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Vourlidas, A.

Publications and source records attributed to Vourlidas, A..

At least 19 records

Elliptic-Cylindrical Analytical Flux Rope Model for Magnetic Clouds

In this paper, we present the elliptic-cylindrical analytical flux rope model, which constitutes the first level of complexity above that of a circular-cylindrical geometry. The framework of this series of models was established by Nieves-Chinchilla et al. with the circular-cylindrical analytical flux rope model. The model describes the magnetic flux rope topology with distorted cross section as a possible consequence of the flux rope interaction with the solar wind. In this model, for the first time, a flux rope is completely described by a nonorthogonal geometry. The Maxwell equations can be consistently solved using tensorial analysis, and relevant physical quantities can be derived, such as magnetic fluxes, number of turns, or Lorentz force distribution. The model is generalized in termsof the radial dependence of the poloidal and axial current density components. The circular-cylindrical reconstruction technique has been adapted to the new geometry for a specific case of the model and tested againstan interplanetary coronal mass ejection observed by the Wind spacecraft on 2005 June 12. In this specific case,from the comparative analysis between the circular-cylindrical and elliptic-cylindrical models, the inclusion ofthe cross-section distortion in the 3D reconstruction results in significant changes in the derived axis orientation,size, central magnetic field, magnetic fluxes, and force-freeness. The case studied in this paper exemplifies the useof the model and reconstruction technique developed. Furthermore, the novel mathematical formulation to modelflux ropes in heliophysics paves the way to the inclusion of more complex magnetic field configurations.

CMEs↗

Is There a CME Rate Floor? CME and Magnetic Flux Values for the Last Four Solar Cycle Minima

The recent prolonged activity minimum has led to the question of whether there is a base level of the solar magnetic field evolution that yields a ''floor'' in activity levels and also in the solar wind magnetic field strength. Recently, a flux transport model coupled with magneto-frictional simulations has been used to simulate the continuous magnetic field evolution in the global solar corona for over 15 years, from 1996 to 2012. Flux rope eruptions in the simulations are estimated (Yeates), and the results are in remarkable agreement with the shape of the SOlar Heliospheric Observatory/Large Angle and Spectrometric Coronagraph Experiment coronal mass ejection (CME) rate distribution. The eruption rates at the two recent minima approximate the observed-corrected CME rates, supporting the idea of a base level of solar magnetic activity. In this paper, we address this issue by comparing annual averages of the CME occurrence rates during the last four solar cycle minima with several tracers of the global solar magnetic field. We conclude that CME activity never ceases during a cycle, but maintains a base level of 1 CME every 1.5 to approx. 3 days during minima. We discuss the sources of these CMEs.

Webb, D. F.↗

CHROMOSPHERE TO 1 au SIMULATION OF THE 2011 MARCH 7th EVENT: A COMPREHENSIVE STUDY OF CORONAL MASS EJECTION PROPAGATION

We perform and analyze the results of a global magnetohydrodynamic simulation of the fast coronal mass ejection (CME) that occurred on 2011 March 7. The simulation is made using the newly developed Alfvén Wave Solar Model (AWSoM), which describes the background solar wind starting from the upper chromosphere and extends to 24 R {sub ⊙}. Coupling AWSoM to an inner heliosphere model with the Space Weather Modeling Framework extends the total domain beyond the orbit of Earth. Physical processes included in the model are multi-species thermodynamics, electron heat conduction (both collisional and collisionless formulations), optically thin radiative cooling, and Alfvén-wave turbulence that accelerates and heats the solar wind. The Alfvén-wave description is physically self-consistent, including non-Wentzel–Kramers–Brillouin reflection and physics-based apportioning of turbulent dissipative heating to both electrons and protons. Within this model, we initiate the CME by using the Gibson-Low analytical flux rope model and follow its evolution for days, in which time it propagates beyond STEREO A . A detailed comparison study is performed using remote as well as in situ observations. Although the flux rope structure is not compared directly due to lack of relevant ejecta observation at 1 au in this event, our results show that the new model can reproduce many of the observed features near the Sun (e.g., CME-driven extreme ultraviolet [EUV] waves, deflection of the flux rope from the coronal hole, “double-front” in the white light images) and in the heliosphere (e.g., shock propagation direction, shock properties at STEREO A ).

