Author name code: amari ADS astronomy entries on 2022-09-14 author:"Amari, Tahar" ------------------------------------------------------------------------ Title: MOVES - V. Modelling star-planet magnetic interactions of HD 189733 Authors: Strugarek, A.; Fares, R.; Bourrier, V.; Brun, A. S.; Réville, V.; Amari, T.; Helling, Ch; Jardine, M.; Llama, J.; Moutou, C.; Vidotto, A. A.; Wheatley, P. J.; Zarka, P. Bibcode: 2022MNRAS.512.4556S Altcode: 2022arXiv220310956S; 2022MNRAS.tmp..872S Magnetic interactions between stars and close-in planets may lead to a detectable signal on the stellar disc. HD 189733 is one of the key exosystems thought to harbour magnetic interactions, which may have been detected in 2013 August. We present a set of 12 wind models at that period, covering the possible coronal states and coronal topologies of HD 189733 at that time. We assess the power available for the magnetic interaction and predict its temporal modulation. By comparing the predicted signal with the observed signal, we find that some models could be compatible with an interpretation based on star-planet magnetic interactions. We also find that the observed signal can be explained only with a stretch-and-break interaction mechanism, while that the Alfvén wings scenario cannot deliver enough power. We finally demonstrate that the past observational cadence of HD 189733 leads to a detection rate of only between 12 and 23 per cent, which could explain why star-planet interactions have been hard to detect in past campaigns. We conclude that the firm confirmation of their detection will require dedicated spectroscopic observations covering densely the orbital and rotation period, combined with scarcer spectropolarimetric observations to assess the concomitant large-scale magnetic topology of the star. Title: HiRISE - High-Resolution Imaging and Spectroscopy Explorer - Ultrahigh resolution, interferometric and external occulting coronagraphic science Authors: Erdélyi, Robertus; Damé, Luc; Fludra, Andrzej; Mathioudakis, Mihalis; Amari, T.; Belucz, B.; Berrilli, F.; Bogachev, S.; Bolsée, D.; Bothmer, V.; Brun, S.; Dewitte, S.; de Wit, T. Dudok; Faurobert, M.; Gizon, L.; Gyenge, N.; Korsós, M. B.; Labrosse, N.; Matthews, S.; Meftah, M.; Morgan, H.; Pallé, P.; Rochus, P.; Rozanov, E.; Schmieder, B.; Tsinganos, K.; Verwichte, E.; Zharkov, S.; Zuccarello, F.; Wimmer-Schweingruber, R. Bibcode: 2022ExA...tmp...21E Altcode: Recent solar physics missions have shown the definite role of waves and magnetic fields deep in the inner corona, at the chromosphere-corona interface, where dramatic and physically dominant changes occur. HiRISE (High Resolution Imaging and Spectroscopy Explorer), the ambitious new generation ultra-high resolution, interferometric, and coronagraphic, solar physics mission, proposed in response to the ESA Voyage 2050 Call, would address these issues and provide the best-ever and most complete solar observatory, capable of ultra-high spatial, spectral, and temporal resolution observations of the solar atmosphere, from the photosphere to the corona, and of new insights of the solar interior from the core to the photosphere. HiRISE, at the L1 Lagrangian point, would provide meter class FUV imaging and spectro-imaging, EUV and XUV imaging and spectroscopy, magnetic fields measurements, and ambitious and comprehensive coronagraphy by a remote external occulter (two satellites formation flying 375 m apart, with a coronagraph on a chaser satellite). This major and state-of-the-art payload would allow us to characterize temperatures, densities, and velocities in the solar upper chromosphere, transition zone, and inner corona with, in particular, 2D very high resolution multi-spectral imaging-spectroscopy, and, direct coronal magnetic field measurement, thus providing a unique set of tools to understand the structure and onset of coronal heating. HiRISE's objectives are natural complements to the Parker Solar Probe and Solar Orbiter-type missions. We present the science case for HiRISE which will address: i) the fine structure of the chromosphere-corona interface by 2D spectroscopy in FUV at very high resolution; ii) coronal heating roots in the inner corona by ambitious externally-occulted coronagraphy; iii) resolved and global helioseismology thanks to continuity and stability of observing at the L1 Lagrange point; and iv) solar variability and space climate with, in addition, a global comprehensive view of UV variability. Title: Necessary Conditions for a Hot Quiet Sun Atmosphere: Chromospheric Flares and Low Corona Twisted Flux Rope Eruptions Authors: Amari, Tahar; Luciani, Jean-Francois; Aly, Jean-Jacques; Canou, Aurelien; Mikic, Zoran; Velli, Marco Bibcode: 2021AGUFMSH12B..05A Altcode: The issue of relevant scales involved in the heating of the solar atmosphere is an important one. Since the temperature already reaches 1 MK a few megameters above the photosphere, observations made by Parker Solar Probe will be able to explore those at larger heights but only indirectly at those lower heights, where small scale coupling between sub-photospheric, chromospheric and coronal structure and dynamics occurs. While Solar Orbiter will be able to bring such observations, modeling appears a complementary interesting approach to interpret those observations Taking a sub-surface dynamo and a sharp realistic VAL- like scale profile from photosphere to corona, with a fixed temperature profile in time, we investigate the necessary conditions implied on the structures and dynamics of the atmosphere to keep this thermal structuration, as well as their implication in the energy budget of the atmosphere. Under those hypothesis we show that :i) the transverse photospheric field below 100km plays a major role; ii) an associated scale of one megameter activity naturally results to produce a zone above the photosphere with high confined electric currents, which then expands into the chromosphere and releases energy(4 500 W/m2) through small-scale eruptions driving sonic motions; iii) meso scale structuration, leads to the formation of larger coherent twisted flux ropes, and associated eruptive like activity in a way similar to large scale eruptive phenomena, as result of cancellation, emergence, and convergence motions. Finally a wave dynamics is also naturally driven in core corona associated to above 300 W/m2. Title: Models and data analysis tools for the Solar Orbiter mission Authors: Rouillard, A. P.; Pinto, R. F.; Vourlidas, A.; De Groof, A.; Thompson, W. T.; Bemporad, A.; Dolei, S.; Indurain, M.; Buchlin, E.; Sasso, C.; Spadaro, D.; Dalmasse, K.; Hirzberger, J.; Zouganelis, I.; Strugarek, A.; Brun, A. S.; Alexandre, M.; Berghmans, D.; Raouafi, N. E.; Wiegelmann, T.; Pagano, P.; Arge, C. N.; Nieves-Chinchilla, T.; Lavarra, M.; Poirier, N.; Amari, T.; Aran, A.; Andretta, V.; Antonucci, E.; Anastasiadis, A.; Auchère, F.; Bellot Rubio, L.; Nicula, B.; Bonnin, X.; Bouchemit, M.; Budnik, E.; Caminade, S.; Cecconi, B.; Carlyle, J.; Cernuda, I.; Davila, J. M.; Etesi, L.; Espinosa Lara, F.; Fedorov, A.; Fineschi, S.; Fludra, A.; Génot, V.; Georgoulis, M. K.; Gilbert, H. R.; Giunta, A.; Gomez-Herrero, R.; Guest, S.; Haberreiter, M.; Hassler, D.; Henney, C. J.; Howard, R. A.; Horbury, T. S.; Janvier, M.; Jones, S. I.; Kozarev, K.; Kraaikamp, E.; Kouloumvakos, A.; Krucker, S.; Lagg, A.; Linker, J.; Lavraud, B.; Louarn, P.; Maksimovic, M.; Maloney, S.; Mann, G.; Masson, A.; Müller, D.; Önel, H.; Osuna, P.; Orozco Suarez, D.; Owen, C. J.; Papaioannou, A.; Pérez-Suárez, D.; Rodriguez-Pacheco, J.; Parenti, S.; Pariat, E.; Peter, H.; Plunkett, S.; Pomoell, J.; Raines, J. M.; Riethmüller, T. L.; Rich, N.; Rodriguez, L.; Romoli, M.; Sanchez, L.; Solanki, S. K.; St Cyr, O. C.; Straus, T.; Susino, R.; Teriaca, L.; del Toro Iniesta, J. C.; Ventura, R.; Verbeeck, C.; Vilmer, N.; Warmuth, A.; Walsh, A. P.; Watson, C.; Williams, D.; Wu, Y.; Zhukov, A. N. Bibcode: 2020A&A...642A...2R Altcode: Context. The Solar Orbiter spacecraft will be equipped with a wide range of remote-sensing (RS) and in situ (IS) instruments to record novel and unprecedented measurements of the solar atmosphere and the inner heliosphere. To take full advantage of these new datasets, tools and techniques must be developed to ease multi-instrument and multi-spacecraft studies. In particular the currently inaccessible low solar corona below two solar radii can only be observed remotely. Furthermore techniques must be used to retrieve coronal plasma properties in time and in three dimensional (3D) space. Solar Orbiter will run complex observation campaigns that provide interesting opportunities to maximise the likelihood of linking IS data to their source region near the Sun. Several RS instruments can be directed to specific targets situated on the solar disk just days before data acquisition. To compare IS and RS, data we must improve our understanding of how heliospheric probes magnetically connect to the solar disk.
Aims: The aim of the present paper is to briefly review how the current modelling of the Sun and its atmosphere can support Solar Orbiter science. We describe the results of a community-led effort by European Space Agency's Modelling and Data Analysis Working Group (MADAWG) to develop different models, tools, and techniques deemed necessary to test different theories for the physical processes that may occur in the solar plasma. The focus here is on the large scales and little is described with regards to kinetic processes. To exploit future IS and RS data fully, many techniques have been adapted to model the evolving 3D solar magneto-plasma from the solar interior to the solar wind. A particular focus in the paper is placed on techniques that can estimate how Solar Orbiter will connect magnetically through the complex coronal magnetic fields to various photospheric and coronal features in support of spacecraft operations and future scientific studies.
Methods: Recent missions such as STEREO, provided great opportunities for RS, IS, and multi-spacecraft studies. We summarise the achievements and highlight the challenges faced during these investigations, many of which motivated the Solar Orbiter mission. We present the new tools and techniques developed by the MADAWG to support the science operations and the analysis of the data from the many instruments on Solar Orbiter.
Results: This article reviews current modelling and tool developments that ease the comparison of model results with RS and IS data made available by current and upcoming missions. It also describes the modelling strategy to support the science operations and subsequent exploitation of Solar Orbiter data in order to maximise the scientific output of the mission.
Conclusions: The on-going community effort presented in this paper has provided new models and tools necessary to support mission operations as well as the science exploitation of the Solar Orbiter data. The tools and techniques will no doubt evolve significantly as we refine our procedure and methodology during the first year of operations of this highly promising mission. Title: Bounding the Energy of Solar Eruptions Authors: Linker, Jon A.; Downs, Cooper; Caplan, Ronald M.; Torok, Tibor; Riley, Pete; Titov, Viacheslav; Lionello, Roberto; Mikic, Zoran; Amari, Tahar Bibcode: 2019AAS...23431704L Altcode: Major solar eruptions such as X-class flares and coronal mass ejections (CMEs) are the fundamental source of solar energetic particles and geomagnetic storms, and are thus key drivers of space weather at Earth. The energy for solar eruptions is recognized to originate in the solar magnetic field, and is believed to be stored as free magnetic energy (energy above the potential field state) prior to eruption. Solar active regions are the site of the most violent activity. Solar active regions can store widely varying amounts of energy, so knowledge of the free energy alone does not necessarily tell us when an eruption is imminent. For estimates of the free energy to provide predictive power, we must know how much energy a region can store - what is the energy bound?

In recent work, we have found that the energy of a particular field, the partially open field (POF), can place a useful bound on the energy of an eruption from real active regions, a much tighter constraint than the energy of the fully open field. However, in general, it is difficult to solve for the POF. In this presentation, we discuss methods for approximating the energy of this field, and show a comparison of the approximation for a case where the solution is known. We discuss the implications for understanding and predicting major solar eruptions.

Research supported by NASA and AFOSR Title: Global Non-Potential Magnetic Models of the Solar Corona During the March 2015 Eclipse Authors: Yeates, Anthony R.; Amari, Tahar; Contopoulos, Ioannis; Feng, Xueshang; Mackay, Duncan H.; Mikić, Zoran; Wiegelmann, Thomas; Hutton, Joseph; Lowder, Christopher A.; Morgan, Huw; Petrie, Gordon; Rachmeler, Laurel A.; Upton, Lisa A.; Canou, Aurelien; Chopin, Pierre; Downs, Cooper; Druckmüller, Miloslav; Linker, Jon A.; Seaton, Daniel B.; Török, Tibor Bibcode: 2018SSRv..214...99Y Altcode: 2018arXiv180800785Y Seven different models are applied to the same problem of simulating the Sun's coronal magnetic field during the solar eclipse on 2015 March 20. All of the models are non-potential, allowing for free magnetic energy, but the associated electric currents are developed in significantly different ways. This is not a direct comparison of the coronal modelling techniques, in that the different models also use different photospheric boundary conditions, reflecting the range of approaches currently used in the community. Despite the significant differences, the results show broad agreement in the overall magnetic topology. Among those models with significant volume currents in much of the corona, there is general agreement that the ratio of total to potential magnetic energy should be approximately 1.4. However, there are significant differences in the electric current distributions; while static extrapolations are best able to reproduce active regions, they are unable to recover sheared magnetic fields in filament channels using currently available vector magnetogram data. By contrast, time-evolving simulations can recover the filament channel fields at the expense of not matching the observed vector magnetic fields within active regions. We suggest that, at present, the best approach may be a hybrid model using static extrapolations but with additional energization informed by simplified evolution models. This is demonstrated by one of the models. Title: Partially Open Fields and Solar Eruptions Authors: Linker, Jon; Mikic, Zoran; Downs, Cooper; Caplan, Ronald M.; Riley, Pete; Torok, Tibor; Titov, Viacheslav S.; Lionello, Roberto; Amari, Tahar Bibcode: 2018tess.conf10905L Altcode: Partially Open Fields and Solar Eruptions*

Major solar eruptions such as X-class flares and coronal mass ejections (CMEs) are the progenitors of solar energetic particles and geomagnetic storms, and are thus key drivers of space weather at Earth. The solar magnetic field is the ultimate source of these massive events, the energy of which is believed to be stored as free magnetic energy (energy above the potential field state) prior to eruption. The amount of free magnetic energy available in a given region is therefore a crucial indicator of its propensity for eruption. However, solar active regions, from which the largest events originate, can store widely varying amounts of energy. Therefore, estimates of the free energy alone are likely to be insufficient for knowing when a region will erupt; we must also estimate the bounds on how much energy can be stored in a given region.

