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A simple model of chromospheric evaporation and condensation driven conductively in a solar flare  

Dana Longcope   Submitted: 2014-09-19 09:01

Magnetic energy released in the corona by solar flares reaches the chromosphere where it drives characteristic upflows and downflows known as evaporation and condensation. These flows are studied here for the case where energy is transported to the chromosphere by thermal conduction. An analytic model is used to develop relations by which the density and velocity of each flow can be predicted from coronal parameters including the flare's energy flux F. These relations are explored and refined using a series of numerical investigations in which the transition region is represented by a simplified density jump. The maximum evaporation velocity, for example, is well approximated by ve≃0.38(F/ρco,0)1/3, where ρco,0 is the mass density of the pre-flare corona. This and the other relations are found to fit simulations using more realistic models of the transition region both performed in this work, and taken from a variety of previously published investigations. These relations offer a novel and efficient means of simulating coronal reconnection without neglecting entirely the effects of evaporation.

Authors: Dana Longcope
Projects: None

Publication Status: ApJ (in press)
Last Modified: 2014-09-22 13:17
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The Role of fast magnetosonic waves in the release and conversion via reconnection of energy stored by a current sheet  

Dana Longcope   Submitted: 2012-07-25 08:27

Using a simple two-dimensional, zero-beta model, we explore the manner by which reconnection at a current sheet releases and dissipates free magnetic energy. We find that only a small fraction (3%-11% depending on current sheet size) of the energy is stored close enough to the current sheet to be dissipated abruptly by the reconnection process. The remaining energy, stored in the larger-scale field, is converted to kinetic energy in a fast magnetosonic disturbance propagating away from the reconnection site, carrying the initial current and generating reconnection-associated flows (inflow and outflow). Some of this reflects from the lower boundary (the photosphere) and refracts back to the X-point reconnection site. Most of this inward wave energy is reflected back again, and continues to bounce between X-point and photosphere until it is gradually dissipated, over many transits. This phase of the energy dissipation process is thus global and lasts far longer than the initial purely local phase. In the process a significant fraction of the energy (25%-60%) remains as undissipated fast magnetosonic waves propagating away from the reconnection site, primarily upward. This flare-generated wave is initiated by unbalanced Lorentz forces in the reconnection-disrupted current sheet, rather than by dissipation-generated pressure, as some previous models have assumed. Depending on the orientation of the initial current sheet the wave front is either a rarefaction, with backward directed flow, or a compression, with forward directed flow.

Authors: Dana Longcope, Lucas Tarr
Projects: None

Publication Status: ApJ accepted
Last Modified: 2012-07-25 14:19
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A Model for the Origin of High Density in Loop-top X-ray Sources  

Dana Longcope   Submitted: 2011-07-14 10:58

Super-hot looptop sources, detected in some large solar flares, are compactsources of HXR emission with spectra matching thermal electron populationsexceeding 30 megakelvins. High observed emission measure, as well as inferenceof electron thermalization within the small source region, both provideevidence of high densities at the looptop; typically more than an order ofmagnitude above ambient. Where some investigators have suggested such densityenhancement results from a rapid enhancement in the magnetic field strength, wepropose an alternative model, based on Petschek reconnection, whereby looptopplasma is heated and compressed by slow magnetosonic shocks generatedself-consistently through flux retraction following reconnection. Under steadyconditions such shocks can enhance density by no more than a factor of four.These steady shock relations (Rankine-Hugoniot relations) turn out to beinapplicable to Petschek's model owing to transient effects of thermalconduction. The actual density enhancement can in fact exceed a factor of tenover the entire reconnection outflow. An ensemble of flux tubes retractingfollowing reconnection at an ensemble of distinct sites will have a collectiveemission measure proportional to the rate of flux tube production. This rate,distinct from the local reconnection rate within a single tube, can be measuredseparately through flare ribbon motion. Typical flux transfer rates and loopparameters yield emission measures comparable to those observed in super-hotsources.