79 ASTRONOMY AND ASTROPHYSICS↗

DERIVING THE PROPERTIES OF CORONAL PRESSURE FRONTS IN 3D: APPLICATION TO THE 2012 MAY 17 GROUND LEVEL ENHANCEMENT

We study the link between an expanding coronal shock and the energetic particles measured near Earth during the ground level enhancement of 2012 May 17. We developed a new technique based on multipoint imaging to triangulate the three-dimensional (3D) expansion of the shock forming in the corona. It uses images from three vantage points by mapping the outermost extent of the coronal region perturbed by the pressure front. We derive for the first time the 3D velocity vector and the distribution of Mach numbers, M {sub FM}, of the entire front as a function of time. Our approach uses magnetic field reconstructions of the coronal field, full magnetohydrodynamic simulations and imaging inversion techniques. We find that the highest M {sub FM} values appear near the coronal neutral line within a few minutes of the coronal mass ejection onset; this neutral line is usually associated with the source of the heliospheric current and plasma sheet. We illustrate the variability of the shock speed, shock geometry, and Mach number along different modeled magnetic field lines. Despite the level of uncertainty in deriving the shock Mach numbers, all employed reconstruction techniques show that the release time of GeV particles occurs when the coronal shock becomes super-critical ( M {sub FM} > 3). Combining in situ measurements with heliospheric imagery, we also demonstrate that magnetic connectivity between the accelerator (the coronal shock of 2012 May 17) and the near-Earth environment is established via a magnetic cloud that erupted from the same active region roughly five days earlier.

79 ASTRONOMY AND ASTROPHYSICS↗

A CIRCULAR-CYLINDRICAL FLUX-ROPE ANALYTICAL MODEL FOR MAGNETIC CLOUDS

We present an analytical model to describe magnetic flux-rope topologies. When these structures are observed embedded in Interplanetary Coronal Mass Ejections (ICMEs) with a depressed proton temperature, they are called Magnetic Clouds (MCs). Our model extends the circular-cylindrical concept of Hidalgo et al. by introducing a general form for the radial dependence of the current density. This generalization provides information on the force distribution inside the flux rope in addition to the usual parameters of MC geometrical information and orientation. The generalized model provides flexibility for implementation in 3D MHD simulations. Here, we evaluate its performance in the reconstruction of MCs in in situ observations. Four Earth-directed ICME events, observed by the Wind spacecraft, are used to validate the technique. The events are selected from the ICME Wind list with the magnetic obstacle boundaries chosen consistently with the magnetic field and plasma in situ observations and with a new parameter (EPP, the Electron Pitch angle distribution Parameter) which quantifies the bidirectionally of the plasma electrons. The goodness of the fit is evaluated with a single correlation parameter to enable comparative analysis of the events. In general, at first glance, the model fits the selected events very well. However, a detailed analysis of events with signatures of significant compression indicates the need to explore geometries other than the circular-cylindrical. An extension of our current modeling framework to account for such non-circular CMEs will be presented in a forthcoming publication.

79 ASTRONOMY AND ASTROPHYSICS↗

MULTI-VIEWPOINT OBSERVATIONS OF A WIDELY DISTRIBUTED SOLAR ENERGETIC PARTICLE EVENT: THE ROLE OF EUV WAVES AND WHITE-LIGHT SHOCK SIGNATURES

On 2012 March 7, two large eruptive events occurred in the same active region within 1 hr from each other. Each consisted of an X-class flare, a coronal mass ejection (CME), an extreme-ultraviolet (EUV) wave, and a shock wave. The eruptions gave rise to a major solar energetic particle (SEP) event observed at widely separated (∼120°) points in the heliosphere. From multi-viewpoint energetic proton recordings we determine the proton release times at STEREO B and A (STB, STA) and the first Lagrange point (L1) of the Sun–Earth system. Using EUV and white-light data, we determine the evolution of the EUV waves in the low corona and reconstruct the global structure and kinematics of the first CME’s shock, respectively. We compare the energetic proton release time at each spacecraft with the EUV waves’ arrival times at the magnetically connected regions and the timing and location of the CME shock. We find that the first flare/CME is responsible for the SEP event at all three locations. The proton release at STB is consistent with arrival of the EUV wave and CME shock at the STB footpoint. The proton release time at L1 was significantly delayed compared to STB. Three-dimensional modeling of the CME shock shows that the particle release at L1 is consistent with the timing and location of the shock’s western flank. This indicates that at L1 the proton release did not occur in low corona but farther away from the Sun. However, the extent of the CME shock fails to explain the SEP event observed at STA. A transport process or a significantly distorted interplanetary magnetic field may be responsible.