The Aly-Sturrock theorem (Aly, ApJ 1991; Sturrock, ApJ 1991) shows that the energy of a fully force-free field cannot exceed the energy of the so-called open field. If the theorem holds, this places an upper limit on the amount of free energy that can be stored. In this paper, we describe how a closely related field, the partially open field (Wolfson & Low ApJ 1992; Hu, ApJ 2004; Aly & Amari, GAFD 2007), may place a much tighter bound on energy storage and yield insights as to when major eruptions from an active region are imminent (Amari et al., Nature, 2014). We demonstrate the idea for AR9077, the source of the July 14, 2000 "Bastille Day" flare/CME.

*Research supported by NASA and AFOSR Title: Magnetic cage and rope as the key for solar eruptions Authors: Amari, Tahar; Canou, Aurélien; Aly, Jean-Jacques; Delyon, Francois; Alauzet, Fréderic Bibcode: 2018Natur.554..211A Altcode: Solar flares are spectacular coronal events that release large amounts of energy. They are classified as either eruptive or confined, depending on whether they are associated with a coronal mass ejection. Two types of model have been developed to identify the mechanism that triggers confined flares, although it has hitherto not been possible to decide between them because the magnetic field at the origin of the flares could not be determined with the required accuracy. In the first type of model, the triggering is related to the topological complexity of the flaring structure, which implies the presence of magnetically singular surfaces. This picture is observationally supported by the fact that radiative emission occurs near these features in many flaring regions. The second type of model attributes a key role to the formation of a twisted flux rope, which becomes unstable. Its plausibility is supported by simulations, by interpretations of some observations and by laboratory experiments. Here we report modelling of a confined event that uses the measured photospheric magnetic field as input. We first use a static model to compute the slowly evolving magnetic state of the corona before the eruption, and then use a dynamical model to determine the evolution during the eruption itself. We find that a magnetic flux rope must be present throughout the entire event to match the field measurements. This rope evolves slowly before saturating and suddenly erupting. Its energy is insufficient to break through the overlying field, whose lines form a confining cage, but its twist is large enough to trigger a kink instability, leading to the confined flare, as previously suggested. Topology is not the main cause of the flare, but it traces out the locations of the X-ray emission. We show that a weaker magnetic cage would have produced a more energetic eruption with a coronal mass ejection, associated with a predicted energy upper bound for a given region. Title: Validating coronal magnetic field reconstruction methods using solar wind simulations and synthetic imagery Authors: Pinto, Rui; Rouillard, Alexis; Génot, Vincent; Amari, Tahar; Buchlin, Eric; Arge, Nick; Sasso, Clementina; Andretta, Vincenzo; Bemporad, Alessandro Bibcode: 2017EGUGA..1913650P Altcode: We present an ongoing effort within the ESA Modeling and Data Analysis Working Group (MADAWG) to determine automatically the magnetic connectivity between the solar surface and any point in interplanetary space. The goal is to produce predictions of the paths and propagation delays of plasma and energetic particle propagation. This is a key point for the data exploitation of the Solar Orbiter and Solar Probe Plus missions, and for establishing connections between remote and in-situ data. The background coronal magnetic field is currently determined via existing surface magnetograms and PFSS extrapolations, but the interface is ready to include different combinations of coronal field reconstruction methods (NLFFF, Solar Models), wind models (WSA, MULTI-VP), heliospheric models (Parker spiral, ENLIL, EUHFORIA). Some model realisations are also based on advanced magnetograms based on data assimilation techniques (ADAPT) and the HELCATS catalogue of simulations. The results from the different models will be combined in order to better assess the modelling uncertainties. The wind models provide synthetic white-light and EUV images which are compared to coronographic imagery, and the heliospheric models provide estimations of synthetic in-situ data wich are compared to spacecraft data. A part of this is work (wind modelling) is supported by the FP7 project #606692 (HELCATS). Title: Space-weather assets developed by the French space-physics community Authors: Rouillard, A. P.; Pinto, R. F.; Brun, A. S.; Briand, C.; Bourdarie, S.; Dudok De Wit, T.; Amari, T.; Blelly, P. -L.; Buchlin, E.; Chambodut, A.; Claret, A.; Corbard, T.; Génot, V.; Guennou, C.; Klein, K. L.; Koechlin, L.; Lavarra, M.; Lavraud, B.; Leblanc, F.; Lemorton, J.; Lilensten, J.; Lopez-Ariste, A.; Marchaudon, A.; Masson, S.; Pariat, E.; Reville, V.; Turc, L.; Vilmer, N.; Zucarello, F. P. Bibcode: 2016sf2a.conf..297R Altcode: We present a short review of space-weather tools and services developed and maintained by the French space-physics community. They include unique data from ground-based observatories, advanced numerical models, automated identification and tracking tools, a range of space instrumentation and interconnected virtual observatories. The aim of the article is to highlight some advances achieved in this field of research at the national level over the last decade and how certain assets could be combined to produce better space-weather tools exploitable by space-weather centres and customers worldwide. This review illustrates the wide range of expertise developed nationally but is not a systematic review of all assets developed in France. Title: Small Scale Dynamo Magnetism And the Heating of the Quiet Sun Solar Atmosphere. Authors: Amari, T. Bibcode: 2015AGUFMSH31B2412A Altcode: The longstanding problem of the solar atmosphere heating has been addressed by many theoretical studies. Two specific mechanisms have been shown to play a key role in those : magnetic reconnection and waves. On the other hand the necessity of treating together chromosphere and corona has also been been stressed, with debates going on about the possibility of heating coronal plasma by energetic phenomena observed in the chromosphere,based on many key observations such as spicules, tornadoes…. We present some recent results about the modeling of quiet Sun heating in which magnetic fields are generated by a subphotospheric fluid dynamo which is connected to granulation. The model shows a topologically complex magnetic field of 160 G on the Sun's surface, agreeing with inferences obtained from spectropolarimetric observations.Those generated magnetic fields emerge into the chromosphere, providing the required energy flux and then small-scale eruptions releasing magnetic energy and driving sonic motions. Some of the more energetic eruptions can affect the very low corona only.It is also found that taking into account a vertical weak network magnetic field then allows to provide energy higher in the corona, while leaving unchanged the physics of chromospheric eruptions. The coronal heating mechanism rests on the eventual dissipation of Alfven waves generated inside the chromosphere and carrying upwards an adequate energy flux, while more energetic phenomena contribute only weakly to the heating of the corona. Title: The Influence of Spatial resolution on Nonlinear Force-free Modeling Authors: DeRosa, M. L.; Wheatland, M. S.; Leka, K. D.; Barnes, G.; Amari, T.; Canou, A.; Gilchrist, S. A.; Thalmann, J. K.; Valori, G.; Wiegelmann, T.; Schrijver, C. J.; Malanushenko, A.; Sun, X.; Régnier, S. Bibcode: 2015ApJ...811..107D Altcode: 2015arXiv150805455D The nonlinear force-free field (NLFFF) model is often used to describe the solar coronal magnetic field, however a series of earlier studies revealed difficulties in the numerical solution of the model in application to photospheric boundary data. We investigate the sensitivity of the modeling to the spatial resolution of the boundary data, by applying multiple codes that numerically solve the NLFFF model to a sequence of vector magnetogram data at different resolutions, prepared from a single Hinode/Solar Optical Telescope Spectro-Polarimeter scan of NOAA Active Region 10978 on 2007 December 13. We analyze the resulting energies and relative magnetic helicities, employ a Helmholtz decomposition to characterize divergence errors, and quantify changes made by the codes to the vector magnetogram boundary data in order to be compatible with the force-free model. This study shows that NLFFF modeling results depend quantitatively on the spatial resolution of the input boundary data, and that using more highly resolved boundary data yields more self-consistent results. The free energies of the resulting solutions generally trend higher with increasing resolution, while relative magnetic helicity values vary significantly between resolutions for all methods. All methods require changing the horizontal components, and for some methods also the vertical components, of the vector magnetogram boundary field in excess of nominal uncertainties in the data. The solutions produced by the various methods are significantly different at each resolution level. We continue to recommend verifying agreement between the modeled field lines and corresponding coronal loop images before any NLFFF model is used in a scientific setting. Title: Small-scale dynamo magnetism as the driver for heating the solar atmosphere Authors: Amari, Tahar; Luciani, Jean-François; Aly, Jean-Jacques Bibcode: 2015Natur.522..188A Altcode: The long-standing problem of how the solar atmosphere is heated has been addressed by many theoretical studies, which have stressed the relevance of two specific mechanisms, involving magnetic reconnection and waves, as well as the necessity of treating the chromosphere and corona together. But a fully consistent model has not yet been constructed and debate continues, in particular about the possibility of coronal plasma being heated by energetic phenomena observed in the chromosphere. Here we report modelling of the heating of the quiet Sun, in which magnetic fields are generated by a subphotospheric fluid dynamo intrinsically connected to granulation. We find that the fields expand into the chromosphere, where plasma is heated at the rate required to match observations (4,500 watts per square metre) by small-scale eruptions that release magnetic energy and drive sonic motions. Some energetic eruptions can even reach heights of 10 million metres above the surface of the Sun, thereby affecting the very low corona. Extending the model by also taking into account the vertical weak network magnetic field allows for the existence of a mechanism able to heat the corona above, while leaving unchanged the physics of chromospheric eruptions. Such a mechanism rests on the eventual dissipation of Alfvén waves generated inside the chromosphere and that carry upwards the required energy flux of 300 watts per square metre. The model shows a topologically complex magnetic field of 160 gauss on the Sun's surface, agreeing with inferences obtained from spectropolarimetric observations, chromospheric features (contributing only weakly to the coronal heating) that can be identified with observed spicules and blinkers, and vortices that may be possibly associated with observed solar tornadoes. Title: Characterizing and predicting the magnetic environment leading to solar eruptions Authors: Amari, Tahar; Canou, Aurélien; Aly, Jean-Jacques Bibcode: 2014Natur.514..465A Altcode: The physical mechanism responsible for coronal mass ejections has been uncertain for many years, in large part because of the difficulty of knowing the three-dimensional magnetic field in the low corona. Two possible models have emerged. In the first, a twisted flux rope moves out of equilibrium or becomes unstable, and the subsequent reconnection then powers the ejection. In the second, a new flux rope forms as a result of the reconnection of the magnetic lines of an arcade (a group of arches of field lines) during the eruption itself. Observational support for both mechanisms has been claimed. Here we report modelling which demonstrates that twisted flux ropes lead to the ejection, in support of the first model. After seeing a coronal mass ejection, we use the observed photospheric magnetic field in that region from four days earlier as a boundary condition to determine the magnetic field configuration. The field evolves slowly before the eruption, such that it can be treated effectively as a static solution. We find that on the fourth day a flux rope forms and grows (increasing its free energy). This solution then becomes the initial condition as we let the model evolve dynamically under conditions driven by photospheric changes (such as flux cancellation). When the magnetic energy stored in the configuration is too high, no equilibrium is possible and the flux rope is `squeezed' upwards. The subsequent reconnection drives a mass ejection. Title: Reconstruction of the solar coronal magnetic field in spherical geometry Authors: Amari, T.; Aly, J. -J.; Canou, A.; Mikic, Z. Bibcode: 2013A&A...553A..43A Altcode: Context. High-resolution vector magnetographs either onboard spacecrafts or satellites (HMI/SDO, etc.) or ground based (SOLIS, etc.) now gives access to vector synoptic maps, composite magnetograms made of multiple interactive active regions, and full disk magnetograms. It thus become possible to reconstruct the coronal magnetic field on the full Sun scale.
Aims: We present a method for reconstructing the global solar coronal magnetic field as a nonlinear force-free field. It is based on a well-posed Grad-Rubin iterative scheme adapted to spherical coordinates
Methods: This method is a natural extension to spherical geometry of the one we previously developed in Cartesian geometry. It is implemented in the code XTRAPOLS, which is a massively parallel code. It allows dealing with the strong constraints put on the computational methods by having to handle the very large amounts of data contained in high-resolution large-scale magnetograms. The method exploits the mixed elliptic-hyperbolic nature of the Grad-Rubin boundary value problem. It uses a finite-difference method for the elliptic part and a method of characteristics for the hyperbolic part. The computed field guarantees to be divergence free up to round-off errors, by introducing a representation in terms of a vector potential satisfying specific gauge conditions. The construction of the latter - called here the restricted DeVore gauge - is described in detail in an appendix.