Authors: D.W. Longcope, S.E. Guidoni
Projects: None

Publication Status: ApJ (accepted)
Last Modified: 2011-07-14 15:24
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A Quantitative Model of Energy Release and Heating by Time-dependent, Localized Reconnection in a Flare with a Thermal Loop-top X-ray Source  

Dana Longcope   Submitted: 2011-06-22 09:57

We present a quantitative model of the magnetic energy stored and thenreleased through magnetic reconnection for a flare on 26 Feb 2004. This flare,well observed by RHESSI and TRACE, shows evidence of non-thermal electrons onlyfor a brief, early phase. Throughout the main period of energy release there isa super-hot (T>30 MK) plasma emitting thermal bremsstrahlung atop the flareloops. Our model describes the heating and compression of such a source bylocalized, transient magnetic reconnection. It is a three-dimensionalgeneralization of the Petschek model whereby Alfvén-speed retraction followingreconnection drives supersonic inflows parallel to the field lines, which formshocks heating, compressing, and confining a loop-top plasma plug. Theconfining inflows provide longer life than a freely-expanding orconductively-cooling plasma of similar size and temperature. Superposition ofsuccessive transient episodes of localized reconnection across a current sheetproduces an apparently persistent, localized source of high-temperatureemission. The temperature of the source decreases smoothly on a time scaleconsistent with observations, far longer than the cooling time of a singleplug. Built from a disordered collection of small plugs, the source need nothave the coherent jet-like structure predicted by steady-state reconnectionmodels. This new model predicts temperatures and emission measure consistentwith the observations of 26 Feb 2004. Furthermore, the total energy released bythe flare is found to be roughly consistent with that predicted by the model.Only a small fraction of the energy released appears in the super-hot source atany one time, but roughly a quarter of the flare energy is thermalized by thereconnection shocks over the course of the flare. All energy is presumed toultimately appear in the lower-temperature T<20 MK, post-flare loops.

Authors: D.W. Longcope, A.C. Des Jardins, T. Carranza-Fulmer, J. Qiu
Projects: RHESSI

Publication Status: Solar Physics, vol. 267, pp.107-139 (2010)
Last Modified: 2011-06-22 12:25
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Slow shocks and conduction fronts from Petschek reconnection of skewed magnetic fields: two-fluid effects  

Dana Longcope   Submitted: 2010-06-04 08:17

In models of fast magnetic reconnection, flux transfer occurs within a small portion of a current sheet triggering stored magnetic energy to be thermalized by shocks. When the initial current sheet separates magnetic fields which are not perfectly anti-parallel, i.e. they are skewed, magnetic energy is first converted to bulk kinetic energy and then thermalized in slow magnetosonic shocks. We show that the latter resemble parallel shocks or hydrodynamic shocks for all skew angles except those very near the anti-parallel limit. As for parallel shocks, the structures of reconnection-driven slow shocks are best studied using two-fluid equations in which ions and electrons have independent temperature. Time-dependent solutions of these equations can be used to predict and understand the shocks from reconnection of skewed magnetic fields. The results differ from those found using a single-fluid model such as magnetohydrodynamics. In the two-fluid model electrons are heated indirectly and thus carry a heat flux always well below the free-streaming limit. The viscous stress of the ions is, however, typically near the fluid-treatable limit. We find that for a wide range of skew angles and small plasma beta an electron conduction front extends ahead of the slow shock but remains within the outflow jet. In such cases conduction will play a more limited role in driving chromospheric evaporation than has been predicted based on single-fluid, anti-parallel models.

Authors: D.W. Longcope, S.J. Bradshaw
Projects: None

Publication Status: ApJ (in press)
Last Modified: 2010-06-07 08:04
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Gas-dynamic shock heating of post-flare loops due to retraction following localized, impulsive reconnection  

Dana Longcope   Submitted: 2008-11-03 13:15

We present a novel model in which shortening of a magnetic flux tube following localized, three-dimensional reconnection generates strong gas-dynamic shocks around its apex. The shortening releases magnetic energy by progressing away from the reconnection site at the Alfvén speed. This launches inward flows along the field lines whose collision creates a pair of gas-dynamic shocks. The shocks raise both the mass density and temperature inside the newly shortened flux tube. Reconnecting field lines whose initial directions differ by more that 100 degrees can produce a concentrated knot of plasma hotter that 20 MK, consistent with observations. In spite of these high temperatures, the shocks convert less than 10% of the liberated magnetic energy into heat - the rest remains as kinetic energy of bulk motion. These gas-dynamic shocks arise only when the reconnection is impulsive and localized in all three dimensions; they are distinct from the slow magnetosonic shocks of the Petschek steady-state reconnection model.

