E. R. Priest

An emerging flux model for the solar flare phenomenon

An outline is presented of the physical processes involved in the emerging flux model, which appears to explain naturally many solar flare observations. The separate physical phases of the basic model include a preflare heating phase as the new flux emerges, an impulsive phase as high-energy particles are accelerated, a flash (or explosive) phase when the H-alpha intensity increases, and a main phase while it decreases. The extent and morphology of the main phase emission depend on the structure of the magnetic field region in which the new flux finds itself imbedded. It is suggested that a (small) simple loop flare occurs if the new flux appears in a region where no great amount of magnetic energy in excess of potential is stored. A two-ribbon flare occurs if the flux emerges near the polarity inversion line of an active region that has begun to develop filaments.

Three‐dimensional magnetic reconnection without null points: 1. Basic theory of magnetic flipping

In two or three dimensions, magnetic reconnection may occur at neutral points and is accompanied by the transport of magnetic field lines across separatrices, the field lines (or flux surfaces in three dimensions) at which the mapping of field lines is discontinuous. Here we show that reconnection may also occur in three dimensions in the absence of neutral points at so-called “quasi-separatrix layers,” where there is a steep gradient in field line linkage. Reconnection is a global property, and so, in order to determine where it can occur, the first step is to enclose the volume being considered by a boundary (such as a spherical surface). Then the mapping of field lines from one part of the boundary to another is determined, and quasi-separatrix layers may be identified as regions where the gradient of the mapping or its inverse is very much larger than normal. The most effective measure of the presence of such layers is the norm of the displacement gradient tensor; their qualitative location is robust and insensitive to the particular surface that is chosen. Reconnection itself occurs when there is a breakdown of ideal MHD and a change of connectivity of plasma elements, where the field line velocity becomes larger than the plasma velocity, so that the field lines slip through the plasma. This breakdown can occur in the quasi-separatrix layers with an electric field component parallel to the magnetic field. In three dimensions the electric field E (and therefore the field line velocity v⊥) depends partly on the imposed values of E (or v⊥) at the boundary and partly on the gradients of the inverse mapping function. We show that the inverse mapping determines the location of the narrow layers where the breakdown of ideal MHD can occur, while the imposed boundary values of v⊥ determine mainly the detailed flow pattern inside the layers. Thus, in general, E (and therefore v⊥) becomes much larger than its boundary values at locations where the gradients of the inverse mapping function are large. An example is given of a sheared X field, where a slow smooth continuous shear flow imposed on the boundary across one quasi-separatrix produces a flipping of magnetic field lines as they slip rapidly through the plasma in the other quasi-separatrix layer. It results in a strong plasma jetting localized in, and parallel to, the separatrix layers.

Kink instability of solar coronal loops as the cause of solar flares

Solar coronal loops are observed to be remarkably stable structures. A magnetohydrodynamic stability analysis of a model loop by the energy method suggests that the main reason for stability is the fact that the ends of the loop are anchored in the dense photosphere. In addition to such line-tying, the effect of a radial pressure gradient is incorporated in the analysis.Two-ribbon flares follow the eruption of an active region filament, which may lie along a magnetic flux tube. It is suggested that the eruption is caused by the kink instability, which sets in when the amount of magnetic twist in the flux tube exceeds a critical value. This value depends on the aspect ratio of the loop, the ratio of the plasma to magnetic pressure and the detailed transverse magnetic structure. For a force-free field of uniform twist the critical twist is 3.3π, and for other fields it is typically between 2π and 6π. Occasionally active region loops may become unstable and give rise to small loop flares, which may also be a result of the kink instability.