Results: We show that XTRAPOLS performs well by applying it to the reconstruction of a particular semi-analytic force-free field that has already been considered by various authors. Title: Progress on Reconstructing the Solar Coronal Magnetic Field above Active region at different scales Authors: Canou, A.; Amari, T. Bibcode: 2013enss.confE.112C Altcode: he low solar corona is dominated by the magnetic field which is created in the Sun's interior by a dynamo process and which then emerges into the atmosphere. This magnetic field plays an important role in most structures and phenomena observed at various wavelengths such as prominences, small and large scale eruptive events, and continuous heating of the plasma. It is therefore important to understand its three-dimensional properties in order to elaborate efficient theoretical models. Unfortunately, the magnetic field is difficult to measure locally in the hot and tenuous corona. But this can be done at the level of the cooler and denser photosphere, and several instruments with high resolution vector magnetographs are currently available (e.g. THEMIS/MTR, SOLIS/VSM, HINODE/SOT/SP or SDO/HMI) or will be available on future programmed missions (e.g. Solar Orbiter, ATST and EST). This has lead solar physicists to develop an approach which consists in reconstructing the coronal magnetic field from boundary data given on the photosphere.

We will present our recent progress and results to solve this problem at the active region scale or the larger one such as the full disk or synoptic one, for which the large amount of data as well as their sparsity on the solar disk, require to develop particular strategies. We will also show how this can be helpful to characterize the many aspects of active regions during their static or pre-eruptive evolution phases. Title: On Some Algorithm for Modeling the Solar Coronal Magnetic Field as MHD Equilibrium on Unstructured Mesh Authors: Amari, T.; Delyon, F.; Alauzet, F.; Frey, P.; Olivier, G.; Aly, J. J.; SDO/HMI Team Bibcode: 2012ASPC..459..189A Altcode: The low solar corona is dominated by the magnetic field which is created inside the sun by a dynamo process and then emerges into the atmosphere. This magnetic field plays an important role in most structures and phenomena observed at various wavelengths such as prominences, small and large scale eruptive events, and continuous heating of the plasma, and therefore it is important to understand its three-dimensional properties in order to elaborate efficient theoretical models. Unfortunately, the magnetic field is difficult to measure locally in the hot and tenuous corona. But this can be done at the level of the cooler and denser photosphere, and several instruments with high resolution vector magnetographs are currently available (THEMIS, Imaging Vector Magnetograph (IVM), the Advanced Stokes Polarimeter (ASP), SOLIS, HINODE , Solar Dynamics Observatory (SDO), or will be shortly availableby future telescopes such as EST and solar missions as SOLAR-ORBITER. This has lead solar physicists to develop an approach which consists in "Reconstructing" the coronal magnetic field from boundary data given on the photosphere. We will present some of the issues we encountered in solving this problem numerically as well our recent progress and results. Title: Quasi-static evolution of the reconstructed magnetic field of an emerging and eruptive active region Authors: Canou, A.; Amari, T. Bibcode: 2012EAS....55..125C Altcode: We study the evolution of the emerging and eruptive Active Region (AR) 10930 for which the coronal magnetic field is reconstructed as a nonlinear force-free field along with vector magnetograms obtained from Hinode/SOT/SP data. We show that the AR evolves quasi-statically during several days through a sequence of equilibria until the time of the eruption. In addition this sequence emphasizes the formation and expansion of a coronal Twisted Flux Rope (TFR) which is related to other observed coronal structures. On the other hand, the pre-eruptive and post-eruptive magnetic configurations show that the pre-eruptive TFR plays a crucial role during the eruption. Title: Coronal relative magnetic helicities and subsurface kinetic helicities of active regions Authors: Petrie, Gordon; Komm, Rudolf; Amari, Tahar Bibcode: 2012shin.confE.117P Altcode: Excess of helicity in coronal magnetic structures has often been linked to their instability and eruption. Moreover, active regions associated with subphotospheric patterns of strong subsurface kinetic helicity have been found to be more flare productive. How are these atmospheric magnetic and subsurface fluid helicities related? Using SOLIS vector magnetic magnetograms, the XTRAPOL nonlinear force-free field extrapolation code and GONG helioseismic data we study the coronal relative magnetic helicities of a set of active regions in combination with their subsurface kinetic helicities in order to better understand the transport processes of helicity in solar activity. Title: Self-gravitating Body with an Internal Magnetic Field. I. New Analytical Equilibria Authors: Aly, J. -J.; Amari, T. Bibcode: 2012ApJ...750....4A Altcode: We construct exact analytical solutions of the equations describing the equilibrium of a self-gravitating magnetized fluid body, possibly rigidly rotating, by superposing two solutions of finite energy defined in the whole space, one describing a non-magnetized gravitating equilibrium (ST1) and the other describing a magnetized non-gravitating equilibrium (ST2). A large number of ST1s can be found in the literature and directly used for our constructions, and we thus concentrate on ST2s, which are difficult to obtain. We derive some of their general properties and exhibit two explicit classes of axisymmetric "elementary" such equilibria. The first one is extracted from the stellar models proposed by Prendergast and by Kutvitskii & Solov'ev, respectively. The second one is constructed by using Palumbo's theory of isodynamic equilibria, for which the magnetic pressure is constant on each flux surface. Both types of ST2s have their magnetic field confined within a bounded region, respectively, of spherical and toroidal shapes. A much more general ST2 can be obtained by juxtaposing n+q elementary ST2s, with n of the first type and q of the second type, in such a way that the magnetic regions do not pairwise overlap. The specific equilibria we obtain by superposition thus have no external field extending to infinity, and may be three dimensional (3D), which invalidates a recent nonexistence conjecture. Moreover, they may be arranged to contain force-free regions. Our superposition method can be considered as a 3D generalization of the axisymmetric splitting method previously developed by Kutvitskii & Solov'ev. Title: Connecting the photosphere to the corona : Reconstructing the Solar Coronal Magnetic Field Authors: Amari, T.; Delyon, F.; Alauzet, F.; Canou, A.; Mikic, Z.; Aly, J. J.; Solis Team; Stanford Sdo/Hmi Team Bibcode: 2012decs.confE..50A Altcode: The low solar corona is dominated by the magnetic field which is created inside the sun by a dynamo process and then emerges into the atmosphere. This magnetic field plays an important role in most structures and phenomena observed at various wavelengths such as prominences, small and large scale eruptive events, and continuous heating of the plasma, and therefore it is important to understand its three-dimensional properties in order to elaborate efficient theoretical models. Unfortunately, the magnetic field is difficult to measure locally in the hot and tenuous corona. But this can be done at the level of the cooler and denser photosphere, and several instruments with high resolution vector magnetographs are currently available (THEMIS, Imaging Vector Magnetograph (IVM), the Advanced Stokes Polarimeter (ASP)), SOLIS, HINODE , Solar Dynamics Observatory (SDO), or will be shortly available and future programmed missions such as , SOLAR-ORBITER. This has lead solar physicists to develop an approach which consists in reconstructing the coronal magnetic field from boundary data given on the photosphere. We will present our recent progress and results to solve this problem at the scale of active regions or larger ones such as full disk or synoptic scales, for which the large amount of data as well as their sparsity on the solar disk, require to develop particular strategies. We will also illustrate the interest of the reconstruction for characterizing the magnetic environments of prominences, emerging sub-photospheric structures and the pre-eruptive ones. Title: Magnetic bubbles and magnetic towers - I. General properties and simple analytical models Authors: Aly, J. -J.; Amari, T. Bibcode: 2012MNRAS.420..237A Altcode: 2011MNRAS.tmp.2086A We consider magnetostatic equilibria in which a bounded region D containing a magnetized plasma is either fully confined by a field-free external medium - magnetic bubble equilibria (MBEqs) - or is confined by both such a medium and line-tying in a dense plasma region - magnetic tower equilibria (MTEqs). We first establish some of their general properties. In particular, we derive a series of useful integral equalities relating the magnetic field and the thermal pressures inside and outside D, respectively. We use them to prove the non-existence of an axisymmetric MBEq with a purely poloidal field, and to discuss some recent results of Braithwaite on MBEq formation by relaxation from an initial non-equilibrium state. We next present two families of exact analytical axisymmetric MBEqs with, respectively, spherical and toroidal shapes. The first family is extracted from Prendergast's model of a self-gravitating magnetized body, while the second one is constructed by using Palumbo's theory of isodynamic equilibria, for which both magnetic and thermal pressures take constant values on any flux surface. MTEqs with a large variety of structures are thus obtained in a simple way: we start from an arbitrary MBEq and just consider the part of it above a given plane cutting the bubble D. For MBEqs and MTEqs in either family, we compute in closed form most of the interesting physical quantities (such as energy, magnetic helicity and twist). Our results are expected to be useful for building up simple models of several astrophysical objects (such as X-ray cavities in the intracluster medium, jets emitted by disc accreting compact objects, eruptive events in stellar coronae and their ejecta). Title: Coronal Mass Ejection Initiation by Converging Photospheric Flows: Toward a Realistic Model Authors: Amari, T.; Aly, J. -J.; Luciani, J. -F.; Mikic, Z.; Linker, J. Bibcode: 2011ApJ...742L..27A Altcode: In the context of coronal mass ejections triggering, we reconsider the class of models in which the evolution of an active region (AR) is driven by imposed boundary motions converging toward the polarity inversion line (PIL). We introduce a new model problem in which there is a large-scale flow with a diverging structure on the photosphere. This flow is reminiscent of that of the well-known moat flow around each of the two spots of a bipolar AR and transports only part of the magnetic flux toward the PIL. It is thus more compatible with observations than the one used in our previous study, which forced the whole positive and negative polarity parts of the AR approaching each other. We also include a diffusion term associated with small-scale turbulent photospheric motions, but keep the associated diffusivity at a low value in the particular study described here. We show that the evolution of an initial sheared force-free field first leads to the formation of a twisted flux rope which stays in equilibrium for some time. Eventually, however, the configuration suffers a global disruption whose underlying mechanism is found by energetic considerations to be nonequilibrium. It begins indeed when the magnetic energy becomes of the order of the energy of an accessible partially open field. For triggering an eruption by converging flows, it is thus not necessary to advect the whole AR toward the PIL, but only its central part. Title: Nonlinear Force-Free and Potential-Field Models of Active-Region and Global Coronal Fields during the Whole Heliosphere Interval Authors: Petrie, G. J. D.; Canou, A.; Amari, T. Bibcode: 2011SoPh..274..163P Altcode: 2010arXiv1010.6283P Between 24 March 2008 and 2 April 2008, the three active regions (ARs) NOAA 10987, 10988 and 10989 were observed daily by the Synoptic Optical Long-term Investigations of the Sun (SOLIS) Vector Spectro-Magnetograph (VSM) while they traversed the solar disk. We use these measurements and the nonlinear force-free magnetic field code XTRAPOL to reconstruct the coronal magnetic field for each active region and compare model field lines with images from the Solar Terrestrial RElations Observatory (STEREO) and Hinode X-ray Telescope (XRT) telescopes. Synoptic maps made from continuous, round-the-clock Global Oscillations Network Group (GONG) magnetograms provide information on the global photospheric field and potential-field source-surface models based on these maps describe the global coronal field during the Whole Heliosphere Interval (WHI) and its neighboring rotations. Features of the modeled global field, such as the coronal holes and streamer-belt locations, are discussed in comparison with extreme ultra-violet and coronagraph observations from STEREO. The global field is found to be far from a minimum, dipolar state. From the nonlinear models we compute physical quantities for the active regions such as the photospheric magnetic and electric current fluxes, the free magnetic energy and the relative helicity for each region each day where observations permit. The interconnectivity of the three regions is addressed in the context of the potential-field source-surface model. Using local and global quantities derived from the models, we briefly discuss the different observed activity levels of the regions. Title: Reconstruction of the solar coronal magnetic field, from active region to large scale Authors: Amari, T.; Canou, A.; Delyon, F.; Aly, J. J.; Frey, P.; Alauzet, F. Bibcode: 2011sf2a.conf..389A Altcode: The low solar corona is dominated by the magnetic field which is created inside the sun by a dynamo process and then emerges into the atmosphere. This magnetic field plays an important role in most structures and phenomena observed at various wavelengths such as prominences, small and large scale eruptive events, and continuous heating of the plasma, and therefore it is important to understand its three-dimensional properties in order to elaborate efficient theoretical models. Unfortunately, the magnetic field is difficult to measure locally in the hot and tenuous corona. But this can be done at the level of the cooler and denser photosphere, and several instruments with high resolution vector magnetographs are currently available (THEMIS, Imaging Vector Magnetograph (IVM), the Advanced Stokes Polarimeter (ASP), SOLIS, HINODE, Solar Dynamics Observatory (SDO), or will be shortly available by future telescopes such as EST and solar missions as SOLAR-ORBITER. This has lead solar physicists to develop an approach which consists in " reconstructing" the coronal magnetic field from boundary data given on the photosphere. We will discuss some of the issues encountered in solving this problem as well our recent progress and results at the scale of active region scales or the larger one such as full sun scale. Title: Nonlinear Force-Free and Potential-Field Models of Active Region and Global Coronal Fields Authors: Petrie, Gordon; Canou, Aurelien; Amari, Tahar Bibcode: 2011shin.confE..48P Altcode: We use daily observations by the Synoptic Optical Long-term Investigations of the Sun (SOLIS) Vector Spectro-Magnetograph (VSM) and the nonlinear force-free magnetic field code XTRAPOL to reconstruct the coronal magnetic field for selected active regions. We compare model field lines with images from the Solar Terrestrial RElations Observatory (STEREO) and Hinode X-ray Telescope (XRT) telescopes. Synoptic maps made from continuous, round-the-clock Global Oscillations Network Group (GONG) magnetograms provide information on the global photospheric field and potential-field source-surface models based on these maps describe the global coronal field.