79 ASTRONOMY AND ASTROPHYSICS↗

LONGITUDINAL PROPERTIES OF A WIDESPREAD SOLAR ENERGETIC PARTICLE EVENT ON 2014 FEBRUARY 25: EVOLUTION OF THE ASSOCIATED CME SHOCK

We investigate the solar phenomena associated with the origin of the solar energetic particle (SEP) event observed on 2014 February 25 by a number of spacecraft distributed in the inner heliosphere over a broad range of heliolongitudes. These include spacecraft located near Earth; the twin Solar TErrestrial RElations Observatory spacecraft, STEREO-A and STEREO-B, located at ∼1 au from the Sun 153° west and 160° east of Earth, respectively; the MErcury Surface Space ENvironment GEochemistry and Ranging mission (at 0.40 au and 31° west of Earth); and the Juno spacecraft (at 2.11 au and 48° east of Earth). Although the footpoints of the field lines nominally connecting the Sun with STEREO-A, STEREO-B and near-Earth spacecraft were quite distant from each other, an intense high-energy SEP event with Fe-rich prompt components was observed at these three locations. The extent of the extreme-ultraviolet wave associated with the solar eruption generating the SEP event was very limited in longitude. However, the white-light shock accompanying the associated coronal mass ejection extended over a broad range of longitudes. As the shock propagated into interplanetary space it extended over at least ∼190° in longitude. The release of the SEPs observed at different longitudes occurred when the portion of the shock magnetically connected to each spacecraft was already at relatively high altitudes (≳2 R{sub ⊙} above the solar surface). The expansion of the shock in the extended corona, as opposite to near the solar surface, determined the SEP injection and SEP intensity-time profiles at different longitudes.

79 ASTRONOMY AND ASTROPHYSICS↗

THE MAJOR GEOEFFECTIVE SOLAR ERUPTIONS OF 2012 MARCH 7: COMPREHENSIVE SUN-TO-EARTH ANALYSIS

During the interval 2012 March 7–11 the geospace experienced a barrage of intense space weather phenomena including the second largest geomagnetic storm of solar cycle 24 so far. Significant ultra-low-frequency wave enhancements and relativistic-electron dropouts in the radiation belts, as well as strong energetic-electron injection events in the magnetosphere were observed. These phenomena were ultimately associated with two ultra-fast (>2000 km s{sup −1}) coronal mass ejections (CMEs), linked to two X-class flares launched on early 2012 March 7. Given that both powerful events originated from solar active region NOAA 11429 and their onsets were separated by less than an hour, the analysis of the two events and the determination of solar causes and geospace effects are rather challenging. Using satellite data from a flotilla of solar, heliospheric and magnetospheric missions a synergistic Sun-to-Earth study of diverse observational solar, interplanetary and magnetospheric data sets was performed. It was found that only the second CME was Earth-directed. Using a novel method, we estimated its near-Sun magnetic field at 13 R{sub ⊙} to be in the range [0.01, 0.16] G. Steep radial fall-offs of the near-Sun CME magnetic field are required to match the magnetic fields of the corresponding interplanetary CME (ICME) at 1 AU. Perturbed upstream solar-wind conditions, as resulting from the shock associated with the Earth-directed CME, offer a decent description of its kinematics. The magnetospheric compression caused by the arrival at 1 AU of the shock associated with the ICME was a key factor for radiation-belt dynamics.