Magnetic reconnection at three-dimensional null points

The skeleton of an isolated null point in three dimensions consists of a ‘spine curve’ and a ‘fan surface’. Two isolated magnetic field lines approach (or recede from) the null point from both directions along the spine, and a continuum of field lines recedes from (or approaches) the null in the plane of the fan surface. Two bundles of field lines approach the null point around the spine (one from each direction) and spread out near the fan. The kinematics of steady reconnection at such a null point is considered, depending on the nature of the imposed boundary conditions on the surface that encloses the null, in particular on a cylindrical surface with its axis along the spine. Three kinds of reconnection are discovered. In ‘spine reconnection’ continuous footpoint motions are imposed on the curved cylindrical surface, crossing the fan and driving singular jetting flow along the spine. In ‘fan reconnection’ continuous footpoint motions are prescribed on the ends of the cylinder, crossing the spine and driving a singular swirling motion at the fan. An antireconnection theorem is proved, which states that steady MHD reconnection in three dimensions with plasma flow across the spine or fan is impossible in an inviscid plasma with a highly subAlfvenic flow and uniform magnetic diffusivity. One implication of this is that reconnection tends to be an inherently nonlinear phenomenon. A linear theory for slow steady reconnection is developed which demonstrates explicitly the nature of the spine singularity in spine reconnection. Finally, the properties of separator reconnection’ in complex configurations containing two null points are discussed by means of analytical examples.

The structure of three‐dimensional magnetic neutral points

The local configurations of three‐dimensional magnetic neutral points are investigated by a linear analysis about the null. It is found that the number of free parameters determining the arrangement of field lines is four. The configurations are first classified as either potential or non‐potential. Then the non‐potential cases are subdivided into three cases depending on whether the component of current parallel to the spine is less than, equal to or greater than a threshold current; therefore there are three types of linear non‐potential null configurations (a radial null, a critical spiral and a spiral). The effect of the four free parameters on the system is examined and it is found that only one parameter categorizes the potential configurations, whilst two parameters are required if current is parallel to the spine. However, all four parameters are needed if there is current both parallel and perpendicular to the spine axis. The magnitude of the current parallel to the spine determines whether the n...