Features of the modeled global field, such as the coronal holes and streamer-belt locations, are presented in comparison with extreme ultra-violet and coronagraph observations from STEREO. From the nonlinear models we compute physical quantities for the active regions such as the photospheric magnetic and electric current fluxes, the free magnetic energy and the relative helicity for each region each day where observations permit. The potential-field source-surface models also provide information on the connectivity of the active region fields to their surroundings and to the heliosphere. Using local and global quantities derived from the models, we briefly discuss the different observed activity levels of the regions. Title: Observational constraints on well-posed reconstruction methods and the optimization-Grad-Rubin method Authors: Amari, T.; Aly, J. -J. Bibcode: 2010A&A...522A..52A Altcode: Context. Grad-Rubin type methods are interesting candidates for reconstructing the force-free magnetic field of a solar coronal region. As input these methods, however, require the normal component Bn of the field on the whole boundary of the numerical box and the force-free function α on the part of the boundary where Bn > 0 (or Bn < 0), while observations provide data only on its lower photospheric part. Moreover, they introduce an unpleasing asymmetry between the opposite polarity parts of the boundary, and certainly do not take full advantage of the available data on α.
Aims: We address these issues resulting from observations. We present a possible way to supply the missing information about Bn and α on the non-photospheric sides of the box, and to use more effectively the data provided by the measurements.
Methods: We introduce the optimization-Grad-Rubin method (OGRM), which is in some sense midway between optimization methods and the standard Grad-Rubin methods. It is based on an iterative scheme in which the α used as a boundary condition is imposed to take identical values at both footpoints of any field line and to be as close as possible to the α provided by the measurements on the photosphere. The degree of “closeness” is measured by an “error functional” containing a weight function reflecting the confidence that can be placed on the observational data.
Results: The new method is implemented in our code XTRAPOL, along with some technical improvements. It is thus tested for two specific choices of the weight function by reconstructing a force-free field from data obtained by perturbing in either a random or a non-random way boundary values provided by an exact solution. Title: Coronal Mass Ejection Initiation: On the Nature of the Flux Cancellation Model Authors: Amari, T.; Aly, J. -J.; Mikic, Z.; Linker, J. Bibcode: 2010ApJ...717L..26A Altcode: 2010arXiv1005.4669A We consider a three-dimensional bipolar force-free magnetic field with a nonzero magnetic helicity, occupying a half-space, and study the problem of its evolution driven by an imposed photospheric flux decrease. For this specific setting of the Flux Cancellation Model describing coronal mass ejections occurring in active regions, we address the issues of the physical meaning of flux decrease, of the influence on field evolution of the size of the domain over which this decrease is imposed, and of the existence of an energetic criterion characterizing the possible onset of disruption of the configuration. We show that (1) the imposed flux disappearance can be interpreted in terms of transport of positive and negative fluxes toward the inversion line, where they get annihilated. (2) For the particular case actually computed, in which the initial state is quite sheared, the formation of a twisted flux rope and the subsequent global disruption of the configuration are obtained when the flux has decreased by only a modest amount over a limited part of the whole active region. (3) The disruption is produced when the magnetic energy becomes of the order of the decreasing energy of a semi-open field, and then before reaching the energy of the associated fully open field. This suggests that the mechanism leading to the disruption is nonequilibrium as in the case where flux is imposed to decrease over the whole region. Title: A Twisted Flux Rope as the Magnetic Structure of a Filament in Active Region 10953 Observed by Hinode Authors: Canou, A.; Amari, T. Bibcode: 2010ApJ...715.1566C Altcode: The presence of twisted flux ropes (TFRs) in pre-eruptive/flaring magnetic configurations is of main interest for our understanding of the structure and dynamics of the solar corona. On the one hand, their presence is a key ingredient in several theoretical models for the magnetic support of material in filaments, or triggering of coronal mass ejections as well as the emergence of structures from the convection zone into the corona. On the other hand, several observations have shown the presence of twist and shear during eruptive and flaring phases of eruptive phenomena. In this paper, we consider the determination of the magnetic structure of active region (AR) 10953 observed by Hinode and reconstructed using our two nonlinear force-free models. We show that the reconstructed magnetic configurations exhibit a TFR along the southern part of the neutral line. Moreover, the location of the magnetic dips within the TFR agrees within a good level of accuracy with the Hα images taken by SMART and the vertically integrated current density recovers the main structure present in Hinode/XRT images. The free magnetic energy is also found to be large enough to power the two C-class flares of the following days. We finally compare our results with those of Su et al. who proposed an interesting model of the same AR in which a TFR is inserted at the same location using the flux rope insertion method. Title: Does the Compression or the Expansion of a Simple Topology Potential Magnetic Field Lead to the Development of Current Sheets? Authors: Aly, J. J.; Amari, T. Bibcode: 2010ApJ...709L..99A Altcode: Janse & Low have most recently addressed the following question. Consider a cylindrical domain containing a simple topology potential magnetic field threading its lower and upper horizontal faces, and a perfectly conducting plasma. Suppose that this domain is made to slowly contract or expand in the vertical direction, so driving the field into a quasi-static evolution through a series of force-free configurations. Then are these configurations smooth, or do they contain current sheets (CSs)? We reexamine here their three-step argument leading to the conclusion that CSs form most generally. We prove analytically that the field has to evolve through "topologically untwisted" and "nonpotential" configurations, thus confirming the first two steps. However, we find the third step—leading to the conclusion that a smooth untwisted force-free field is necessarily potential—to be very disputable. Title: Nonlinear Force-Free Magnetic Field Modeling of AR 10953: A Critical Assessment Authors: De Rosa, Marc L.; Schrijver, C. J.; Barnes, G.; Leka, K. D.; Lites, B. W.; Aschwanden, M. J.; Amari, T.; Canou, A.; McTiernan, J. M.; Régnier, S.; Thalmann, J. K.; Valori, G.; Wheatland, M. S.; Wiegelmann, T.; Cheung, M. C. M.; Conlon, P. A.; Fuhrmann, M.; Inhester, B.; Tadesse, T. Bibcode: 2009SPD....40.3102D Altcode: Nonlinear force-free field (NLFFF) modeling seeks to provide accurate representations of the structure of the magnetic field above solar active regions, from which estimates of physical quantities of interest (e.g., free energy and helicity) can be made. However, the suite of NLFFF algorithms have failed to arrive at consistent solutions when applied to (thus far, two) cases using the highest-available-resolution vector magnetogram data from Hinode/SOT-SP (in the region of the modeling area of interest) and line-of-sight magnetograms from SOHO/MDI (where vector data were not available). One issue is that NLFFF models require consistent, force-free vector magnetic boundary data, and vector magnetogram data sampling the photosphere do not satisfy this requirement. Consequently, several problems have arisen that are believed to affect such modeling efforts. We use AR 10953 to illustrate these problems, namely: (1) some of the far-reaching, current-carrying connections are exterior to the observational field of view, (2) the solution algorithms do not (yet) incorporate the measurement uncertainties in the vector magnetogram data, and/or (3) a better way is needed to account for the Lorentz forces within the layer between the photosphere and coronal base. In light of these issues, we conclude that it remains difficult to derive useful and significant estimates of physical quantities from NLFFF models. Title: A Critical Assessment of Nonlinear Force-Free Field Modeling of the Solar Corona for Active Region 10953 Authors: De Rosa, Marc L.; Schrijver, Carolus J.; Barnes, Graham; Leka, K. D.; Lites, Bruce W.; Aschwanden, Markus J.; Amari, Tahar; Canou, Aurélien; McTiernan, James M.; Régnier, Stéphane; Thalmann, Julia K.; Valori, Gherardo; Wheatland, Michael S.; Wiegelmann, Thomas; Cheung, Mark C. M.; Conlon, Paul A.; Fuhrmann, Marcel; Inhester, Bernd; Tadesse, Tilaye Bibcode: 2009ApJ...696.1780D Altcode: 2009arXiv0902.1007D Nonlinear force-free field (NLFFF) models are thought to be viable tools for investigating the structure, dynamics, and evolution of the coronae of solar active regions. In a series of NLFFF modeling studies, we have found that NLFFF models are successful in application to analytic test cases, and relatively successful when applied to numerically constructed Sun-like test cases, but they are less successful in application to real solar data. Different NLFFF models have been found to have markedly different field line configurations and to provide widely varying estimates of the magnetic free energy in the coronal volume, when applied to solar data. NLFFF models require consistent, force-free vector magnetic boundary data. However, vector magnetogram observations sampling the photosphere, which is dynamic and contains significant Lorentz and buoyancy forces, do not satisfy this requirement, thus creating several major problems for force-free coronal modeling efforts. In this paper, we discuss NLFFF modeling of NOAA Active Region 10953 using Hinode/SOT-SP, Hinode/XRT, STEREO/SECCHI-EUVI, and SOHO/MDI observations, and in the process illustrate three such issues we judge to be critical to the success of NLFFF modeling: (1) vector magnetic field data covering larger areas are needed so that more electric currents associated with the full active regions of interest are measured, (2) the modeling algorithms need a way to accommodate the various uncertainties in the boundary data, and (3) a more realistic physical model is needed to approximate the photosphere-to-corona interface in order to better transform the forced photospheric magnetograms into adequate approximations of nearly force-free fields at the base of the corona. We make recommendations for future modeling efforts to overcome these as yet unsolved problems. Title: Evidence for a Pre-Eruptive Twisted Flux Rope Using the Themis Vector Magnetograph Authors: Canou, A.; Amari, T.; Bommier, V.; Schmieder, B.; Aulanier, G.; Li, H. Bibcode: 2009ApJ...693L..27C Altcode: Although there is evidence that twisted structures form during large-scale eruptive events, it is not yet clear whether these exist in the pre-eruptive phase as twisted flux ropes (TFRs) in equilibrium. This question has become a major issue since several theoretical mechanisms can lead to the formation of TFRs. These models consider either the evolution of a coronal configuration driven by photospheric changes or the emergence of TFR from the convection zone. We consider as a target for addressing this issue the active region NOAA AR 10808 known at the origin of several large-scale eruptive phenomena, and associated with the emergence of a δ-spot. Using the THEMIS vector magnetogram as photospheric boundary conditions for our nonlinear force-free reconstruction model of the low corona and without any other assumption, we show that the resulting pre-eruptive configuration exhibits a TFR above the neutral line of the emerging δ-spot. In addition, the free magnetic energy of this configuration could even be large enough to explain such resulting large-scale eruptive events. Title: Magnetic flux ropes: Fundamental structures for eruptive phenomena Authors: Amari, Tahar; Aly, Jean-Jacques Bibcode: 2009IAUS..257..211A Altcode: We consider some general aspects of twisted magnetic flux ropes (TFR), which are thought to play a fundamental role in the structure and dynamics of large scale eruptive events. We first discuss the possibility to show the presence of a TFR in a pre-eruptive configuration by using a model along with observational informations provided by a vector magnetograph. Then we present, in the framework of a generic model in which the coronal field is driven into an evolution by changes imposed at the photospheric level, several mechanisms which may lead to the formation and the disruption of a TFR, including the development of a MHD instability, and we discuss the issues of the energy and helicity contents of an erupting configuration. Finally we report some results of a recent and more ambitious approach to the physics of TFRs in which one tries to describe in a consistent way their rising through the convection zone, their emergence through the photosphere, and their subsequent evolution in the corona. Title: Coronal Closure of Subphotospheric MHD Convection for the Quiet Sun Authors: Amari, T.; Luciani, J. F.; Aly, J. J. Bibcode: 2008ApJ...681L..45A Altcode: We use our resistive layer model (RLM), which stresses the importance of the resistivity at the photospheric interface, to study the evolution of a solar coronal quiet region driven by subphotospheric convection. The initial version of the RLM is improved by introducing a new Boussinesq MHD model for the upper part of the convection zone (CZ), while the low-beta corona is still described by a MHD model. We compute the evolution of a weak magnetic field introduced initially in the CZ. We observe its amplification by the turbulence, the concentration of the photospheric flux at the boundaries of the convection cells, the coalescence and the cancellation of flux elements, and the transfer of about 10% of the magnetic energy into the corona. The currents associated with the nonpotential coronal field are found to be organized in filament-like localized structures due to the photospheric vortices and the complexity of the magnetic topology. Their resistive dissipation contributes to the heating of the quiet corona. Title: Non-Linear Force-Free Field Modeling of a Solar Active Region Around the Time of a Major Flare and Coronal Mass Ejection Authors: De Rosa, M. L.; Schrijver, C. J.; Metcalf, T. R.; Barnes, G.; Lites, B.; Tarbell, T.; McTiernan, J.; Valori, G.; Wiegelmann, T.; Wheatland, M.; Amari, T.; Aulanier, G.; Démoulin, P.; Fuhrmann, M.; Kusano, K.; Régnier, S.; Thalmann, J. Bibcode: 2008AGUSMSP31A..06D Altcode: Solar flares and coronal mass ejections are associated with rapid changes in coronal magnetic field connectivity and are powered by the partial dissipation of electrical currents that run through the solar corona. A critical unanswered question is whether the currents involved are induced by the advection along the photosphere of pre-existing atmospheric magnetic flux, or whether these currents are associated with newly emergent flux. We address this problem by applying nonlinear force-free field (NLFFF) modeling to the highest resolution and quality vector-magnetographic data observed by the recently launched Hinode satellite on NOAA Active Region 10930 around the time of a powerful X3.4 flare in December 2006. We compute 14 NLFFF models using 4 different codes having a variety of boundary conditions. We find that the model fields differ markedly in geometry, energy content, and force-freeness. We do find agreement of the best-fit model field with the observed coronal configuration, and argue (1) that strong electrical currents emerge together with magnetic flux preceding the flare, (2) that these currents are carried in an ensemble of thin strands, (3) that the global