Authors: D.W. Longcope, S.E. Guidoni, and M.G. Linton
Projects: None

Publication Status: ApJ Letters (accepted)
Last Modified: 2008-11-03 15:12
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Subject will be restored when possible  

Dana Longcope   Submitted: 2007-11-16 11:16

A model is investigated describing the resistive dissipation of a finite, two-dimensional current sheet subject to suddenly enhanced resistivity. The resistivity rapidly diffuses the current to a distance where it couples to fast magnetosonic modes. The current then propagates away as a sheath moving at the local Alfvén speed. A current density peak remains at the X-point producing a steady electric field independent of the resistivity. This transfers flux across the separatrix at a rate consistent with the external wave propagation. The majority of the magnetic energy stored by the initial current sheet is converted into kinetic energy, far from the reconnection site, during the fast mode propagation.

Authors: D.W. Longcope and E.R. Priest
Projects: None

Publication Status: To appear in Physics of Plasmas
Last Modified: 2007-11-16 11:39
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Subject will be restored when possible  

Dana Longcope   Submitted: 2007-09-27 14:30

We present a topological model for energy storage and subsequent release in a sheared arcade of either infinite or finite extent. This provides a quantitative picture of a twisted flux rope produced through reconnection in a two-ribbon flare. It quantifies relationships between the initial shear, the amount of flux reconnected and the total axial flux in the twisted rope. The model predicts reconnection occurring in a sequence which progresses upward even if the reconnection sites themselves do not move. While some of the field lines created through reconnection are shorter, and less sheared across the polarity inversion line, reconnection also produces a significant number of field lines with shear even greater than that imposed by the photospheric motion. The most highly sheared of these is the overlying flux rope. Since it is produced by a sequence of reconnections, the flux rope has twist far in excess of that introduced into the arcade through shear motions. The energy storage agrees well with previous calculations using the full equations of magnetohydrodynamics, and the agreement improves as the topology is defined using increasingly finer detail. This is the first comparative study of the application of a topological model to a continuous flux distribution. As such it demonstrates how the coarseness with which the photospheric flux distribution is partitioned affects the accuracy of prediction in topological models.

Authors: D.W. Longcope and C. Beveridge
Projects: None

Publication Status: accepted by ApJ
Last Modified: 2007-09-28 05:01
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Subject will be restored when possible  

Dana Longcope   Submitted: 2007-09-27 14:26

We introduce two different generalizations of relative helicity which may be applied to a portion of the coronal volume. Such a quantity is generally referred to as the self-helicity of the field occupying the sub-volume. Each definition is a natural application of the traditional relative helicity but relative to a different reference field. One of the generalizations, which we term additive self-helicity, can be considered a generalization of twist helicity to volumes which are neither closed nor thin. It shares with twist the property of being identically zero for any portion of a potential magnetic field. The other helicity, unconfined self-helicity, is independent of the shape of the volume occupied by the field portion and is therefore akin to the sum of twist and writhe helicity. We demonstrate how each kind of self-helicity may be evaluated in practice. \ \ The set of additive self-helicities may be used as a constraint in the minimization of magnetic energy to produce a piece-wise constant α equilibrium. This class of fields falls into a hierarchy, along with the flux constrained equilibria and potential fields, of fields with monotonically decreasing magnetic energies. Piece-wise constant α field generally have fewer unphysical properties than genuinely constant α fields, whose twist α is uniform throughout the entire corona.

Authors: D.W. Longcope and A. Malanushenko
Projects: None

Publication Status: accepted by ApJ
Last Modified: 2007-09-27 14:26
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Subject will be restored when possible  

Dana Longcope   Submitted: 2007-09-27 14:26

We introduce two different generalizations of relative helicity which may be applied to a portion of the coronal volume. Such a quantity is generally referred to as the self-helicity of the field occupying the sub-volume. Each definition is a natural application of the traditional relative helicity but relative to a different reference field. One of the generalizations, which we term additive self-helicity, can be considered a generalization of twist helicity to volumes which are neither closed nor thin. It shares with twist the property of being identically zero for any portion of a potential magnetic field. The other helicity, unconfined self-helicity, is independent of the shape of the volume occupied by the field portion and is therefore akin to the sum of twist and writhe helicity. We demonstrate how each kind of self-helicity may be evaluated in practice. The set of additive self-helicities may be used as a constraint in the minimization of magnetic energy to produce a piece-wise constant α equilibrium. This class of fields falls into a hierarchy, along with the flux constrained equilibria and potential fields, of fields with monotonically decreasing magnetic energies. Piece-wise constant α field generally have fewer unphysical properties than genuinely constant α fields, whose twist α is uniform throughout the entire corona.