Dynamics and structure of quiescent solar prominences

1 Introduction to Quiescent Solar Prominences (E R Priest).- 1.1 Basic Description.- 1.1.1 Different Types.- 1.1.2 Properties.- 1.1.3 Development.- 1.1.4 Structure.- 1.1.5 Eruption.- 1.2 Basic Equations of MHD.- 1.2.1 Magnetohydrostatics.- 1.2.2 Waves.- 1.2.3 Instabilities.- 1.3 Prominence Puzzles.- 2 Overall Properties and Steady Flows (B Schmieder).- 2.1 Basic Properties.- 2.1.1 Description and Classification.- 2.1.2 Fine Structure in H?.- 2.1.3 Evolution of Filaments During the Solar Cycle.- 2.2 Physical Characteristics: Density and Temperature.- 2.2.1 Density and Ionization Degree.- 2.2.2 Non LTE Models.- 2.2.3 Turbulent Velocity and Electron Temperature.- 2.3 Velocity Field and Mass Flux.- 2.3.1 Instrumentation.- 2.3.2 H? Profile Analysis.- 2.3.3 Vertical Motions.- 2.3.4 Horizontal Motions.- 2.3.5 Oscillations.- 2.4 Instability.- 2.4.1 Disparition Brusque of Filaments.- 2.4.2 Model Support.- 2.4.3 Post-Flare Loops and Loop Prominences.- 2.5 Conclusion.- 3 Prominence Environment (O Engvold).- 3.1 Introduction.- 3.2 Helmet Streamers.- 3.2.1 Eclipse Photography.- 3.2.2 Morphology.- 3.2.3 Location of Current Sheet.- 3.2.4 Brightness.- 3.3 Coronal Cavities.- 3.3.1 Brightness and Structure.- 3.3.2 Temperature and Density.- 3.4 Filament Channels.- 3.4.1 Association with Neutral Lines.- 3.4.2 Poleward Migration of Filament Channels.- 3.4.3 Presence of Prominences.- 3.4.4 Temperature and Electron Pressure.- 3.4.5 Cool Matter in the Filament Channels.- 3.5 Prominence-Corona Transition Region.- 3.5.1 Line Emission.- 3.5.2 Empirical Modelling.- 3.5.3 A Fragmented and Dynamic Transition Region.- 3.6 Prominences and Environment.- 3.6.1 Magnetic Fields and Chromospheric Structure.- 3.6.2 Association with Supergranulation Network.- 3.6.3 Dynamics.- 3.6.4 The Mass of Coronal Cavity and Prominence.- 3.6.5 Coronal Voids - a Source of Prominence Mass?.- 3.7 Modelling of the Helmet Streamer/Prominence Complex.- 3.7.1 Helmet Streamer and Cavity.- 3.7.2 Magnetic Field Topology.- 3.7.3 Siphon-Type Models.- 3.8 Conclusions.- 4 Observation of Prominence Magnetic Fields (J L Leroy).- 4.1 Historical Steps.- 4 2 Investigations Based on the Polarimetry of Spectral Lines.- 4.2.1 Zeeman Effect.- 4.2.2 HanleEffect.- 4.2.3 180 1 Introduction to Quiescent Solar Prominences (E R Priest).- 1.1 Basic Description.- 1.1.1 Different Types.- 1.1.2 Properties.- 1.1.3 Development.- 1.1.4 Structure.- 1.1.5 Eruption.- 1.2 Basic Equations of MHD.- 1.2.1 Magnetohydrostatics.- 1.2.2 Waves.- 1.2.3 Instabilities.- 1.3 Prominence Puzzles.- 2 Overall Properties and Steady Flows (B Schmieder).- 2.1 Basic Properties.- 2.1.1 Description and Classification.- 2.1.2 Fine Structure in H?.- 2.1.3 Evolution of Filaments During the Solar Cycle.- 2.2 Physical Characteristics: Density and Temperature.- 2.2.1 Density and Ionization Degree.- 2.2.2 Non LTE Models.- 2.2.3 Turbulent Velocity and Electron Temperature.- 2.3 Velocity Field and Mass Flux.- 2.3.1 Instrumentation.- 2.3.2 H? Profile Analysis.- 2.3.3 Vertical Motions.- 2.3.4 Horizontal Motions.- 2.3.5 Oscillations.- 2.4 Instability.- 2.4.1 Disparition Brusque of Filaments.- 2.4.2 Model Support.- 2.4.3 Post-Flare Loops and Loop Prominences.- 2.5 Conclusion.- 3 Prominence Environment (O Engvold).- 3.1 Introduction.- 3.2 Helmet Streamers.- 3.2.1 Eclipse Photography.- 3.2.2 Morphology.- 3.2.3 Location of Current Sheet.- 3.2.4 Brightness.- 3.3 Coronal Cavities.- 3.3.1 Brightness and Structure.- 3.3.2 Temperature and Density.- 3.4 Filament Channels.- 3.4.1 Association with Neutral Lines.