pattern of these currents and of field lines are compatible with a large-scale twisted flux rope topology, and (4) that the ~1032~erg change in energy associated with the coronal electrical currents suffices to power the flare and its associated coronal mass ejection. We discuss the relative merits of these models in a general critique of our present abilities to model the coronal magnetic field based on surface vector field measurements. Title: Nonlinear Force-free Field Modeling of a Solar Active Region around the Time of a Major Flare and Coronal Mass Ejection Authors: Schrijver, C. J.; DeRosa, M. L.; Metcalf, T.; Barnes, G.; Lites, B.; Tarbell, T.; McTiernan, J.; Valori, G.; Wiegelmann, T.; Wheatland, M. S.; Amari, T.; Aulanier, G.; Démoulin, P.; Fuhrmann, M.; Kusano, K.; Régnier, S.; Thalmann, J. K. Bibcode: 2008ApJ...675.1637S Altcode: 2007arXiv0712.0023S Solar flares and coronal mass ejections are associated with rapid changes in field connectivity and are powered by the partial dissipation of electrical currents in the solar atmosphere. A critical unanswered question is whether the currents involved are induced by the motion of preexisting atmospheric magnetic flux subject to surface plasma flows or whether these currents are associated with the emergence of flux from within the solar convective zone. We address this problem by applying state-of-the-art nonlinear force-free field (NLFFF) modeling to the highest resolution and quality vector-magnetographic data observed by the recently launched Hinode satellite on NOAA AR 10930 around the time of a powerful X3.4 flare. We compute 14 NLFFF models with four different codes and a variety of boundary conditions. We find that the model fields differ markedly in geometry, energy content, and force-freeness. We discuss the relative merits of these models in a general critique of present abilities to model the coronal magnetic field based on surface vector field measurements. For our application in particular, we find a fair agreement of the best-fit model field with the observed coronal configuration, and argue (1) that strong electrical currents emerge together with magnetic flux preceding the flare, (2) that these currents are carried in an ensemble of thin strands, (3) that the global pattern of these currents and of field lines are compatible with a large-scale twisted flux rope topology, and (4) that the ~1032 erg change in energy associated with the coronal electrical currents suffices to power the flare and its associated coronal mass ejection. Title: Coronal Mass Ejection Initiation and Complex Topology Configurations in the Flux Cancellation and Breakout Models Authors: Amari, T.; Aly, J. J.; Mikic, Z.; Linker, J. Bibcode: 2007ApJ...671L.189A Altcode: We present some new results showing that the flux cancellation model for coronal mass ejections (CMEs) works well also in a complex-topology magnetic field. We consider as a model problem the case of the flux-cancellation-driven evolution of a quadrupolar configuration. We find that (1) during the first phase, the field evolves slowly, with a twisted flux rope in equilibrium being created at some time; (2) nonequilibrium sets in at a critical time and the configuration experiences a major global disruption. These features are similar to those previously obtained for a bipolar configuration. Some differences between the two cases are however observed: (1) the presence of an X-point above the twisted flux rope makes the expulsion of the latter much easier due to the weaker confinement near this point; this difference may be at the origin of the existence of two classes of CMEs-fast and slow; (2) the energy W(t) of the configuration remains smaller than the energy Wσ(t) of the associated totally open field, and then the disruption does not occur when W(t)~Wσ(t), as in the bipolar case. Rather we get nonequilibrium when W(t)~WSO(t), where WSO(t) is the energy of a semiopen field which has its open lines connected to the two central spots on which flux cancellation is imposed. A consequence of our results is that the topological complexity of a preerupting configuration cannot be taken as a criterion for eliminating the flux cancellation model in favor of the well-known breakout model. Title: Structure and evolution of the solar coronal magnetic field Authors: Aly, J. J.; Amari, T. Bibcode: 2007GApFD.101..249A Altcode: No abstract at ADS Title: Resolution of the 180° Ambiguity for Inverse Horizontal Magnetic Field Configurations Authors: Li, Jing; Amari, Tahar; Fan, Yuhong Bibcode: 2007ApJ...654..675L Altcode: A well-known problem in solar physics is that solutions for the transverse magnetic field direction are ambiguous with respect to a 180° reversal in the field direction. In this paper we focus on three methods for the removal of the 180° ambiguity applied to three MHD models. These methods are (1) the reference field method, (2) the method of magnetic pressure gradient, and (3) the magnetic field divergence-free method. All three methods are noniterative, and methods 2 and 3 are analytical and fast. We apply these methods to three MHD equilibrium model fields: (1) an analytical solution of a nonlinear force-free magnetic field equilibrium from Low, (2) a simulation of an emerging twisted flux tube from Fan & Gibson, and (3) a pre-eruptive twisted magnetic flux rope equilibrium reached by relaxation from Amari et al. We measure the success of methods within ``inverse horizontal field'' regions in the boundary, which are mathematically defined by B⊥˙∇⊥Bz>0. When such regions overlap with the magnetic field neutral lines, they are known as ``bald patches'' (BPs) or inverse topology. Our most important conclusion is that the magnetic divergence-free method is far more successful than the other two methods within BPs. This method requires a second level of measurements of the vertical magnetic field. As high-quality multilevel magnetograms will come online in the near future, our work shows that multilayer magnetic field measurements will be highly desirable to objectively and successfully tackle the 180° ambiguity problem. Title: Well posed reconstruction of the solar coronal magnetic field Authors: Amari, T.; Boulmezaoud, T. Z.; Aly, J. J. Bibcode: 2006A&A...446..691A Altcode: We present and compare two methods for the reconstruction of the solar coronal magnetic field, assumed to be force-free, from photospheric boundary data. Both methods rely on a well posed mathematical boundary value problem and are of the Grad-Rubin type, i.e., the couple ({B},α) is computed iteratively. They do differ from each other on the one hand by the way they address the zero-divergence of {B} issue, and on the other hand by the scheme they use for computing α at each iteration. The comparison of the two methods is done by numerically computing two examples of nonlinear force-free fields associated to large scale strong electric current distributions, whose exact forms can be otherwise determined semi-analytically. In particular, the second solution has a large nonlinearity even in the weak field region - a feature which is not present in the actual magnetograms, but is interesting to consider as it does allow to push the methods to the limits of their range of validity. The best results obtained with those methods give a relative vector error smaller than 0.01. For the latter extreme case, our results show that higher resolution reconstructions with bounded convergence improve the approximated solution, which may be of some interest for the treatment of the data of future magnetographs. Title: Self and mutual magnetic helicities in coronal magnetic configurations Authors: Régnier, S.; Amari, T.; Canfield, R. C. Bibcode: 2005A&A...442..345R Altcode: Together with the magnetic energy, the magnetic helicity is an important quantity used to describe the nature of a magnetic field configuration. In the following, we propose a new technique to evaluate various components of the total magnetic helicity in the corona for an equilibrium reconstructed magnetic field. The most meaningful value of helicity is the total relative magnetic helicity which describes the linkage of the field lines even if the volume of interest is not bounded by a magnetic surface. In addition if the magnetic field can be decomposed into the sum of a closed field and a reference field (following , Berger 1999 in Magnetic Helicity in Space and Laboratory Plasmas, ed. M. R. Brown, R. C. Canfield, & A. A. Pevtsov, 1), we can introduce three other helicity components: the self helicity of the closed field, the mutual helicity between the closed field and the reference field, and the vacuum helicity (self helicity of the reference field). To understand the meaning of those quantities, we derive them from the potential field (reference) and the force-free field computed with the same boundary conditions for three different cases: a single twisted flux tube derived from the extended Gold-Hoyle solutions, a simple magnetic configuration with three balanced sources and a constant distribution of the force-free parameter, and the AR 8210 magnetic field observed from 17:13 UT to 21:16 UT on May 1, 1998. We analyse the meaning of the self and mutual helicities: the self and mutual helicities correspond to the twist and writhe of confined flux bundles, and the crossing of field lines in the magnetic configuration respectively. The main result is that the magnetic configuration of AR 8210 is dominated by the mutual helicity and not by the self helicity (twist and writhe). Our results also show that although not gauge invariant the vacuum helicity is sensitive to the topological complexity of the reference field. Title: Non-Current-free Coronal Closure of Subphotospheric MHD Models Authors: Amari, T.; Luciani, J. F.; Aly, J. J. Bibcode: 2005ApJ...629L..37A Altcode: We propose a method that allows the matching of two classes of models that have been well developed so far, but largely independently from each other: (1) convection zone (CZ) models, which generally either end up below the photosphere or are matched with an external potential field, and (2) coronal models of eruptive processes and heating, which usually consider the evolution of current-carrying magnetic fields driven by given photospheric changes. In our approach, the thin turbulent photospheric layer between the two large regions is modeled as a resistive layer across which the physical quantities suffer stiff variations. We show that this layer enables the transport of an electric current into the corona through the tangential component of the electric field (continuous across the various interfaces), as well as good conservation of the global magnetic helicity. To illustrate our general approach, we present in detail a model problem in which the rising of an initially twisted flux rope through the CZ is described kinematically while the physics inside the corona is described by a full magnetohydrodynamic model. We show that the evolution leads to the emergence of magnetic flux and electric current into the corona, with the creation of a flux rope that eventually suffers a dynamical transition toward fast expansion. Title: Coronal Magnetohydrodynamic Evolution Driven by Subphotospheric Conditions Authors: Amari, T.; Luciani, J. F.; Aly, J. J. Bibcode: 2004ApJ...615L.165A Altcode: We consider the approach to the theory of formation, evolution, and major disruption of coronal twisted flux ropes, in which subphotospheric structures play a crucial role. We set a boundary value problem in the corona in which the boundary conditions at the photospheric level are determined by a simple kinematic model describing the rising of a tube throughout the convection zone. In addition to peculiar features like the existence of areas of flux concentration on the lower boundary and the bending of the polarity inversion line, we find that the coronal configuration suffers a transition from arcade to rope topology and (later) a transition from a slow quasi-static evolution to a dynamic nonequilibrium one, both these critical phenomena occurring during the phase of decrease of the net photospheric flux. There is a continuous injection of magnetic helicity into the corona, and the magnetic energy remains smaller than that of the corresponding open field. Contrary to what has been observed in some other simulations, the formation of the equilibrium flux rope prior to the disruption is not associated with some reconnection on the ``photospheric'' surface. This may possibly suggest the utility of different observational diagnostics. Title: 3D magnetic configuration of the Hα filament and X-ray sigmoid in NOAA AR 8151 Authors: Régnier, S.; Amari, T. Bibcode: 2004A&A...425..345R Altcode: We investigate the structure and relationship of an Hα filament and an X-ray sigmoid observed in active region NOAA 8151. We first examine the presence of such structures in the reconstructed 3D coronal magnetic field obtained from the non-constant-α force-free field hypothesis using a photospheric vector magnetogram (IVM, Mees Solar Observatory). This method allows us to identify several flux systems: a filament (height 30 Mm, aligned with the polarity inversion line (PIL), magnetic field strength at the apex 49 G, number of turns 0.5-0.6), a sigmoid (height 45 Mm, aligned with the PIL, magnetic field strength at the apex 56 G, number of turns 0.5-0.6) and a highly twisted flux tube (height 60 Mm, magnetic field strength at the apex 36 G, number of turns 1.1-1.2). By searching for magnetic dips in the configuration, we identify a filament structure which is in good agreement with the Hα observations. We find that both filament and sigmoidal structures can be described by a long twisted flux tube with a number of turns less than 1 which means that these structures are stable against kinking. The filament and the sigmoid have similar absolute values of α and Jz in the photosphere. However, the electric current density is positive in the filament and negative in the sigmoid: the filament is right-handed whereas the sigmoid is left-handed. This fact can explain the discrepancies between the handedness of magnetic clouds (twisted flux tubes ejected from the Sun) and the handedness of their solar progenitors (twisted flux bundles in the low corona). The mechanism of eruption in AR 8151 is more likely not related to the development of instability in the filament and/or the sigmoid but is associated with the existence of the highly twisted flux tube (∼1.1-1.2 turns). Title: Eruptive Behavior Originating in Active Regions Authors: Linker, J. A.; Mikic, Z.; Lionello, R.; Riley, P.; Amari, T. Bibcode: 2003AGUFMSH41A..04L Altcode: Coronal mass ejections (CMEs) are spectacular manifestations of solar acitivy. These immense eruptions of plasma and magnetic field are propelled outward from the sun with velocities as high as 2000 km/s. The fastest CMEs typically originate from active regions on the Sun. MHD models of the eruption of large scale coronal fields have demonstrated significant energy release in idealized 2D (Antiochos et al., ApJ 512, 985, 1999) and 3D (Linker et al., Phys. Plasmas 10, 1971, 2003) geometry. Eruptive behavior has also been shown for a 3D localized arcade (Amari et al., ApJ 529, L49, 2000). In active regions on the Sun, both the localized field due to the active region and the overlying fields in the large scale corona are important. We describe MHD computations of the eruptive behavior of a localized active region field (modeled as a localized bipole) within a large-scale dipolar configuration. We discuss the differences between this more realistic configuration and the idealized configurations that have been considered previously. Work supported by NASA and the Center for Integrated Space Weather Modeling (an NSF Science and Technology Center). Title: Coronal Mass Ejection: Initiation, Magnetic Helicity, and Flux Ropes. II. Turbulent Diffusion-driven Evolution Authors: Amari, T.; Luciani, J. F.; Aly, J. J.; Mikic, Z.; Linker, J. Bibcode: 2003ApJ...595.1231A Altcode: We consider a three-dimensional bipolar magnetic field B, occupying a half-space, which is driven into evolution by the slow turbulent diffusion of its normal component on the boundary. The latter is imposed by fixing the tangential component of the electric