric physics.

Aims. Our aim is to investigate the resistive relaxation of a magnetic loop that contains braided magnetic flux but no net current or helicity. The loop is subject to line-tied boundary conditions. We investigate the dynamical processes that occur during this relaxation, in particular the magnetic reconnection that occurs, and discuss the nature of the final equilibrium. Methods. The three-dimensional evolution of a braided magnetic field is followed in a series of resistive MHD simulations. Results. It is found that, following an instability within the loop, a myriad of thin current layers forms, via a cascade-like process. This cascade becomes more developed and continues for a longer period of time for higher magnetic Reynolds number. During the cascade, magnetic flux is reconnected multiple times, with the level of this "multiple reconnection" positively correlated with the magnetic Reynolds number. Eventually the system evolves into a state with no more small-scale current layers. This final state is found to approximate a non-linear force-free field consisting of two flux tubes of oppositely-signed twist embedded in a uniform background field. © 2010 ESO.

Magnetic reconnection at a three-dimensional null point is the natural extension of the familiar two-dimensional X-point reconnection. Three dimensional null points are found in abundance in the solar corona, where they are thought to be an important feature with regards to the coronal heating problem. A model is set up here for reconnection at a 3D magnetic null point, by solving the kinematic, steady, resistive MHD equations in its vicinity. A steady magnetic field is assumed, as well as the existence of a localised diffusion region surrounding the null point. Particular attention is focused on the way that the magnetic flux changes its connections as a result of the reconnection process. The nature of the flows and the reconnection is found to be fundamentally different depending on the orientation of the electric current.