Authors: D.W. Longcope and A. Malanushenko
Projects: None

Publication Status: accepted by ApJ
Last Modified: 2007-09-28 05:02
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Subject will be restored when possible  

Dana Longcope   Submitted: 2007-09-27 14:25

We introduce two different generalizations of relative helicity which may be applied to a portion of the coronal volume. Such a quantity is generally referred to as the self-helicity of the field occupying the sub-volume. Each definition is a natural application of the traditional relative helicity but relative to a different reference field. One of the generalizations, which we term additive self-helicity, can be considered a generalization of twist helicity to volumes which are neither closed nor thin. It shares with twist the property of being identically zero for any portion of a potential magnetic field. The other helicity, unconfined self-helicity, is independent of the shape of the volume occupied by the field portion and is therefore akin to the sum of twist and writhe helicity. We demonstrate how each kind of self-helicity may be evaluated in practice. The set of additive self-helicities may be used as a constraint in the minimization of magnetic energy to produce a piece-wise constant α equilibrium. This class of fields falls into a hierarchy, along with the flux constrained equilibria and potential fields, of fields with monotonically decreasing magnetic energies. Piece-wise constant α field generally have fewer unphysical properties than genuinely constant α fields, whose twist α is uniform throughout the entire corona.

Authors: D.W. Longcope and A. Malanushenko
Projects: None

Publication Status: accepted by ApJ
Last Modified: 2007-09-27 14:25
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Subject will be restored when possible  

Dana Longcope   Submitted: 2007-09-27 14:25

We introduce two different generalizations of relative helicity which may be applied to a portion of the coronal volume. Such a quantity is generally referred to as the self-helicity of the field occupying the sub-volume. Each definition is a natural application of the traditional relative helicity but relative to a different reference field. One of the generalizations, which we term additive self-helicity, can be considered a generalization of twist helicity to volumes which are neither closed nor thin. It shares with twist the property of being identically zero for any portion of a potential magnetic field. The other helicity, unconfined self-helicity, is independent of the shape of the volume occupied by the field portion and is therefore akin to the sum of twist and writhe helicity. We demonstrate how each kind of self-helicity may be evaluated in practice. \ The set of additive self-helicities may be used as a constraint in the minimization of magnetic energy to produce a piece-wise constant α equilibrium. This class of fields falls into a hierarchy, along with the flux constrained equilibria and potential fields, of fields with monotonically decreasing magnetic energies. Piece-wise constant α field generally have fewer unphysical properties than genuinely constant α fields, whose twist α is uniform throughout the entire corona.

Authors: D.W. Longcope and A. Malanushenko
Projects: None

Publication Status: accepted by ApJ
Last Modified: 2007-09-27 14:25
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Modeling and measuring the flux reconnected and ejected by the two-ribbon flare/CME event on 7 November 2004  

Dana Longcope   Submitted: 2006-11-24 14:06

Observations of the large two-ribbon flare on 7 November 2004 made using SOHO and TRACE data are interpreted in terms of a three-dimensional magnetic field model. Photospheric flux evolution indicates that -1.4e43 Mx^2 of magnetic helicity was injected into the active region during the 40-hour build-up prior to the flare. The magnetic model places a lower bound of 8e31} ergs on the energy stored by this motion. It predicts that 5e21 Mx of flux would need to be reconnected during the flare in order to release the stored energy. This total reconnection compares favorably with the flux swept up by the flare ribbons which we measure using high time cadence TRACE images in 1600A. Reconnection in the model must occur in a specific sequence which would produce a twisted flux rope containing significantly less flux and helicity (1e21 Mx and -3e42 Mx^2 respectively) than the active region as a whole. The predicted flux compares favorably with values inferred from the magnetic cloud observed by Wind. This combined analysis yields the first quantitative picture of the flux processed through a two-ribbon flare and CME.

