Theory Of Reconnection Research Articles

Why stellar astronomers should be interested in the sun

By all accounts, the Sun is a garden-variety star with an average age, a standard size, a regular temperature, norormal mass, an ordinary structure, and a typical chemical composition. Only one feature makes it special - the Sun is our star. It is located in the center of our solar system, and therefore, is responsible for all life on Earth. Astronomically speaking, the Sun is the only star in the sky that we can study up-close and personal. The unaided human eye does a better job of resolving the Sun than the finest telescope does for any other star. Stellar astronomers issue a press release whenever they can lay a few pixels of some state-of-the-art instrument across a nearby supergiant. The resolution of the Sun, however, is something we can see routinely in the magnificent images that are downloaded every day from the Transition Region and Coronal Explorer (TRACE) spacecraft. In a very real sense, the Sun is the Rosetta Stone of the Stars. Observations of the Sun deflecting starlight ushered in a new way of thinking about gravity. Zeeman effect observations of the Sun showed that stellar atmospheres were controlled by magnetic fields. The discovery of solar helium founded the science of stellar spectroscopy. Measurements of the solar mass, radius, and temperature allowed scientists to probe the interiors of stars for the first time. tim ancient age of the Sun implied that stars shine as a result of thermonuclear fusion. Observations of solar flares flamulated developments in rapid magnetic reconnection theory. The study of solar coronal holes led to a deeper understanding of the role that mass loss plays in the evolution of stars. Detailed analysis of the solar activity cycle inspired the development of Magneto-Hydrodynamic (MHD) dynamo theory. The detection and understanding; of the solar corona uncovered one of the longest unsolved mysteries in all of astrophysics — the coronal-heating problem. And the list goes on. The Sun is indeed a Laboratory for Astrophysics, but it is more than that. The Sun is a Laboratory for all of Physics. This paper describes 20th century physics discoveries that are directly attributable to solar observations. It is in the form of a Top Ten List, and was inspired originally by a talk given by Dr. Eugene N. Parker; subsequent discussions with Dr. Parker have molded it into its present form.

Fast Reconnection in a Two‐Stage Process

Magnetic reconnection plays an essential role in the generation and evolution of astrophysical magnetic fields. The best tested and most robust reconnection theory is that of Parker and Sweet. According to this theory, the reconnection rate scales with magnetic diffusivity λΩ as λ. In the interstellar medium, the Parker-Sweet reconnection rate is far too slow to be of interest. Thus, a mechanism for fast reconnection seems to be required. We have studied the magnetic merging of two oppositely directed flux systems in weakly ionized, but highly conducting, compressible gas. In such systems, ambipolar diffusion steepens the magnetic profile, leading to a thin current sheet. If the ion pressure is small enough and the recombination of ions is fast enough, the resulting rate of magnetic merging is fast and independent of λΩ. Slow recombination or sufficiently large ion pressure leads to slower merging, which scales with λΩ as λ. We derive a criterion for distinguishing these two regimes and discuss applications to the weakly ionized ISM and to protoplanetary accretion disks.

A parallel algorithm for global magnetic reconnection studies

A new algorithm is presented for the computation of two-dimensional magnetic reconnection in plasmas. Both resistive magnetohydrodynamic (MHD) and two-fluid models are considered. It has been implemented on several parallel platforms and shows good scalability up to 32 CPUs for reasonable problem sizes. A fixed, non-uniform rectangular mesh is used to resolve the different spatial scales in the reconnection problem. The resistive MHD version uses an implicit/explicit hybrid method, while the two-fluid version uses an alternating-direction implicit (ADI) method with high-order artificial dissipation. The technique has proven useful for comparing several different theories of collisional and collisionless reconnection.