- 3.4.2 Poleward Migration of Filament Channels.- 3.4.3 Presence of Prominences.- 3.4.4 Temperature and Electron Pressure.- 3.4.5 Cool Matter in the Filament Channels.- 3.5 Prominence-Corona Transition Region.- 3.5.1 Line Emission.- 3.5.2 Empirical Modelling.- 3.5.3 A Fragmented and Dynamic Transition Region.- 3.6 Prominences and Environment.- 3.6.1 Magnetic Fields and Chromospheric Structure.- 3.6.2 Association with Supergranulation Network.- 3.6.3 Dynamics.- 3.6.4 The Mass of Coronal Cavity and Prominence.- 3.6.5 Coronal Voids - a Source of Prominence Mass?.- 3.7 Modelling of the Helmet Streamer/Prominence Complex.- 3.7.1 Helmet Streamer and Cavity.- 3.7.2 Magnetic Field Topology.- 3.7.3 Siphon-Type Models.- 3.8 Conclusions.- 4 Observation of Prominence Magnetic Fields (J L Leroy).- 4.1 Historical Steps.- 4 2 Investigations Based on the Polarimetry of Spectral Lines.- 4.2.1 Zeeman Effect.- 4.2.2 HanleEffect.- 4.2.3 180 Ambiguity.- 4.2.4 Instrumental Achievements.- 4.3 Indirect Magnetic Field Determinations.- 4.4 Magnetic Field at the Photospheric Level.- 4.5 Main Features of the Magnetic Field in Quiescent Prominences.- 4.5.1 Field Strength.- 4.5.2 Angle with Horizontal.- 4.5.3 Angle with Prominence Axis.- 4.5.4 Magnetic Structure with Normal or Inverse Polarity.- 4.5.5 Homogeneity of the Field.- 4.6 Some Important Problems.- 4.6.1 Magnetic Field in Sub Arc Second Structures.- 4.6.2 Paradox of Fine Vertical Structures.- 4.6.3 Determination of Currents.- 4.6.4 Evolution of Prominence Magnetic Structure.- 5 The Formation of Solar Prominences (J M Malherbe).- 5.1 Introduction.- 5.2 Overview of Observations.- 5.3 Main MHD Instabilities Involved in Prominence Formation.- 5.3.1 Radiative Thermal Instability.- 5.3.2 Resistive Instabilities.- 5.4 Steady Reconnection in Current Sheets.- 5.4.1 Incompressible and Compressible Theories.- 5.4.2 Unification of Different Regimes.- 5.5 Static Models.- 5.5.1 Condensation in a Loop.- 5.5.2 Condensation in an Arcade.- 5.5.3 Condensation in a Sheared Magnetic Field.- 5.5.4 Condensation in a Current Sheet.- 5.6 Dynamic Models: Injection from the Chromosphere into Closed Loops.- 5.6.1 Surge-Like Models.- 5.6.2 Evaporation Models.- 5.7 Dynamic Models: Condensation in Coronal Current Sheets.- 5.7.1 Numerical Simulations.- 5.7.2 Role of Shock Waves in Condensation Process.- 5.8 Unsolved Problems.- 5.9 Conclusion.- 6 Structure and Equilibrium of Prominences (U Anzer).- 6.1 Introduction.- 6.2 Prominence Models.- 6.2.1 Global Structure.- 6.2.1.1 Two-Dimensional Equilibria.- 6.2.1.1.1 Models with Normal Magnetic Polarity.- 6.2.1.1.2 Models with Inverse Magnetic Polarity.- 6.2.1.1.3 Force-Free Fields.- 6.2.1.2 Quasi-Three-Dimensional Models.- 6.2.1.3 Support by Alfven Waves.- 6.2.2 Internal Structure and Thermal Equilibrium.- 6.2.2.1 Hydrostatic Equilibrium.- 6.2.2.2 Thermal Equilibrium.- 6.3 Concluding Remarks.- 7 Stability and Eruption of Prominences (A W Hood).- 7.1 Introduction.- 7.2 Description of MHD Instabilities.- 7.3 Methods of Solution.- 7.3.1 Normal Modes.- 7.3.2 Energy Method.- 7.3.3 Non Equilibrium.- 7.4 Effect of the Dense Photosphere.- 7.4.1 Physical Arguments.- 7.4.2 Ballooning Modes.- 7.5 Coronal Arcades.- 7.5.1 Distributed Current Models - Eruptive Instability.- 7.5.2 Localised Modes - Small Scale Structure.- 7.5.3 Arcades Containing a Current Sheet.- 7.6 Thermal Stability.- 7.7 Resistive Instabilities - Tearing Modes.- 7.7.1 Introduction.- 7.7.2 Estimate of Tearing Mode Growth Rate.- 7.7.3 Effect of Line Tying.- 7.8 Simple Model of Prominence Eruption and a Coronal Mass Ejection.- 7.9 Conclusions and Future Work.- References.