field and leads to flux cancellation. We first present general analytical considerations on this problem and then construct a class of explicit solutions in which B keeps evolving quasi-statically through a sequence of force-free configurations without exhibiting any catastrophic behavior. Thus, we report the results of a series of numerical simulations in which B evolves from different force-free states, the electric field on the boundary being imposed to have a vanishing electrostatic part (the latter condition is not enforced in the analytical model, and thus it is possible a priori for the results of the two types of calculations to be different). In all the cases, we find that the evolution conserves the magnetic helicity and exhibits two qualitatively different phases. The first one, during which a twisted flux rope is created, is slow and almost quasi-static, while the second one is associated with a disruption, which is confined for a small initial helicity and global for a large initial helicity. Our calculations may be relevant for modeling the coronal mass ejections that have been observed to occur in the late dispersion phase of an active region. In particular, they may allow us to understand the role played by a twisted flux rope in these events. Title: Force-free Fields in Active Regions: Magnetic configurations and Energetics Authors: Regnier, S.; Canfield, R. C.; Amari, T. Bibcode: 2003SPD....34.0103R Altcode: 2003BAAS...35..805R To determine the 3D configuration of solar active regions and to define boundary conditions for MHD codes, we reconstruct the coronal magnetic field from photospheric measurements. For that, we consider the active region in an equilibrium state. Three hypotheses are then often used: the potential field (no electric current), the linear force-free field (the current density is α times the magnetic field, α is a constant), the nonlinear force-free field (α is a function of space). We here compare those three models in terms of connectivity changes and energetics for two different active regions: AR 8151 and AR 8210. AR 8151 shows dramatical changes between these models whereas AR 8210 configuration stays close to the potential field. The structure of the filament and of the sigmoid observed in AR 8151 can only be determined in the nonlinear force-free field: both structures are identified with twisted flux tubes with ∼ 0.5-0.6 turns. Interestingly, the filament is a right-handed structure whereas the sigmoid is left-handed! This work is a part of the Solar MURI project. Title: Coronal Mass Ejection: Initiation, Magnetic Helicity, and Flux Ropes. I. Boundary Motion-driven Evolution Authors: Amari, T.; Luciani, J. F.; Aly, J. J.; Mikic, Z.; Linker, J. Bibcode: 2003ApJ...585.1073A Altcode: In this paper we study a class of three-dimensional magnetohydrodynamic model problems that may be useful to understand the role of twisted flux ropes in coronal mass ejections. We construct in a half-space a series of force-free bipolar configurations with different helicity contents and bring them into an evolution by imposing to their footpoints on the boundary slow motions converging toward the inversion line. For all the cases that have been computed, this process leads, after a phase of quasi-static evolution, to the formation of a twisted flux rope by a reconnection process and to the global disruption of the configuration. In contrast with the results of some previous studies, however, the rope is never in equilibrium. It thus appears that the presence of a rope in the preeruptive phase is not a necessary condition for the disruption but may be the product of the disruption itself. Moreover, the helicity keeps an almost constant value during the evolution, and the problem of the origin of the helicity content of an eruptive configuration appears to be that of the initial force-free state. In addition to these numerical simulations, we report some new relations for the time variations of the energy and the magnetic helicity and develop a simple analytical model in which the magnetic field evolution exhibits essential features quite similar to those observed during the quasi-static phase in the numerics. Title: Magnetic Field Topology in Prominences Authors: Lionello, Roberto; Mikić, Zoran; Linker, Jon A.; Amari, Tahar Bibcode: 2002ApJ...581..718L Altcode: We present a study of the magnetic field lines of a prominence using MHD and thermodynamic/hydrodynamic (TH) models. Previous modeling of prominences has tended to emphasize either magnetic field modeling or TH modeling in isolation. In this paper, we combine these approaches to model a long-lived filament observed in 1996 August-September. In our new approach, we (1) use magnetograms to prescribe the boundary conditions for the magnetic flux in three-dimensional MHD simulations, (2) show that observed magnetic flux changes can produce a fluxrope and that the dipped (concave upward) portion of the field lines form in the approximate location of the observed prominence, and (3) show that TH computations, using the computed geometry of magnetic field lines that are in three-dimensional MHD equilibrium, have condensations forming in the dipped portions of the field lines. Title: Global budget for an eruptive active region . I. Equilibrium reconstruction approach Authors: Bleybel, A.; Amari, T.; van Driel-Gesztelyi, L.; Leka, K. D. Bibcode: 2002A&A...395..685B Altcode: We present results on the magnetic structure of NOAA Active Region #7912 which was involved in a long duration flare on 14 October 1995, and was the source region for a magnetic cloud observed by the WIND spacecraft from October 18-20. Using vector magnetograms from the Imaging Vector Magnetograph (``IVM''), we reconstruct the magnetic field above this active region, assuming it is in a non-linear force-free state. This reconstruction is used to determine global properties of the active region magnetic field including topology, magnetic energy, and relative magnetic helicity. A comparison of some global quantities before and after the eruptive event is discussed. We show that the magnetic energy and relative helicity of the active region decreased after the eruption, consistent with the ejection of a large amount of helicity (in the magnetic cloud). We also show that the relaxed post-flare state still contains nonlinearities and is not consistent with a linear force-free state as predicted by Taylor's theory of relaxation. These results agree with those of recent numerical simulations concerning plasmoid ejection and helicity redistribution in the disruption of magnetic configurations. We propose as an explanation that the anchoring of field lines in the photosphere prevents a full cascade to the Taylor state, and that a variational formulation in which the action functional would describe this constraint should be derived. Title: Non-constant-α force-free field of active region NOAA 8210 Authors: Régnier, S.; Amari, T.; Canfield, R. C. Bibcode: 2002ESASP.505...65R Altcode: 2002IAUCo.188...65R; 2002solm.conf...65R We investigate the 3D coronal magnetic configuration of the active region NOAA 8210 (AR8210). This active region observed on May 1, 1998 is the site of numerous flares. Using the non-constant-α force-free hypothesis, we determine the coronal magnetic field of AR8210. The EIT/SOHO observations and the reconstructed magnetic configuration suggest that the initiation of the eruptive events is related to the existence of a complex topology (e.g. separatrix surfaces). From some characteristic parameters before and after the eruptions, we note that the magnetic energy (the free magnetic budget) decreases by 28% (55%, respectively). Title: 3D Coronal magnetic field from vector magnetograms: non-constant-alpha force-free configuration of the active region NOAA 8151 Authors: Régnier, S.; Amari, T.; Kersalé, E. Bibcode: 2002A&A...392.1119R Altcode: The Active Region 8151 (AR 8151) observed in February 1998 is the site of an eruptive event associated with a filament and a S-shaped structure, and producing a slow Coronal Mass Ejection (CME). In order to determine how the CME occurs, we compute the 3D coronal magnetic field and we derive some relevant parameters such as the free magnetic energy and the relative magnetic helicity. The 3D magnetic configuration is reconstructed from photospheric magnetic magnetograms (IVM, Mees Solar Observatory) in the case of a non-constant-alpha force-free (nlff) field model. The reconstruction method is divided into three main steps: the analysis of vector magnetograms (transverse fields, vertical density of electric current, ambiguity of 180deg), the numerical scheme for the nlff magnetic field, the interpretation of the computed magnetic field with respect to the observations. For AR 8151, the nlff field matches the coronal observations from EIT/SOHO and from SXT/Yohkoh. In particular, three characteristic flux tubes are shown: a highly twisted flux tube, a long twisted flux tube and a quasi-potential flux tube. The maximum energy budget is estimated to 2.6*E31 erg and the relative magnetic helicity to 4.7*E34 G2 cm4. From the simple photospheric magnetic distribution and the evidence of highly twisted flux tubes, we argue that the flux rope model is the most likely to describe the initiation mechanism of the eruptive event associated with AR 8151. Title: From the SunA~éÂ’s atmosphere to the EarthA~éÂ’s atmosphere: an overview of scientific models available for space weather developments Authors: Lathuillère, C.; Menvielle, M.; Lilensten, J.; Amari, T.; Radicella, S. M. Bibcode: 2002AnGeo..20.1081L Altcode: Space weather aims at setting operational numerical tools in order to nowcast, forecast and quantify the solar activity events, the magnetosphere, ionosphere and thermosphere responses and the consequences on our technological societies. These tools can be divided in two parts. The first has a geophysical base (Sun, interplanetary medium, magnetosphere, atmosphere). The second concerns technological applications (telecommunications, spacecraft orbits, power plants ...). In this paper, we aim at giving an overview of the models that belong to the first class (geophysics) that might serve in the future as a basis for building global operational codes. For each model, we consider the physics underneath, the input and output parameters, and whether it is already operational, whether it may become operational in the near future, or if it is an academic research tool. Relevant references are given in order to serve as a starting point for further readings. Title: Helicity injection and redistribution during relaxation of solar/astrophysical plasmas Authors: Amari, T.; Luciani, J. Bibcode: 2002cosp...34E3036A Altcode: 2002cosp.meetE3036A We will discuss various MHD processes occurring in the context of evolution of solar coronal magnetic configurations, due to some boundary (photospheric) constraints. Several model problems will be presented and their implication in the injection of magnetic helicity as well triggering of confined and large scale disruptions will be dis- cussed. The nature of the relaxation state reached after the disruption will be discussed in the context of Taylor's theory of plasma relaxation. We will show some recent nu- merical results (relevant to astrophysical/solar disruptions), indicating that although this theory seems to be in agreement with experiments in Reversed Field pinch De- vices (but not in Tokamaks), it exhibits strong discrepancies with these astrophysical disruptions. Title: Non-constant-alpha force-free reconstruction of the coronal magnetic field. Example of the active region NOAA 8151 Authors: Regnier, S.; AMARI, T.; Kersale, E. Bibcode: 2001AGUFMSH11C0729R Altcode: We present the method and results of a non-constant-alpha force-free reconstruction of the 3D coronal magnetic field of an active region. AR 8151 observed in February 1998 exhibits a filament, a system of coronal loops, and a sigmoid. In order to determine the magnetic configuration of such structures, a non-constant-alpha force-free method (Amari et al 1997, Solar Physics 174, 129) is used to reconstruct the coronal magnetic field using the photospheric vector magnetograms as boundary condition. We compare the geometric and the topological changes in the magnetic configurations given by the three following methods: current-free field, constant-alpha force-free field and non-constant-alpha force-free field. The comparison between the observations (SXT/Yohkoh, EIT/SOHO) and the three models confirms that the non-constant-alpha force-free field matches the observations. In particular, the sigmoid can be reproduced by twisted flux tubes with a height of 40,000 or 60,000 km, and the system of coronal loops is well described by an untwisted flux tube (40,000 km). We also look for the magnetic dips which are combined with the filament material. The possible magnetic configurations for supporting the filament are either a quadrupolar magnetic field or a long twisted flux tube. From the chromospheric and magnetic observations, we conclude that the most likely configuration is the long twisted flux tube with a height of 30,000 km. In summary, with the non-constant-alpha force-free field we are able to reconstruct the coronal magnetic structures such as the system of coronal loops and the sigmoid, and to determine the structure of the magnetic field lines supporting the filament material. Title: Magnetohydrodynamic modeling of prominence formation within a helmet streamer Authors: Linker, J. A.; Lionello, R.; Mikić, Z.; Amari, T. Bibcode: 2001JGR...10625165L Altcode: We present a 2.5-D axisymmetric MHD model to self-consistently describe the formation of a stable prominence that supports cool, dense material in the lower corona. The upper chromosphere and transition region are included in the calculation. Reducing the magnetic flux along the neutral line of a sheared coronal arcade forms a magnetic field configuration with a flux rope topology. The prominence forms when dense chromospheric material is brought up and condenses in the corona. The prominence sits at the base of a helmet streamer structure. The dense material is supported against gravity in the dips of the magnetic field lines in the flux rope. Further reduction in magnetic flux leads to an eruption of the prominence, ejecting material into the solar wind. Title: Reconstruction of the Coronal Magnetic Field for Active Region NOAA 8151 Authors: Régnier, S.; Amari, T. Bibcode: 2001IAUS..203..441R Altcode: No abstract at ADS Title: Are the EIT waves really waves? Authors: Delannee, C.; Amari, T. Bibcode: 2000SPD....31.0603D Altcode: 2000BAAS...32R.838D One sample of EIT wave is presented and discussed. The bright front of the wave present two parts: one stationnary and one moving arch. The stationnary part of the wave is compared to the magnetic field lines extrapolated in spherical coordinates with the potential assumptions. The stationnary part is located where the footpoints of the separatrixes of the magnetic field are. Another case of a moving arch of an EIT wave is analyzed in conjonction with a numerical simulation of the ejection of a magnetic flux rope. The phenomelogy and the morphology of the both the moving arch and the electric currents created by the ejection of the flux rope are similar. We conclude that the EIT wave phenomenon is possibly related to the generation of electric currents while the magnetic field lines are openning during a coronal mass ejection. Title: Are the EIT waves really waves? Authors: Delannee, C.; Amari, T. Bibcode: 2000BAAS...32S.837D Altcode: No abstract at ADS Title: Photospheric Magnetic Flux Changes as a Trigger for Coronal Mass Ejections Authors: Linker, J. A.; Lionello, R.; Mikic, Z.; Amari, T. Bibcode: 2000SPD....31.0281L Altcode: 2000BAAS...32..825L Eruptive solar phenomena, such as coronal mass ejections, are believed to be initiated by the release of energy stored in the coronal magnetic field. Nonpotential magnetic field structures with significant amounts of free magnetic energy are known to exist in the corona. However, the mechanism(s) by which this energy is released are not well understood. Previously, we have shown that the emergence of new magnetic flux can lead to disruption of a helmet streamer, with