Error field locked modes thresholds in rotating plasmas, anomalous braking and spin-up

The mechanisms of nonlinear interaction of external helical fields with a rotating plasma are investigated analyzing the results of recent systematic experiments on the Joint European Torus (JET) [A. Gibson et al., Phys. Plasmas 5, 1839 (1998)] that widen the previous data base collected on Compass-D [T. C. Hender et al., Nucl. Fusion 32, 2091 (1992)], Doublet III-D [R. J. La Haye et al., Nucl. Fusion 32, 2119 (1992)] and JET. The empirical scaling laws governing the onset of “error field” locked modes are re-assessed and interpreted in terms of existing driven reconnection theories and with new models. In particular the important mechanisms of plasma rotation braking, and spin up, associated with error fields are analyzed in detail and interpreted.

Fast reconnection in a two-stage process

Magnetic reconnection plays an essential role in the generation and evolution of astrophysical magnetic fields. The best tested and most robust reconnection theory is that of Parker and Sweet. According to this theory, the reconnection rate scales with magnetic diffusivity λΩ as λ. In the interstellar medium, the Parker-Sweet reconnection rate is far too slow to be of interest. Thus, a mechanism for fast reconnection seems to be required. We have studied the magnetic merging of two oppositely directed flux systems in weakly ionized, but highly conducting, compressible gas. In such systems, ambipolar diffusion steepens the magnetic profile, leading to a thin current sheet. If the ion pressure is small enough and the recombination of ions is fast enough, the resulting rate of magnetic merging is fast and independent of λΩ. Slow recombination or sufficiently large ion pressure leads to slower merging, which scales with λΩ as λ. We derive a criterion for distinguishing these two regimes and discuss applications to the weakly ionized ISM and to protoplanetary accretion disks.

Motion of Flare Footpoint Emission and Inferred Electric Field in Reconnecting Current Sheets

A systematic motion of Hα kernels during solar flares can be regarded as the chromospheric signature of progressive magnetic reconnection in the corona, in that the magnetic field lines swept through by the kernel motion are those connected to the diffusion region at the reconnection point. In this paper, we present high-cadence and high-resolution Hα-1.3 A observations of an impulsive flare that exhibits a systematic kernel motion and relate them to the reconnecting current sheet (RCS) in the corona. Through analyses of X-ray and microwave observations, we further examine the role of the macroscopic electric field inside the RCS in accelerating electrons. We measure the velocity of the kernel motion to be 20-100 km s-1. This is used together with the longitudinal magnetic field to infer an electric field as high as 90 V cm-1 at the flare maximum. This event shows a special magnetic field configuration and motion pattern of Hα kernels, in that a light bridge divides a flare kernel into two parts that move in different manners: one moving into the stronger magnetic field and the other moving along the isogauss contour of the longitudinal magnetic field. The temporal variation of the electric field inferred from the former type of kernel motion is found to be correlated with 20-85 keV hard X-ray light curves during the rise of the major impulsive phase. This would support the scenario of magnetic energy release via current dissipation inside the RCS, along with the hypothesis of the DC electric field acceleration of X-ray-emitting electrons below 100 keV. However, there is no good temporal correlation between the hard X-ray emission and the inferred electric field from the other motion pattern. Furthermore, the microwave emission, which supposedly comes from higher energy electrons, shows a time profile and electron spectrum that differs from those of the X-ray bursts. We conclude that either the two-dimensional magnetic reconnection theory related to the Hα kernel motion is applicable to only some part of the flare region due to its special magnetic geometry, or the electron acceleration is dominated by other mechanisms depending on the electron energy.

Improved theory of forced magnetic reconnection due to an error field and its application to seed island formation for the NTM

A seed island is required for destabilizing the neoclassical tearing mode (NTM), which degrades confinement in long sustained, high confinement, high beta plasmas. The seed island formation due to an MHD event, such as a sawtooth crash, is investigated by applying an improved boundary layer theory of forced magnetic reconnection. This improved theory introduces non-constant-ψ matching and reveals the complicated nature of the reconnection described by two reconnected fluxes. In the initial evolution, these reconnected fluxes grow on a timescale consisting of the ideal timescale, the MHD event timescale and the resistive kink timescale. The surface current is negative, Δ'(t) < 0, to be consistent with NTM theory. The theory also yields a new integral equation which includes the typical timescale of the resistive kink mode and allows us to investigate the time evolution of the seed island at time t ∼ τA S1/3.