79 ASTRONOMY AND ASTROPHYSICS↗

Tracking the evolution of a coherent magnetic flux rope continuously from the inner to the outer corona

The magnetic flux rope (MFR) is believed to be the underlying magnetic structure of coronal mass ejections (CMEs). However, it remains unclear how an MFR evolves into and forms the multi-component structure of a CME. In this paper, we perform a comprehensive study of an extreme-ultraviolet (EUV) MFR eruption on 2013 May 22 by tracking its morphological evolution, studying its kinematics, and quantifying its thermal property. As EUV brightenings begin, the MFR starts to rise slowly and shows helical threads winding around an axis. Meanwhile, cool filamentary materials descend spirally down to the chromosphere. These features provide direct observational evidence of intrinsically helical structure of the MFR. Through detailed kinematical analysis, we find that the MFR evolution has two distinct phases: a slow rise phase and an impulsive acceleration phase. We attribute the first phase to the magnetic reconnection within the quasi-separatrix layers surrounding the MFR, and the much more energetic second phase to the fast magnetic reconnection underneath the MFR. We suggest that the transition between these two phases is caused by the torus instability. Moreover, we identify that the MFR evolves smoothly into the outer corona and appears as a coherent structure within the white-light CME volume. The MFR in the outer corona was enveloped by bright fronts that originated from plasma pile-up in front of the expanding MFR. The fronts are also associated with the preceding sheath region followed by the outmost MFR-driven shock.

79 ASTRONOMY AND ASTROPHYSICS↗

A plasma β transition within a propagating flux rope

We present a 2.5 dimensional magnetohydrodynamic simulation of a magnetic flux rope (FR) propagating in the heliosphere and investigate the cause of the observed sharp plasma β transition. Specifically, we consider a strong internal magnetic field and an explosive fast start, such that the plasma β is significantly lower in the FR than in the sheath region that is formed ahead. This leads to an unusual FR morphology in the first stage of propagation, while the more traditional view (e.g., from space weather simulations like Enlil) of a pancake-shaped FR is observed as it approaches 1 AU. We investigate how an equipartition line, defined by a magnetic Weber number, surrounding a core region of a propagating FR, can demarcate a boundary layer where there is a sharp transition in the plasma β. The substructure affects the distribution of toroidal flux, with the majority of the flux remaining in a small core region that maintains a quasi-cylindrical structure. We quantitatively investigate a locus of points where the kinetic energy density of the relative inflow field is equal to the energy density of the transverse magnetic field (i.e., effective tension force). The simulation provides compelling evidence that at all heliocentric distances the distribution of toroidal magnetic flux away from the FR axis is not linear, with 80% of the toroidal flux occurring within 40% of the distance from the FR axis. Thus, our simulation displays evidence that the competing ideas of a pancaking structure observed remotely can coexist with a quasi-cylindrical magnetic structure seen in situ.

79 ASTRONOMY AND ASTROPHYSICS↗

Inner heliospheric evolution of a 'STEALTH' CME derived from multi-view imaging and multipoint in situ observations. I. Propagation to 1 AU

Coronal mass ejections (CMEs) are the main driver of space weather. Therefore, a precise forecasting of their likely geo-effectiveness relies on an accurate tracking of their morphological and kinematical evolution throughout the interplanetary medium. However, single viewpoint observations require many assumptions to model the development of the features of CMEs. The most common hypotheses were those of radial propagation and self-similar expansion. The use of different viewpoints shows that, at least for some cases, those assumptions are no longer valid. From radial propagation, typical attributes that can now be confirmed to exist are over-expansion and/or rotation along the propagation axis. Understanding the 3D development and evolution of the CME features will help to establish the connection between remote and in situ observations, and hence help forecast space weather. We present an analysis of the morphological and kinematical evolution of a STEREO-B-directed CME on 2009 August 25-27. By means of a comprehensive analysis of remote imaging observations provided by the SOHO, STEREO, and SDO missions, and in situ measurements recorded by Wind, ACE, and MESSENGER, we prove in this paper that the event exhibits signatures of deflection, which are usually associated with changes in the direction of propagation and/or also with rotation. The interaction with other magnetic obstacles could act as a catalyst of deflection or rotation effects. We also propose a method to investigate the change of the CME tilt from the analysis of height-time direct measurements. If this method is validated in further work, it may have important implications for space weather studies because it will allow for inference of the interplanetary counterpart of the CME's orientation.