liberation of a significant fraction of the stored magnetic energy. Specifically, eruption can be triggered when magnetic flux of opposite polarity emerges near the neutral line, canceling some of the ambient flux. Prior to eruption, a stable flux rope forms, which is a candidate magnetic structure for prominence support. In this paper, we will describe how other changes to the photospheric magnetic flux can lead to essentialy the same eruptive process, and we will discuss the relationship of these changes to flux reduction. Using full thermodynamic MHD simulations of global coronal structure, we will also show that chromospheric material can indeed be trapped in flux rope structures and lifted against the solar gravity. Research supported by NASA. Title: Helicity Redistribution during Relaxation of Astrophysical Plasmas Authors: Amari, T.; Luciani, J. F. Bibcode: 2000PhRvL..84.1196A Altcode: We present the first 3D numerical MHD simulations that show that Taylor's relaxation conjecture is not satisfied in some MHD evolution of magnetic configurations encountered in solar physics. We show that magnetic helicity can be slowly injected through the boundary into a magnetic configuration which then evolves into a MHD disruption, with the formation in finite time of a current sheet through which reconnection occurs, leading to a release of magnetic energy. While helicity is well conserved during the process, it is shown that the relaxed state is far from the constant- α linear force-free field that would be predicted by Taylor's conjecture. Title: A Twisted Flux Rope Model for Coronal Mass Ejections and Two-Ribbon Flares Authors: Amari, T.; Luciani, J. F.; Mikic, Z.; Linker, J. Bibcode: 2000ApJ...529L..49A Altcode: We present a new approach to the theory of large-scale solar eruptive phenomena such as coronal mass ejections and two-ribbon flares, in which twisted flux tubes play a crucial role. We show that it is possible to create a highly nonlinear three-dimensional force-free configuration consisting of a twisted magnetic flux rope representing the magnetic structure of a prominence (surrounded by an overlaying, almost potential, arcade) and exhibiting an S-shaped structure, as observed in soft X-ray sigmoid structures. We also show that this magnetic configuration cannot stay in equilibrium and that a considerable amount of magnetic energy is released during its disruption. Unlike most previous models, the amount of magnetic energy stored in the configuration prior to its disruption is so large that it may become comparable to the energy of the open field. Title: Non Linear Force-Free Reconstruction of a Flaring Active Region Authors: Bleybel, A.; Amari, T.; van Driel-Gesztelyi, L.; Leka, K. D. Bibcode: 1999ESASP.448..709B Altcode: 1999ESPM....9..709B; 1999mfsp.conf..709B No abstract at ADS Title: Magnetic and Dynamic Evolution of an Active Region Authors: Régnier, S.; Solomon, J.; Vial, J. C.; Amari, T.; Mickey, D. Bibcode: 1999ESASP.448..519R Altcode: 1999mfsp.conf..519R; 1999ESPM....9..519R No abstract at ADS Title: Multi-Instrument Study Of The Evolution Of An Active Region Authors: Regnier, S.; Amari, T.; Solomon, J.; Vial, J. C.; Mickey, D. Bibcode: 1999ESASP.446..571R Altcode: 1999soho....8..571R We follow, for about half a solar rotation, the dynamic evolution of an acive region (AR 8151) which exhibited a single heading sunspot and a more diffuse following magnetic flux and a filament eruption on 12 February 1998 at 13:51. For longitudinal magnetic observations, we use the MDI (SoHO) magnetograph and for vector magnetic fields the IVM (Mees Solar Observatory, Hawaii). The dynamic evolution is derived from time-sequence images in the Fe XII line (195 Angstrom) from EIT (SoHO). Density and abundance diagnostic of the filament are obtained from SoHO spectrometers (CDS, SUMER). Title: An iterative method for the reconstructionbreak of the solar coronal magnetic field. I. Method for regular solutions Authors: Amari, T.; Boulmezaoud, T. Z.; Mikic, Z. Bibcode: 1999A&A...350.1051A Altcode: We present a method for reconstructing the coronal magnetic field, assumed to be in a non-linear force-free state, from its values given in the photosphere by vector magnetograph measurements. In this paper, that is the first of a series, we propose a method that solves the boundary value problem set in the functional space of regular solutions (i.e., that do not contain current sheets). This is an iterative method introduced by Grad and Rubin. It is associated with a well-posed boundary-value problem. We present some results obtained with this method on two exact solutions of the magnetostatic equations, used as theoretical magnetograms. Unlike some other extrapolations methods, that are associated with ill-posed boundary value problems, our method allows extrapolation to arbitrarily large heights, with no blowing up due to the presence in these methods of an intrinsic instability that makes errors growing up exponentially. Title: On the Role of Magnetic Flux Ropes for Helicity Injection and Ejection in the Solar Corona Authors: Amari, T.; Luciani, J. F.; Mikic, Z. Bibcode: 1999ASPC..184...70A Altcode: We present some work on the role of magnetic flux ropes for the structure and dynamics of the corona in term of its magnetic helicity content and redistribution for solar eruptive and non eruptive events. We show that is possible to construct 3D MHD solutions that represents the first type of models for prominence magnetic support as highly twisted non linear force-free type configuration. We also present some results for the disruption of twisted magnetic flux rope in non eruptive and eruptive confined events. Title: On the removal of the sign ambiguitybreak in the photospheric transverse magnetic field Authors: Boulmezaoud, T. Z.; Amari, T. Bibcode: 1999A&A...347.1005B Altcode: We present a method for removing the ambiguity in the transverse component of the photospheric magnetic field measured by vector magnetographs. The method is based upon the use of the divergence-free condition satisfied by the magnetic field in the sense of least squares. The method requires the measurement of the longitudinal component of the magnetic field at two depth levels in the photosphere. The method is is shown to be efficient when compared to other existing methods on some particular analytical force-free magnetic fields. Title: Three-dimensional Solutions of Magnetohydrodynamic Equationsfor Prominence Magnetic Support: Twisted Magnetic Flux Rope Authors: Amari, T.; Luciani, J. F.; Mikic, Z.; Linker, J. Bibcode: 1999ApJ...518L..57A Altcode: The search for a background magnetic configuration favorable for prominence support has been given a great deal of attention for several decades. The most recent theoretical studies seem to agree that a promising candidate for the support of the dense and cooler prominence material, which fulfills several of the theoretical and observational requirements such as twist, shear along the neutral line, and dips, is a magnetic flux rope. The most convincing models take an infinitely long periodic configuration that consists of a linear constant-α force-free magnetic field. These models, however, assume values of α that are close to its maximum possible value. In this Letter, we report our recent results, which show that it is indeed possible to produce a configuration that consists of a twisted magnetic flux tube embedded in an overlaying, almost potential, arcade such that high electric currents (and therefore values of α) are confined to the inner twisted magnetic flux rope. We present two MHD processes--corresponding to two different types of boundary conditions--that produce such a configuration. Our results show that the process associated variations of Bz at the photospheric level by applying an electric field involving diffusion is much more efficient for creating a structure with more twist and dips. Title: Confined Disruption of a Three-dimensional Twisted Magnetic Flux Tube Authors: Amari, T.; Luciani, J. F. Bibcode: 1999ApJ...515L..81A Altcode: In this Letter, we study the evolution of a magnetic flux tube confined by an overlaying arcade, considering the gradual build up of the twist in the flux tube. During a first stage, the magnetic field evolves quasi-statically through a sequence of force-free equilibria, building up self-helicity (twist) in the flux rope. When a sufficient amount of twist is injected in the system, it cannot reach a neighboring equilibrium and experiences a major disruption in which the magnetic field of the flux tube reconnects with the overlaying arcade. After the relaxation is completed, the configuration remains globally closed and consists of two almost untwisted flux tubes and a closed overlaying arcade. The model might represent a basis for a unified theory of noneruptive and eruptive flares, in which twisted magnetic flux tubes play a crucial role. Title: Magnetohydrodynamic models of solar coronal magnetic fields. Authors: Amari, T.; Luciani, J. F.; Mikic, Z. Bibcode: 1999PPCF...41..779A Altcode: The authors present some results concerning the possibility of determining the structure of solar active regions using measurements of the vector magnetic field on the Sun's surface as boundary conditions for the new numerical extrapolation codes. From these computations the main features of these configurations, shear and twist (which are particular forms of magnetic helicity), are then used as ingredients to define model problems and solved for the magnetohydrodynamic (MHD) analysis of solar eruptive phenomena, in which ejection (or redistribution) of helicity occurs. Title: A regularization method for the extrapolationbreak of the photospheric solar magnetic field. I. Linear force-free field Authors: Amari, T.; Boulmezaoud, T. Z.; Maday, Y. Bibcode: 1998A&A...339..252A Altcode: We present a method for reconstructing the magnetic field B above the photosphere \{z=0\} as the solution of the boundary value problem (BVP) for a bounded regular force-free magnetic field in Omega =\{z>0\} from its boundary values supposed to be given on \{z=0\}. We propose a way for regularizing the class of standard extrapolation methods which turns out to diverge quickly with height, because of the ill posedness of the BVP that prevents extrapolation at a reasonable height. Our method, which is a Projection Method, allows us to improve considerably the possible height of extrapolation that can be reached by non regularized or even approximate filtering method. In this paper, because of its linear nature the method is applied to the case of linear force-free field. Title: Reconstructing the Solar Coronal Magnetic Field as a Force-Free Magnetic Field Authors: Amari, T.; Aly, J. J.; Luciani, J. F.; Boulmezaoud, T. Z.; Mikic, Z. Bibcode: 1997SoPh..174..129A Altcode: We present some preliminary results on different mathematical problems encountered in attempts to reconstruct the coronal magnetic field, assumed to be in a force-free state, from its values in the photosphere. We discuss the formulations associated with these problems, and some new numerical methods that can be used to get their approximate solutions. Both the linear constant-α and the nonlinear cases are considered. We also discuss the possible use of dynamical 3D MHD codes to construct approximate solutions of the equilibrium force-free equations, which are needed for testing numerical extrapolation schemes. Title: Current sheets in two-dimensional potential magnetic fields. III. Formation in complex topology configurations and application to coronal heating. Authors: Aly, J. J.; Amari, T. Bibcode: 1997A&A...319..699A Altcode: We study the spontaneous formation of a current sheet (CS) in an x-invariant y-symmetric magnetic field B(y,z,t) occupying the half-space {z>0}, and embedded in a pressureless perfectly conducting plasma. At the initial time t=0, B(y,z,0) is potential and quadrupolar, and therefore its lines in a poloidal plane have a complex topology: there is either one separatrix, which contains a neutral X-point or is tangent to the y-axis (X- and U-topology, respectively), or two separatrices extending to infinity (I-topology). For t>=0, the field is made to evolve quasi-statically by imposing its footpoints on the boundary {z=0} to move parallel to the y-axis at the slow velocity v(y,t). It thus passes through a sequence of configurations which are either potential equilibria or quasi-potential singular equilibria, the latter containing a CS, assumed a priori to be vertical. We compute analytically B(y,z,t) and its free-energy contents δ W (t) as functionals of B_z_(y,0,t) (this boundary value depending on B_z_(y,0,0) and v(y,t)), and also, when there is a CS, of the unknown heights z_1_(t) and z_2_(t) of its bottom and top, respectively. We derive equations satisfied by the latter quantities, and use them to show that: (i) When the initial field is of the U- or I-type, a CS - and a vertical one indeed - is actually present at time t if and only if the potential field B^p^(y,z,t) associated to B_z_(y,0,t) has a X-topology. (ii) When the initial field is of the X-type, a CS exists in general at each time t>0, but it is vertical if and only if a quite specific condition is satisfied - which may not be the case for arbitrarily chosen data and puts a limit on the generality of our model. Finally, we derive for z_1_(t), z_2_(t), B(y,z,t) and δW(t) useful approximate explicit expressions, which are valid just after the CS has started forming at some time t_c_>=0. As an application, we consider a plasma heating process in which a field evolving through a sequence of singular equilibria as described above, relaxes at each time t_k_ = k τ_D_ (k=1,2, ...,N) to a new potential equilibrium, the vertical CS being destroyed by some reconnection process. We present an estimate of the resulting heating rate, which is found to depend on the ratio τ_D_/τ_ev_ (assumed to be <<1) of a given phenomenological dissipation time τ_D_ to the ideal evolution time τ_ev_ of the system. The relevance of this process for heating a stellar corona is briefly discussed. Title: Two efficient methods for reconstructing the coronal magnetic field as a linear force-free field. Authors: Boulmezaoud, T. Z.; Amari, T.; Maday, Y. Bibcode: 1997joso.proc...53B Altcode: No abstract at ADS Title: Very Fast Opening of a Three-dimensional Twisted Magnetic Flux Tube Authors: Amari, T.; Luciani, J. F.; Aly, J. J.; Tagger, M. Bibcode: 1996ApJ...466L..39A Altcode: This Letter is devoted to the still open problem of the evolution of a three-dimensional coronal flux tube embedded in a low-beta ideal plasma and having its footpoints twisted by slow photospheric motions. Such a process has been simulated with a recently developed magnetohydrodynamic code. In the particular calculation reported here, the system occupies a large cubic box. The field is initially potential, being generated by an underlying horizontal dipole, and it is twisted by two vortices located on the lower face {z = 0} of the box, on both sides of the neutral line. In a first phase, the field roughly evolves quasi-statically through a sequence of force-free configurations. Thus, it enters a dynamical phase during which it suffers a very fast expansion, closely approaching after some finite time a semi-open configuration. The energy increases monotonically during all the evolution, and it tends to a limit, which is equal to about 80% of the energy of the totally open field associated with Bz. Title: Plasmoid formation in a single sheared arcade and application to coronal mass ejections. Authors: Amari, T.; Luciani, J. F.; Aly, J. J.; Tagger, M. Bibcode: 1996A&A...306..913A Altcode: We address the question whether a plasmoid can be produced and ejected by an isolated x-invariant arcade located in a half-space, when its footpoints are sheared parallel to the x-axis, but no converging y-motions are applied. We use a recently developed MHD numerical code based upon a new efficient semi-implicit method, and well adapted for treating long time evolution problems in which small spatial scales develop spontaneously. Starting from a configuration created by a dipole located under the photosphere, we follow numerically the evolution of the sheared arcade. In the ideal case, and in contrast to previous