An ionospheric convection signature of antiparallel reconnection

This paper sets out a critical test of the antiparallel merging hypothesis. For the conflicting theories of antiparallel and subsolar reconnection, we model the location of reconnection regions on the dayside magnetopause, their ionospheric footprints, and the resulting ionospheric convection patterns. We show that antiparallel reconnection, under particular seasonal and solar wind conditions, gives rise to a distinctive ionospheric convection signature. Specifically, around midwinter with a quasi‐steady solar wind and IMF Bz &lt; 0 and |By| ∼ |Bz|, we predict equatorward flow in the noon sector with poleward flow either side of noon if the antiparallel merging hypothesis is correct. In contrast, we predict poleward flow in the noon sector in midwinter under these solar wind conditions if the subsolar reconnection hypothesis is correct and in other seasons under both hypotheses. We go on to present radar and spacecraft data for an interval which satisfies the above seasonal and solar wind criteria, demonstrating that the convection signature of antiparallel merging is present. This is not consistent with the subsolar merging hypothesis.

Towards a self-consistent theory of turbulent reconnection

Fast reconnection due to turbulent dissipation has long been hypothesized. This classic idea is critically examined in 3D reduced magnetohydrodynamic turbulence, by taking into account the backreaction of small-scale magnetic fields. We find that the backreaction leads to such a dramatic reduction in a global reconnection rate as to recover the original Sweet–Parker scaling. In 2D limit, the global reconnection rate is shown to be enhanced over the Sweet–Parker result by a factor of magnetic Mach number. These results are consequences of mean square magnetic potential balance.

Improved theory of forced magnetic reconnection due to boundary perturbation

Boundary layer theory of forced magnetic reconnection due to an externally applied boundary perturbation is improved by introducing correct asymptotic matching which takes into account the effect of inertia in the inner layer precisely. The improved theory yields an integral equation for the time evolution of the reconnected flux. The initial evolution of the reconnection process is characterized by some significant features represented by the reconnected flux and an inner-layer reconnected flux. The typical time scales of the reconnected flux and of the inner-layer reconnected flux include the time scale of the boundary perturbation and exclude the Sweet-Parker time scale. The role of stability against the tearing modes in the reconnection process is also clarified. A current sheet induced on a resonant surface is in such a direction as to oppose the progress of the reconnection, because the equilibrium is stable against tearing modes in the absence of the boundary perturbation.

Three-dimensional reconnection on the Sun

A brief review is given of the theory of magnetic reconnection in three dimensions. The key elements of a three-dimensional null point are its spine and its fan, which consist, respectively, of a field line and a surface of field lines that pass through the null. The fans of two nulls intersect in general in a field line called a separator that joins the nulls. Several different types of reconnection have been proposed, namely: spine reconnection, fan reconnection, separator reconnection and quasi-separatrix layer reconnection. In addition, a new exact solution for reconnective annihilation has been recently discovered. A summary is also given of the impressive evidence of reconnection at work on the Sun provided by a range of observations from the Yohkoh and SOHO satellites, both of solar flares and of coronal heating events.

Recent developments in collisionless reconnection theory: Applications to laboratory and space plasmas

Recent developments in the theory and simulation of nonlinear collisionless reconnection hold the promise for providing solutions to some outstanding problems in laboratory and space plasma physics. Examples of such problems are sawtooth oscillations in tokamaks, magnetotail substorms, and impulsive solar flares. In each of these problems, a key issue is the identification of fast reconnection rates that are insensitive to the mechanism that breaks field lines (resistivity and/or electron inertia). The classical models of Sweet–Parker and Petschek sought to resolve this issue in the realm of resistive magnetohydrodynamics (MHD). However, the plasmas mentioned above are weakly collisional, and hence obey a generalized Ohm’s law in which the Hall current and electron pressure gradient terms play a crucial role. Recent theoretical models and simulations on impulsive (or triggered) as well as quasisteady reconnection governed by a generalized Ohm’s law are reviewed. In the impulsive reconnection problem, not only is the growth rate fast but the time derivative of the growth rate changes rapidly. In the steady-state reconnection problem, explicit analytical expressions are obtained for the geometric characteristics (that is, length and width) of the reconnection layer and the reconnection rate. Analytical results are tested by Hall MHD simulations. While some of the geometric features of the reconnection layer and the weak dependence of the reconnection rate on resistivity are reminiscent of Petschek’s classical model, the underlying wave and particle dynamics mediating the reconnection dynamics in the presence of the Hall current and electron pressure gradient are qualitatively different. Quantitative comparisons are made between theory and observations from laboratory as well as space plasmas.