79 ASTRONOMY AND ASTROPHYSICS↗

THE HEIGHT EVOLUTION OF THE ''TRUE'' CORONAL MASS EJECTION MASS DERIVED FROM STEREO COR1 AND COR2 OBSERVATIONS

Using combined STEREO-A and STEREO-B EUVI, COR1, and COR2 data, we derive deprojected coronal mass ejection (CME) kinematics and CME ''true'' mass evolutions for a sample of 25 events that occurred during 2007 December to 2011 April. We develop a fitting function to describe the CME mass evolution with height. The function considers both the effect of the coronagraph occulter, at the beginning of the CME evolution, and an actual mass increase. The latter becomes important at about 10-15 R{sub Sun} and is assumed to mostly contribute up to 20 R{sub Sun }. The mass increase ranges from 2% to 6% per R{sub Sun} and is positively correlated to the total CME mass. Due to the combination of COR1 and COR2 mass measurements, we are able to estimate the ''true'' mass value for very low coronal heights (<3 R{sub Sun }). Based on the deprojected CME kinematics and initial ejected masses, we derive the kinetic energies and propelling forces acting on the CME in the low corona (<3 R{sub Sun }). The derived CME kinetic energies range between 1.0-66 Multiplication-Sign 10{sup 23} J, and the forces range between 2.2-510 Multiplication-Sign 10{sup 14} N.

79 ASTRONOMY AND ASTROPHYSICS↗

Tracking the Momentum Flux of a CME and Quantifying Its Influence on Geomagnetically Induced Currents at Earth

We investigate a coronal mass ejection (CME) propagating toward Earth on 29 March 2011. This event is specifically chosen for its predominately northward directed magnetic field, so that the influence from the momentum flux onto Earth can be isolated. We focus our study on understanding how a small Earth-directed segment propagates. Mass images are created from the white-light cameras onboard STEREO which are also converted into mass height-time maps (mass J-maps). The mass tracks on these J-maps correspond to the sheath region between the CME and its associated shockfront as detected by in situ measurements at L1. A time series of mass measurements from the STEREOCOR-2A instrument is made along the Earth propagation direction. Qualitatively, this mass time series shows a remarkable resemblance to the L1 in situ density series. The in situ measurements are used as inputs into a three-dimensional (3-D) magnetospheric space weather simulation from the Community Coordinated Modeling Center. These simulations display a sudden compression of the magnetosphere from the large momentum flux at the leading edge of the CME, and predictions are made for the time derivative of the magnetic field (dBdt) on the ground. The predicted dBdt values were then compared with the observations from specific equatorially located ground stations and showed notable similarity. This study of the momentum of a CME from the Sun down to its influence on magnetic ground stations on Earth is presented as a preliminary proof of concept, such that future attempts may try to use remote sensing to create density and velocity time series as inputs to magnetospheric simulations.

time series analysis↗

DERIVATION OF THE MAGNETIC FIELD IN A CORONAL MASS EJECTION CORE VIA MULTI-FREQUENCY RADIO IMAGING

The magnetic field within the core of a coronal mass ejection (CME) on 2010 August 14 is derived from analysis of multi-wavelength radio imaging data. This CME's core was found to be the source of a moving type IV radio burst, whose emission is here determined to arise from the gyrosynchrotron process. The CME core's true trajectory, electron density, and line-of-sight depth are derived from stereoscopic observations, constraining these parameters in the radio emission models. We find that the CME carries a substantial amount of mildly relativistic electrons (E < 100 keV) in a strong magnetic field (B < 15 G), and that the spectra at lower heights are preferentially suppressed at lower frequencies through absorption from thermal electrons. We discuss the results in light of previous moving type IV burst studies, and outline a plan for the eventual use of radio methods for CME magnetic field diagnostics.

79 ASTRONOMY AND ASTROPHYSICS↗

DIRECT EVIDENCE FOR A FAST CORONAL MASS EJECTION DRIVEN BY THE PRIOR FORMATION AND SUBSEQUENT DESTABILIZATION OF A MAGNETIC FLUX ROPE

Magnetic flux ropes play a central role in the physics of coronal mass ejections (CMEs). Although a flux-rope topology is inferred for the majority of coronagraphic observations of CMEs, a heated debate rages on whether the flux ropes pre-exist or whether they are formed on-the-fly during the eruption. Here, we present a detailed analysis of extreme-ultraviolet observations of the formation of a flux rope during a confined flare followed about 7 hr later by the ejection of the flux rope and an eruptive flare. The two flares occurred during 2012 July 18 and 19. The second event unleashed a fast (>1000 km s{sup -1}) CME. We present the first direct evidence of a fast CME driven by the prior formation and destabilization of a coronal magnetic flux rope formed during the confined flare on July 18.