attempts effected in such a geometry, our simulations show that, after a long phase of slow evolution, the poloidal magnetic configuration strongly inflates, while the electric current concentrates into a thin layer extending vertically in the central region, as predicted by analytical studies. Adding a small amount of resistivity then leads to the formation of a rising plasmoid, with stronger flows appearing along the separatrices. Title: Champs magnetiques : le cosmos EN filigrane. Authors: Bel, N.; Amari, T. Bibcode: 1995C&E...307...58B Altcode: No abstract at ADS Title: The solar corona's magnetism. Authors: Amari, T.; Démoulin, P. Bibcode: 1993Rech...24..258A Altcode: No abstract at ADS Title: Solar Flare High-Energy Electron Spectra Authors: Heristchi, D.; Amari, T. Bibcode: 1992SoPh..142..209H Altcode: It is shown that the solar flare electron spectra in a large energy range fit well with a power law in energy. This is used as a basis to discuss the possible division of solar flares into various groups, and also to compare the spectra of electrons in interplanetary space and at the flare site. Title: Extended massive current sheet in a two-dimensional constant-alpha force-free field - A model for quiescent prominences Authors: Amari, T.; Aly, J. J. Bibcode: 1992A&A...265..791A Altcode: We consider a simple 2D analytical model of a solar prominence represented by a massive current sheet supported in a uniform gravitational field by an external constant-alpha force-free magnetic field. We show that it is possible to construct so-called inverse configurations above either bipolar or quadrupolar photospheric regions by a suitable adjustment of the free parameters of the model, namely the boundary flux distribution, the current in the sheet, and the value of alpha. It turns out that such configurations may exist only for large value of alpha, and thus in highly sheared magnetic fields, a result which should prove important for our understanding of the formation of the prominences of the Kuperus-Raadu type. Title: Prominence Sheets Supported by Constant-Current Force-free Fields. II. Imposition of Normal Photospheric Field Component and Prominence Surface Current Authors: Ridgway, C.; Amari, T.; Priest, E. R. Bibcode: 1992ApJ...385..718R Altcode: Attention is given to a method of constructing longitudinally invariant magnetic field configurations in which a symmetric finite vertical current sheet is in magnetohydrostatic equilibrium between the combined forces exerted by a background constant-current force-free field and a uniform gravitational field. Both the normal magnetic field component along the photosphere and the current density along the prominence sheet are imposed as functions of position. The method is used to generate both N- and I-type configurations by selecting a convenient form for the imposed functions. Consideration is given to the evolution of these configurations as the strength of the current (and hence the mass) is increased while all other parameters are held fixed. It is shown that in general the sheet loses equilibrium near its upper extremity as I is increased beyond a certain value. Title: Prominence Sheets Supported by Constant-Current Force-free Fields. I. Imposition of Normal Magnetic Field Components at the Current Sheet and the Photosphere Authors: Ridgway, C.; Amari, T.; Priest, E. R. Bibcode: 1991ApJ...378..773R Altcode: We present an analytical model for the support of a prominence (represented by a sheet of mass and current) in a constant-current force-free field. The model allows us to produce both normal-type and inverse-type configurations which are in equilibrium everywhere along the sheet and for which the field is locally bounded. Title: Formation of current sheets in force-free magnetic fields. Authors: Vekstein, G.; Priest, E. R.; Amari, T. Bibcode: 1991A&A...243..492V Altcode: It is shown that the evolution of coronal magnetic fields in response to slow photospheric footpoint motions in general produces states with current sheets rather than smooth force-free equilibria. When a separatrix surface is present, shearing motions of a two-dimensional double arcade in general produce a current sheet all along the separatrix, whether the motions are infinitesimal or of finite amplitude; local singularities in the horizontal field component occur at the footpoints of the separatrix where it becomes tangential to the solar surface although the flux function is regular there. The particular case of equal lobes and an antisymmetric shear gives a smooth field without current sheets. When there is an X-type neutral line (or separator) present, converging or divering motions create a current sheet with Y-points at its ends; shearing motions create a current sheet all along the separattrices, which coalesce at two cusp-points to give a single current sheet near the original separator. In general these current sheets could heat the corona as they dissipate, but when new flux emerges into a highly sheared field they could also trigger a solar flare. Title: A Twisted Flux-Tube Model for Solar Prominences. III. Magnetic Support Authors: Ridgway, C.; Priest, E. R.; Amari, T. Bibcode: 1991ApJ...367..321R Altcode: The model for the support of a solar prominence in a twisted flux tube by Priest et al. (1989) is here extended to consider large deviations of the tube from cylindrical symmetry. The prominence is modeled as a finite current sheet with mass which is locally free from singularities in the magnetic field. Analytical solutions are found to the nonlinear force-free equations for the structure around the prominence for two functional forms of the field component parallel to the prominence axis. An associated mixed boundary-value problem is also solved in which the prominence is connected at its base to the photosphere, and the normal magnetic field components along the prominence and the photosphere are imposed. Title: Weak solutions of magnetostatics: an aspect of current sheet theory. Authors: Amari, T. Bibcode: 1991gamp.conf..173A Altcode: This paper is only concerned with the processes of formation of a current sheet (CS) during the quasi-static evolution towards weak equilibrium of classical magnetostatic equilibria embedded in a perfectly conducting plasma. The author is mainly interested in the spontaneous process of classical magnetostatic equilibria embedded in a perfectly conducting plasma. Contents: 1. Introduction. 2. 2D quasi potential singular equilibria (QPSE): spontaneous formation of a CS, asymptotic formation of QPSE. 3. 2D QFFSE: evolution towards a 2D force-free field, T- and X-like topology. 4. 3D force-free solutions. Title: Weak Solutions of Magnetostatics Authors: Amari, T. Bibcode: 1991assm.conf..173A Altcode: No abstract at ADS Title: The creation of the magnetic environment for prominence formation in a coronal arcade Authors: Amari, T.; Démoulin, P.; Browning, P.; Hood, A.; Priest, E. Bibcode: 1991A&A...241..604A Altcode: The possibility of prominence formation in sheared coronal arcades is investigated. The creation of a dip at the summit of field lines is a likely requirement before a prominence can form; then dense plasma can be supported against gravity by the Lorentz force. It is proved that, in fact, no shear profile can create a dip in a two-dimensional force-free arcade if the photospheric field is bipolar. However, numerical investigations show that shearing an arcade can induce very flat field lines. It is investigated, in order of magnitude, how this flattening of the field can increase the free fall time of a dense plasma. Also, the interaction between shear and twist is analyzed; the critical twist needed to have a dip is a decreasing function of shear. Title: Extended massive current sheet in a two-dimensional constant-alpha force-free field - A model for quiescent prominences. I - Theory Authors: Amari, T.; Aly, J. J. Bibcode: 1990A&A...231..213A Altcode: We present an analytical model of extended massive current sheet Σ in equilibrium in a 2 D x-invariant constant-α force-free field, and a vertical gravitational field. We show in particular that there is a maximal mass that can be supported by the magnetic field and that the topology of the field lines is always of the "Kippenhahn-Schlüter" type. This model can be used to describe the magnetic support of solar quiescent prominences. This work is an extension of Amari and Aly (1989) in which the simpler approximation of a prominence by a filament was considered. Title: Current Sheets in Two-Dimensional Potential Magnetic Fields - Part Two - Asymptotic Limits of Indefinitely Sheared Force-Free Fields Authors: Amari, T.; Aly, J. J. Bibcode: 1990A&A...227..628A Altcode: We compute analytically the singular state B∞ which is approached asymptotically by an arcade-like x-invariant force- free field in {z > 0} when indefinitely sheared. B∞ is a field which is potential everywhere in {z > 0} but on a current sheet in equilibrium extending up to infinity; it is determined from the values of Bz on the boundary plane {z = 0} and of a number A1 characterizing the magnetic surface from which the sheet is starting. Title: Structure of two-dimensional magnetostatic equilibria in the presence of gravity Authors: Amari, T.; Aly, J. J. Bibcode: 1990GMS....58..327A Altcode: Results are presented from an analytical study of three different 2D, x-invariant equilibrium models for a plasma that occupies the half-space and is subject to both a magnetic field and a constant vertical gravitational field. The models are differentiated by their assumptions concerning the spatial distribution of matter; while models 1 and 2, respectively, take the plasma to be concentrated in a vertical sheet and in the filament, model 3's plasma occupies all of half-space and possesses a uniform temperature. In all three cases, attention is given to the existence and uniqueness of solutions. Nonequilibrium phenomena are noted. Title: Support of a Prominence by a Constant-Current Force-Free Field Authors: Ridgway, C.; Amari, T.; Priest, E. R. Bibcode: 1990PDHO....7..166R Altcode: 1990dysu.conf..166R; 1990ESPM....6..166R No abstract at ADS Title: Two Dimensional Quasi-static Boundary Value Problems of Solar Magnetostatics. Authors: Amari, T. Bibcode: 1990ppsa.conf..193A Altcode: No abstract at ADS Title: Quasi-potential-singular-equilibria and evolution of the coronal magnetic field due to photospheric boundary motions Authors: Amari, T.; Aly, J. J. Bibcode: 1990GMS....58..245A Altcode: Novel general properties are presented of configurations in a class of 2D, x-invariant magnetostatic equilibria, showing that the general condition of equilibrium at the extremities of the current sheet implies a heretofore unsuspected constraint on the magnetic field. Attention is given to situations in which singular states are obtained asymptotically by means of an arcadelike, x-invariant force-free field that is indefinitely sheared. A method is given for the analytical computation of such asymptotic states, as the solutions of boundary-value problems. Title: Current sheets in two-dimensional potential magnetic fields. I - General properties Authors: Aly, J. J.; Amari, T. Bibcode: 1989A&A...221..287A Altcode: The equilibrium of a set of current sheets embedded in a potential magnetic field is studied as well as some general properties of quasi-potential singular equilibrium (QPSE). Representations were established for an x-invariant magnetic field which is potential everywhere but on a set of singular surfaces. It is shown that, in a QPSE, the current sheets are analytical curves. An analytical curve may always be interpreted as a current sheet embedded in a QPSE. Title: Non-equilibrium of a cylindrical magnetic arcade Authors: Steele, C. D. C.; Hood, A. W.; Priest, E. R.; Amari, T. Bibcode: 1989SoPh..123..127S Altcode: A cylindrically-symmetric magnetic arcade with its axis on the photosphere is perturbed by means of an alteration in the pressure along the base. The perturbation is examined with a view to finding equilibrium configurations close to the original equilibrium. It is found that equilibria can only be found when the integral of the excess pressure along the base is zero. In other cases no equilibria can be found and the arcade is likely either to collapse or, in the case of a coronal mass ejection, to erupt. For an initial arcade whose field increases linearly with radial distance from the axis, the neighbouring equilibria have been found. Title: Two-dimensional isothermal magnetostatic equilibria in a gravitational field. I - Unsheared equilibria Authors: Amari, T.; Aly, J. J. Bibcode: 1989A&A...208..361A Altcode: Some new results concerning the structure and the quasi-static evolution of two-dimensional x-invariant magnetostatic equilibria in the half-space (z greater than 0) are presented. The plasma pressure p and the gravity are taken into account, but the field is assumed to be shearless (Bx = 0). The values of Bz and of p are given on the boundary (z =0). The problem of the existence of solutions is discussed, and some of their general properties are determined. Title: Interaction between a line current and a two-dimensional constant-alpha force-free field - an analytical model for quiescent prominences Authors: Amari, T.; Aly, J. J. Bibcode: 1989A&A...208..261A Altcode: A simple analytical model describing the equilibrium of a massive line current submitted to the action of a vertical gravitational field and of a two-dimensional constant-alpha force-free magnetic field is described. This model is then applied to the problem of the magnetic support of quiescent prominences. It is shown in particular that the introduction of a background force-free field instead of a potential one may be a clue for solving difficulties which appear when some previous models are confronted with the observations. Title: An analytical study of the structure of two-dimensional magnetostatic equilibria in the presence of gravity. Authors: Amari, T.; Aly, J. J. Bibcode: 1989sasf.confP.271A Altcode: 1989IAUCo.104P.271A; 1988sasf.conf..271A No abstract at ADS Title: Two-dimensional non-symmetric models of quiescent prominences in potential magnetic fields Authors: Aly, J. J.; Amari, T. Bibcode: 1988A&A...207..154A Altcode: The authors present a general method which allows to construct in the half-space {z > 0} non-y-symmetric x invariant models describing the equilibrium of a massive current sheet submitted to the action of a vertical gravitational field and of a potential magnetic field. They also derive general relations which determine the current and the mass of the sheet and the total energy of the configuration from the only value of the magnetic field on the plane {z = 0}. Title: Some integral properties of two-dimensional force-free fields supporting massive current sheets Authors: Amari, T.; Aly, J. J. Bibcode: 1988A&A...193..291A Altcode: A set of useful integral relations satisfied by any x-invariant nonlinear force-free field occupying the half-space z greater than zero and supporting a massive current sheet against the action of a vertical gravitational field is derived. These relations are used to prove a nonexistence theorem for the solutions of a boundary value problem which determines the equilibrium of a massive sheet when the amount of mass per unit of flux of the background nonlinear force-free field is given. Title: Some New Results in the Theory of Two-Dimensional Magnetostatic Equilibria Authors: Aly, J. J.; Amari, T. Bibcode: 1985tphr.conf..319A Altcode: No abstract at ADS Title: Some new results in the theory of two-dimensional magnetostatic equilibria. Authors: Aly, J. J.; Amari, T. Bibcode: 1985MPARp.212..319A Altcode: X-invariant magnetostatic equilibria in the half-space {z > 0} have been very often considered in theoretical models for prominences or two-ribbon flares. In this paper, the authors report some new results on the structure and quasi-static evolution of such equilibria. These results concern the two following limiting situations: (1) the field is force-free and the value of Bz as well as the positions of the feet of the lines are given on {z = 0}; (2) plasma pressure p and gravity are taken into account, but the field is shearless (Bx = 0); the values of Bz and of p are given on {z = 0}.