Time-dependent magnetic reconnection in two-dimensional periodic geometry

We compare the predictions of incompressible, analytic reconnection theory with numerical simulations performed using a time-dependent, doubly periodic code. The properties of the simulated current sheets are shown to be in good quantitative agreement with recent planar analytic reconnection solutions based on X-point merging driven by sheared incompressible flows. We conclude that the analytic treatment is not seriously compromised by assuming an open flow geometry and a one-dimensional current layer. The analytic models, when augmented by nonlinear saturation arguments, are also shown to provide resistive scaling laws that accord well with computed merging rates. By way of contrast, we have found no computational evidence for the osculation of separatrices in current sheets, even for the case of classical head-on reconnection in which all shearing flows are absent. We attribute this to the dynamic nature of the simulated current sheet. Our simulations provide some evidence that dynamic current sheets can break up into magnetic islands, but whether this fragmentation can be attributed to the tearing mode instability remains unclear.

Reconnection theory in three dimensions

One of the most interesting aspects of magnetic reconnection theory in three-dimensions, as opposed to two, is that electric fields are generated with a component parallel to the magnetic field. When the magnetic field has null points, the parallel electric field occurs on the separator field line joining the null points, but if null points are absent, then the region of parallel electric field typically extends over a much broader region. The exact distribution of the parallel electric field is determined by the way the plasma flow drives the reconnection. Topologically, there are two basic types of reconnection, known as spine reconnection and fan reconnection, but it is not yet clear how these two types are related to actual reconnection processes occurring in the Sun. Several important advances have been made recently in applying reconnection theory to three-dimensional configurations such as flares and X-ray bright points where magnetic reconnection is thought to be important. However, our knowledge of the generation of electric fields in these configurations still remains incomplete, and this makes it difficult to understand the relationship between magnetic reconnection and the acceleration of energetic particles.

Magnetic reconnection observed in the pre-flare phase of AR 7186 of 1992 June 4

A direct observation of a magnetic reconnection event that occurred in the flare of AR 7186 of 1992 June 4 and observed by both the Soft X-ray Telescope (SXT) aboard the Yohkoh spacecraft and the Solar Flare Telescope (SFT, NAOJ, Mitaka), is reported in this article. Phenomena predicted by the theory of reconnection, such as the necessary inflow of field lines into the current sheet, the outflow of thermal plasma expelled by the current sheet, the evaporation and H αflare kernels caused by the outflow, and the opening-out of magnetic filed lines, have been confirmed in the observations. Based on an analysis of the observations, a phenomenological model of magnetic field line reconnection is sketched.

Basic physics of collisionless three-dimensional reconnection in the solar corona related to Yohkoh observations

New results concerning magnetic reconnection in the solar corona are reviewed. We apply the collisionless 3D reconnection theory — more exactly, the model of a high-temperature turbulent-current non-neutral current sheet — to the coronal conditions derived from the observations with the HXT and SXT onboard Yohkoh. New interpretations are discussed of the Yohkoh data on the site and mechanism of magnetic energy transformation into kinetic and thermal energies of superhot plasmas and accelerated high-energy particles. Open issues are the focus of our attention.