Authors: D. Longcope, C. Beveridge, J. Qiu, B. Ravindra, G. Barnes and S. Dasso
Projects: SoHO-MDI

Publication Status: to appear in Solar Physics Topical Issue on Sun-Earth Events
Last Modified: 2007-03-11 12:20
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Quantifying Magnetic Reconnection and the Heat it Generates  

Dana Longcope   Submitted: 2004-10-22 17:35

Theories have long implicated magnetic reconnection in many aspects of coronal activity including the general process of coronal heating. Magnetic reconnection is fundamentally a change in field line topology resulting from some non-ideal term in the generalized Ohm's law. Such a non-ideal effect may dissipate energy directly, or it may not, but it will topologically change field lines at a rate proportional to the integrated electric field, dot{Phi}. In any model where magnetic reconnection heats the corona the heating rate will scale with this rate of reconnection. We find that the observed scaling between heating power and reconnection rate is consistent with models where photospheric motions stress the coronal fields quasi-statically and reconnection releases the energy suddenly, but does not necessarily dissipate it. Such models are, in particular, consistent with the observation that X-ray luminosity of a structure scales almost linearly with the magnetic flux of that structure.

Authors: Dana Longcope
Projects: Soho-MDI

Publication Status: Proceedings of SOHO-15 (submitted)
Last Modified: 2004-10-22 17:38
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Inferring a photospheric velocity field from a sequence of vector magnetograms: The Minimum Energy Fit  

Dana Longcope   Submitted: 2004-05-17 09:42

We introduce a technique for inferring a photospheric velocity from a sequence of vector magnetograms. The technique, called The Minimum Energy Fit, demands that the photospheric flow agree with the observed photospheric field evolution according to the magnetic induction equation. It selects, from all consistent flows, that with the smallest overall flow speed by demanding that it minimize an energy functional. Partial or imperfect velocity information, obtained independently, may be incorporated by demanding a velocity consistent with the induction equation which minimizes the squared difference with flow components otherwise known. The combination of low velocity and consistency with the induction equation are desirable when using the magnetogram data and associated flow as boundary conditions of a numerical simulation. The technique is tested on synthetic magnetograms generated by specified flow fields and shown to yield reasonable agreement. It also yields believable flows from magnetograms of NOAA AR8210 made with the Imaging Vector Magnetogram at the Mees Solar Observatory.

Authors: D.W. Longcope
Projects: None

Publication Status: ApJ (in press)
Last Modified: 2004-05-17 09:42
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A comparison of the Minimum Current Corona to a magnetohydrodynamic simulation of quasi-static coronal evolution  

Dana Longcope   Submitted: 2004-03-01 13:12

We use two different models to study the evolution of the coronal magnetic field which results from a simple photospheric field evolution. The first, the Minimum Current Corona (MCC), is a self-consistent model for quasi-static evolution which yields an analytic expression approximating the net coronal currents and the free magnetic energy stored by them. For the second model calculation, the non-linear, time-dependent equations of ideal magnetohydrodynamics are solved numerically subject to line-tied photospheric boundary conditions. In both models high current-density concentrations form vertical sheets along the magnetic separator. The time history of the net current carried by these concentrations is quantitatively similar in each of the models. The magnetic energy of the line-tied simulation is significantly greater than that of the MCC, in accordance with the fact that the MCC is a lower bound on energies of all ideal models. The difference in energies can be partially explained from the different magnetic helicity injection in the two models. This study demonstrates that the analytic MCC model accurately predicts the locations of significant equilibrium current accumulations. The study also provides one example in which the energetic contributions of two different MHD constraints, line-tying constraints and flux constraints, may be quantitatively compared. In this example line-tying constraints store at least an order of magnitude more energy than do flux constraints.

Authors: D.W. Longcope and T. Magara
Projects: None

Publication Status: ApJ (in press)
Last Modified: 2004-03-01 13:12
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Magnetic Helicity Propagation from Inside the Sun  

Dana Longcope   Submitted: 2003-10-01 11:58

Models of twisted flux tube evolution provide a picture of how magnetic helicity is propagated through the solar convection zone into the corona. According to the models, helicity tends toward an approximately uniform length-density along a tube, rather than concentrating at wider portions. Coronal fields lengthen rapidly during active region emergence, requiring additional helicity to propagate from the submerged flux tube. Recent observations of emerging active regions show an evolution consistent with this prediction, and no evidence of helicity concentrating in wider sections.

Authors: Dana Longcope
Projects: None

Publication Status: Submitted to Poroceedings of IAU XXV JD3
Last Modified: 2003-10-01 11:58
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A Viscoelastic Theory of Turbulent Fluid Permeated with Fibril Magnetic Fields  

Dana Longcope   Submitted: 2003-08-26 17:53

The solar convection zone is a turbulent plasma interacting with a magnetic field. Its magnetic field is often described as fibrillar since it consists of slender flux tubes occupying a small fraction of the total volume. It is well-known that plasma flow will exert a force on these magnetic fibrils, but few models have accounted for the back-reaction of the fibrils on the flow. We present a model in which the back-reaction of the fibrils on the flow is manifest as viscoelastic properties. On short time scales the fibrils react elastically with a shear modulus proportional to their overall magnetic energy density. On longer times scales they produce an effective viscosity resulting from collective aerodynamic drag. The viscosity due to flux tubes in the solar convection zone can be comparable to that attributed to turbulence there. These forces might have observable effects on the convection zone flows.