79 ASTRONOMY AND ASTROPHYSICS↗

The Longitudinal Properties of a Solar Energetic Particle Event Investigated Using Modern Solar Imaging

We use combined high-cadence, high-resolution, and multi-point imaging by the Solar-Terrestrial Relations Observatory (STEREO) and the Solar and Heliospheric Observatory to investigate the hour-long eruption of a fast and wide coronal mass ejection (CME) on 2011 March 21 when the twin STEREO spacecraft were located beyond the solar limbs. We analyze the relation between the eruption of the CME, the evolution of an Extreme Ultraviolet (EUV) wave, and the onset of a solar energetic particle (SEP) event measured in situ by the STEREO and near-Earth orbiting spacecraft. Combined ultraviolet and white-light images of the lower corona reveal that in an initial CME lateral "expansion phase," the EUV disturbance tracks the laterally expanding flanks of the CME, both moving parallel to the solar surface with speeds of approx 450 km/s. When the lateral expansion of the ejecta ceases, the EUV disturbance carries on propagating parallel to the solar surface but devolves rapidly into a less coherent structure. Multi-point tracking of the CME leading edge and the effects of the launched compression waves (e.g., pushed streamers) give anti-sunward speeds that initially exceed 900 km/s at all measured position angles. We combine our analysis of ultraviolet and white-light images with a comprehensive study of the velocity dispersion of energetic particles measured in situ by particle detectors located at STEREO-A (STA) and first Lagrange point (L1), to demonstrate that the delayed solar particle release times at STA and L1 are consistent with the time required (30-40 minutes) for the CME to perturb the corona over a wide range of longitudes. This study finds an association between the longitudinal extent of the perturbed corona (in EUV and white light) and the longitudinal extent of the SEP event in the heliosphere.

acceleration of particles↗

Remote and In Situ Observations of an Unusual Earth-Directed Coronal Mass Ejection from Multiple Viewpoints

During June 16-21, 2010, an Earth-directed Coronal Mass Ejection (CME) event was observed by instruments onboard STEREO, SOHO, MESSENGER and Wind. This event was the first direct detection of a rotating CME in the middle and outer corona. Here, we carry out a comprehensive analysis of the evolution of the CME in the interplanetary medium comparing in-situ and remote observations, with analytical models and three-dimensional reconstructions. In particular, we investigate the parallel and perpendicular cross section expansion of the CME from the corona through the heliosphere up to 1 AU. We use height-time measurements and the Gradual Cylindrical Shell (GCS) technique to model the imaging observations, remove the projection effects, and derive the 3-dimensional extent of the event. Then, we compare the results with in-situ analytical Magnetic Cloud (MC) models, and with geometrical predictions from past works. We nd that the parallel (along the propagation plane) cross section expansion agrees well with the in-situ model and with the Bothmer & Schwenn [1998] empirical relationship based on in-situ observations between 0.3 and 1 AU. Our results effectively extend this empirical relationship to about 5 solar radii. The expansion of the perpendicular diameter agrees very well with the in-situ results at MESSENGER ( 0:5 AU) but not at 1 AU. We also find a slightly different, from Bothmer & Schwenn [1998], empirical relationship for the perpendicular expansion. More importantly, we find no evidence that the CME undergoes a significant latitudinal over-expansion as it is commonly assumed

Nieves-Chinchilla, T.↗

Global Energetics of Large Solar Eruptive Events

We have evaluated the energetics of the larger solar eruptive events recorded with a variety of spacecraft instruments between February 2002 and December 2006. All of the energetically important components of the flares and of the accompanying coronal mass ejections and solar energetic particles have been evaluated as accurately as the observations allow. These components include the following : (1) the total energy in the high temperature plasma determined from the RHESSI thermal X-ray observations; (2) the total energies in accelerated electrons above 20 keV and ions above 1 MeV from RHESSI hard X-ray and gamma-ray observations, respectively; (3) the potential and kinetic energies of the CME from SOHO/LASCO observations; (4) the solar energetic particle (SEP) energy estimates from in situ measurements on ACE, GOES, and SOHO; (5) the total radiated energy from the SORCEITSI measurements where available, and otherwise from the Flare Irradiance Spectral Model (FISM). The results are assimilated and discussed relative to the probable amount of non potential magnetic energy estimated to be available in the flaring active regions from MDI line-of-sight magnetograms.

Dennis, Brian R.↗