Flare-like energy release by flux pile-up reconnection

Flux pile-up magnetic merging solutions are discussed using the simple robust arguments of traditional steady-state reconnection theory. These arguments determine a unique scaling for the field strength and thickness of the current layer, namely Bs∼η−1/3, l∼η2/3, which are consistent with a variety of plasma inflow conditions. Next we demonstrate that flux pile-up merging can also be understood in terms of exact magnetic annihilation solutions. Although simple annihilation models cannot provide unique reconnection scalings, we show that the previous current sheet scalings derive from an optimized solution in which the peak dynamic and magnetic pressures balance in the reconnection region. The build-up of magnetic field in the current sheet implicit in flux pile-up solutions naturally leads to the idea of saturation. Hydromagnetic pressure effects limit the magnetic field in the sheet, yielding an upper limit on the reconnection rate for such solutions. This rate is still far superior to the Sweet–Parker merging rate, which can be derived by seeking solutions that avoid all forms of saturation. Finally we compare time dependent numerical simulations of the coalescence instability with the optimized flux pile-up models. This comparison suggests that merging driven by the relatively slow approach of large flux systems may be favored in practice.

Alfvén resonances and forced reconnection

The correspondence between the forced magnetic reconnection induced by perturbing the boundary of the simple Taylor model and the surface-wave-induced magnetic reconnection given by Alfven resonance theory is pointed out explicitly by showing that the theory of forced magnetic reconnection is actually embedded in the Alfven resonance theory. The advantages of viewing the forced reconnection as surface-wave-induced reconnection are briefly discussed in the context of the formation of small-scale structures at the magnetospheric boundary and solar coronal heating.

TRACE observation of damped coronal loop oscillations: implications for coronal heating

The imaging telescope on board the Transition Region and Coronal Explorer (TRACE) spacecraft observed the decaying transversal oscillations of a long [(130 +/- 6) x 10(6) meters], thin [diameter (2.0 +/- 0.36) x 10(6) meters], bright coronal loop in the 171 angstrom Fe(IX) emission line. The oscillations were excited by a solar flare in the adjacent active region. The decay time of the oscillations is 14.5 +/- 2.7 minutes for an oscillation with a frequency 3.90 +/- 0.13 millihertz. The coronal dissipation coefficient is estimated to be eight to nine orders of magnitude larger than the theoretically predicted classical value. The larger dissipation coefficient may solve existing difficulties with wave heating and reconnection theories.

Experimental studies of magnetic reconnection

Laboratory magnetic reconnection experiments have been performed for nearly 20 years. Elegant experiments by Stenzel and Gekelman [R. L. Stenzel and W. Gekelman, Phys. Rev. Lett. 42, 1055 (1979); W. Gekelman and R. L. Stenzel, Phys. Rev. Lett. 54, 2414 (1985)] focused on the measurement of field quantities with a single movable probe in a highly reproducible plasma. Observations included a very thin current sheet (on the order of c/ωpe), accelerated electrons, and whistler waves. The argon ions were unmagnetized in these experiments. Recent magnetohydrodynamic (MHD) experiments by Yamada and Ono have used merging plasmoids [M. Yamada, Y. Ono, A. Hayakawa, M. Katsurai, and F. W. Perkins, Phys. Rev. Lett. 65, 721 (1990); Y. Ono, M. Yamada, T. Akao, T. Tajima, and R. Matsumoto, Phys. Rev. Lett. 76, 3328 (1996)] and have measured three dimensional effects and ion acceleration. We have observed correlations between magnetic reconnection and energetic ion flow events with merging force free spheromaks at the Swarthmore Spheromak Experiment (SSX) [T. W. Kornack, P. K. Sollins, and M. R. Brown, Phys. Rev. E 58, R36 (1998)]. The reconnection layer is measured with linear and two dimensional probe arrays and ion flow is directly measured with a retarding grid energy analyzer. Flow has been measured both in the plane of the reconnection layer and out of the plane. The outflow velocity is nearly Alfvénic in the reconnection plane and the scale of the magnetic structures is consistent with collisionless reconnection theories (on the order of c/ωpi). Results from the two dimensional array show the formation of magnetic islands correlated with super-Alfvénic ions accelerated normal to the layer.