A FLUX-TUBE TECTONICS MODEL FOR SOLAR CORONAL HEATING DRIVEN BY THE MAGNETIC CARPET

We explore some of the consequences of the magnetic carpet for coronal heating. Observations show that most of the magnetic flux in the quiet Sun emerges as ephemeral regions and then quickly migrates to supergranule boundaries. The original ephemeral concentrations fragment, merge, and cancel over a time period of 10-40 hr. Since the network photospheric flux is likely to be concentrated in units of 1017 Mx or smaller, there will be myriads of coronal separatrix surfaces caused by the highly fragmented photospheric magnetic configuration in the quiet network. We suggest that the formation and dissipation of current sheets along these separatrices are an important contribution to coronal heating. The dissipation of energy along sharp boundaries we call, by analogy with geophysical plate tectonics, the tectonics model of coronal heating. Similar to the case on Earth, the relative motions of the photospheric sources will drive the formation and dissipation of current sheets along a hierarchy of such separatrix surfaces at internal dislocations in the corona. In our preliminary assessment of such dissipation we find that the heating is fairly uniform along the separatrices, so that each elementary coronal flux tube is heated uniformly. However, 95% of the photospheric flux closes low down in the magnetic carpet and the remaining 5% forms large-scale connections, so the magnetic carpet will be heated more effectively than the large-scale corona. This suggests that unresolved observations of coronal loops should exhibit enhanced heating near their feet in the carpet, while the upper parts of large-scale loops should be heated rather uniformly but less strongly.

A twisted flux-tube model for solar prominences. I. General properties

It is proposed that a solar prominence consists of cool plasma supported in a large-scale curved and twisted magnetic flux tube. As long as the flux tube is untwisted, its curvature is concave toward the solar surface, and so it cannot support dense plasma against gravity. However, when it is twisted sufficiently, individual field lines may acquire a convex curvature near their summits and so provide support. Cool plasma then naturally tends to accumulate in such field line dips either by injection from below or by thermal condensation. As the tube is twisted up further or reconnection takes place below the prominence, one finds a transition from normal to inverse polarity. When the flux tube becomes too long or is twisted too much, it loses stability and its true magnetic geometry as an erupting prominence is revealed more clearly. 56 refs.

The magnetohydrodynamics of current sheets

A universal phenomenon in cosmic plasmas is the creation of sheets of intense current near X-type neutral points (where the magnetic field vanishes). These sheets are important as sites where the magnetic-field energy is converted efficiently into heat and bulk kinetic energy and where particles can be accelerated to high energies. Examples include disruptions in laboratory Tokamaks, substorms in the Earths magnetosphere and flares on the Sun. During those phenomena the antiparallel magnetic-field lines on both sides of a current sheet can be cut and reconnect with each other, so changing the global topology of the field. The author summarises the examples of current sheets and describes how they are formed. Then the basic behaviour of a one-dimensional sheet is presented, together with an account of the linear tearing-mode instability that can cause the field lines in such a sheet to reconnect. Such reconnection may develop in different ways: it may arise from a spontaneous instability or it may be driven, either from outside by motions or locally by a resistivity enhancement. The last three sections describe the various processes that may occur during the non-linear development of tearing as well as the many numerical and laboratory experiments that are aiding the understanding of this intriguing cosmical process.

Mean Field Model for the Formation of Filament Channels on the Sun

The coronal magnetic field is subject to random footpoint motions that cause small-scale twisting and braiding of field lines. We present a mean field theory describing the effects of such small-scale twists on the large-scale coronal field. This theory assumes that the coronal field is force free, with electric currents flowing parallel or antiparallel to magnetic field lines. Random footpoint motions are described in terms of diffusion of the mean magnetic field at the photosphere. The appropriate mean field equations are derived, and a numerical method for solving these equations in three dimensions is presented. Preliminary results obtained with this method are also presented. In particular the formation of filament channels is studied. Filament channels are regions where the coronal magnetic field is strongly aligned with the underlying polarity inversion line in the photosphere. It is found that magnetic flux cancellation plays an important role in the formation of such channels. Various models of the coronal field are presented, including some in which the axial field is assumed to originate from below the photosphere. The models reproduce many of the observed features of filament channels, but the observed hemisphere pattern of dextral and sinistral channels remains a mystery.