Authors: D. W. Longcope, T.C.B. McLeish and G.H. Fisher
Projects: None

Publication Status: Astrophysical Journal (in press)
Last Modified: 2003-08-26 17:53
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Helicity Transport and Generation in the Solar Convection Zone  

Dana Longcope   Submitted: 2003-04-24 10:50

Magnetic helicity provides a theoretical tool for characterizing the solar dynamo and the evolution of the coronal field. The magnetic helicity may be inferred from several types of observation including vector magnetograms of the photospheric magnetic fields. The helicity of an active region reflects, to some degree, the twist in the magnetic field below it. Photospheric observations reveal a tendency for left-handed chirality in the Northern hemisphere, although one-quarter to one-third of the active regions twist in the opposite sense. This means that coronal magnetic field has negative helicity in the North. Sub-photospheric fields will have left-handed twist in the North, although the net helicity also depends on the writhe of the flux tube axes. We show that buffeting by turbulence, the so-called Sigma-effect, can explain the handedness and level of intrinsic variation of observed twist. This mechanism does not generate helicity, rather it produces twist and writhe of opposite signs. In this scenario, helicity of one sign propagates into the corona, while opposing helicity propagates downward in the form of torsional Alfvén waves.

Authors: Longcope, D.W. and Pevtsov, A.A.
Projects:

Publication Status: COSPAR, Adv. in Space Research, in press
Last Modified: 2003-04-28 11:25
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Topology is Destiny: Reconnection energetics in the corona  

Dana Longcope   Submitted: 2000-06-05 16:05

Magnetic reconnection is clearly at work in the solar corona reorganizing and simplifying the magnetic field. It has also been hypothesized that this reorganization process somehow supplies the energy heating the corona. We propose a quantitative model relating the topological role (simplification) and the energetic role (heating) of magnetic reconnection. This model is used to analyze multi-wavelength observations of an X-ray bright point. In the model, motion of photospheric sources drives reconnection of coronal flux. If reconnec- reconnection occurs only sporadically then energy is stored in the coronal field, and released by topological reconnection. We simulate the dynamical response of the plasma to such an energy release, and translate this into predicted observational signatures. The resulting predictions are difficult to reconcile with the observations. This suggests that while reconnection is important in the corona, energy dissipation is governed by other factors, not all of which relate to the topology of the field.

Authors: D. W. Longcope and C. C. Kankelborg
Projects:

Publication Status: Earth Planets Space (MR2000 proceedings) (submitted)
Last Modified: 2000-06-05 16:05
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Abstracts by Author
A simple model of chromospheric evaporation and condensation driven conductively in a solar flare
The Role of fast magnetosonic waves in the release and conversion via reconnection of energy stored by a current sheet
A Model for the Origin of High Density in Loop-top X-ray Sources
A Quantitative Model of Energy Release and Heating by Time-dependent, Localized Reconnection in a Flare with a Thermal Loop-top X-ray Source
Slow shocks and conduction fronts from Petschek reconnection of skewed magnetic fields: two-fluid effects
Gas-dynamic shock heating of post-flare loops due to retraction following localized, impulsive reconnection
Subject will be restored when possible
Subject will be restored when possible
Subject will be restored when possible
Subject will be restored when possible
Subject will be restored when possible
Subject will be restored when possible
Modeling and measuring the flux reconnected and ejected by the two-ribbon flare/CME event on 7 November 2004
Quantifying Magnetic Reconnection and the Heat it Generates
Inferring a photospheric velocity field from a sequence of vector magnetograms: The Minimum Energy Fit
A comparison of the Minimum Current Corona to a magnetohydrodynamic simulation of quasi-static coronal evolution
Magnetic Helicity Propagation from Inside the Sun
A Viscoelastic Theory of Turbulent Fluid Permeated with Fibril Magnetic Fields
Helicity Transport and Generation in the Solar Convection Zone
Topology is Destiny: Reconnection energetics in the corona
Self-organized criticality from separator reconnection in

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