A current ribbon model for energy storage and release with application to the flare of 7 January 1992

Observations of the flare on 7 January 1992 are interpreted using a topological model of the magnetic field. The model, developed here, applies a theory of three-dimensional reconnection to the inferred magnetic field configuration for 7 January. In the model field a new bipole ( 10²¹ Mx) emerges amidst pre-existing active region flux. This emergence gives rise to two current ribbons along the boundaries (separators) separating the distinct, new and old, flux systems. Sudden reconnection across these boundary curves transfers 3 ×10²⁰ Mx of flux from the bipole into the surrounding flux. The model also predicts the simultaneous (sympathetic) flaring of the two current ribbons. This explains the complex two-loop structure noted in previous observations of this flare. We subject the model predictions to comparisons with observations of the flare. The locations of current ribbons in the model correspond closely with those of observed soft X-ray loops. In addition the footpoints and apexes of the ribbons correspond with observed sources of microwave and hard X-ray emission. The magnitude of energy stored by the current ribbons compares favorably to the inferred energy content of accelerated electrons in the flare.     

POST-FLARE LOOPS OF 26 JUNE 1992 – IV. Formation and Expansion of Hot and Cool Loops

Observations of the post-flare loops after the X3.9 flare which occurred on 25 June, 1992 at 20:11 UT by the Yohkoh/SXT in X-rays, as well as in H obtained at 5 different observatories, have provided a unique, longest ever, set of data for a study of the relationship between the hot and cool post-flare loops as they evolve. At any given time, the altitude difference between the hot X-ray loops of 6–7× 10⁶ K and the cool H loops of 1.5× 10⁴ K is related to the expansion rate of the loop systems and their cooling time. Therefore, measurements of the expansion rate and relative height of hot and cool loops can provide direct observational values for their cooling times. We measured the altitude of hot and cool loops for 15 and 19 hours, respectively, and found that the cooling time increased as the density of the loops decreased. We found a reasonably good agreement between the observed cooling times and those obtained from model calculations, although the observed values were always somewhat longer than the theoretical ones. Taking into account evolutionary effects, we also found similar shapes and configurations of hot and cool loops during the entire observing period and confirmed that, at any time, hot loops are at higher altitude than cool loops, suggesting that cool loops indeed evolve from hot loops. These results were used to check the validity of the reconnection model.     

Solar flares: The gradual phase

One has to distinguish between two kinds of the gradual phase of flares: (1) a gradual phase during which no energy is released so that we see only cooling after the impulsive phase (a confined flare), and (2) a gradual phase during which energy release continues (a dynamic flare).The simplest case of (1) is a single-loop flare which might provide an excellent opportunity for the study of cooling processes in coronal loops. But most confined flares are far more complicated: they may consist of sets of unresolved elementary loops, of conglomerates of loops, or they form arcades the components of which may be excited sequentially. Accelerated particles as well as hot and cold plasma can be ejected from the flare site (coronal tongues, flaring arches, sprays, bright and dark surges) and these ejecta may cool more slowly than the source flare itself.However, the most important flares on the Sun are flares of type (2) in which a magnetic field opening is followed by subsequent reconnection of fieldlines that may continue for many hours after the impulsive phase. Therefore, the main attention in this review is paid to the gradual phase of this category of long-decay flares. The following items are discussed in particular: The wide energy range of dynamic flares: from eruptions of quiescent filaments to most powerful cosmic-ray flares. Energy release at the reconnection site and modelling of the reconnection process. The post-flare loops: evidence for reconnection; observations at different wavelengths; energy deposit in the chromosphere, chromospheric ablation, and velocity fields; loops in emission; shrinking loops; magnetic modelling. The gradual phase in X-rays and on radio waves. Post-flare X-ray arches: observations, interpretation, and modelling; relation to metric radio events and mass ejections, multiple-ribbon flares and anomalous events, hybrid events, possible relations between confined and dynamic flares.     

The post flare loops observed at the total eclipse of February 16, 1980

A post flare loop system was observed on the west limb at the total solar eclipse of February 16, 1980 in Kenya. Analyzing the monochromatic images and the flash spectra, we obtained the following results: (1) the lower part of the post flare loop system is characterized mainly by distinct cool loops of H and Fe x 6374. Fe x 6374 emitting plasma (T _e = 1.0 × 10⁶ K) is highly concentrated in the loops. The 6374 loops are broader in diameter and located very close to but a little higher than the corresponding H loops. The electron densities of the dense part in H and Fe x 6374 loops are 10¹¹ cm^-3 and 6 × 10⁹cm^-3, respectively; (2) the Ca xv emitting region (3.5 × 10⁶ K) is confined to the upper part of the post flare loops. The electron density of this hot region is estimated as 8 × 10⁹ cm^-3 from the Ca xv line intensity ratio, I(5694)I(5445). These observational results led us to construct an empirical model of the post flare loop system which is consistent with the reconnection model of Kopp and Pneuman (1976).Contributions from the Kwasan and Hida Observatories, University of Kyoto, No. 267.     

Structure and dynamics of cool flare loops

MSDP observations of the 16 May, 1981 two-ribbon flare are used to study the physical structure and the dynamical behaviour of cool flare loops. The loops have been detected in the H line just after the flare maximum and they appeared in absorption against the disk. Using the first-order differential cloud model (DCM1) technique, we derive empirically some basic plasma parameters at 15 points along one loop leg. The flow velocities and the true heights have been reconstructed with respect to a geometrical projection. Subsequently, detailed non-LTE models of cool loops have been constructed in order to fit H source function values previously derived from DCM1 analysis. It is demonstrated that this source function is rather sensitive to the radial component of the flow velocity (the so-called Doppler brightening) and to enhanced irradiation of the loops from the underlying flare ribbons. In this way, we have been able to estimate quantitatively all plasma parameters which determine the physical structure of cool loops (i.e., the temperature, pressure, density), as well as the momentum-balance condition within the loops. For these dark loops we have arrived at relatively low gas pressures of the order of 0.1–0.5 dyne cm^-2 with corresponding electron densities around 10¹¹ cm^-3. Pressure-gradient forces have been found to be of small importance in the momentum-balance equation, and thus they cannot explain departures from a free-fall motion found in our MSDP data analysis. We propose three possible solutions to this problem.     

Post-flare loops of 26 June 1992

We observed the large post-flare loop system, which developed after the X 3.9 flare of 25 June 1992 at 2011 UT, in H with the Multichannel Subtractive Double Pass Spectrograph at Pic-du-Midi and in X-rays with the it Yohkoh/SXT instrument. Following the long-term development of cool and hot plasmas, we have determined the emission measure of the cool plasma and, for the first time, the temporal evolution of the hot-loop emission measure and temperature during the entire gradual phase. Thus, it was possible to infer the temporal variation of electron densities, leading to estimates of cooling times. A gradual decrease of the hot-loop emission measure was observed, from 4 × 10³⁰ cm^–5 at 2300 UT on 25 June 1992 to 3 × 10²⁸ cm^–5 at 1310 UT on 26 June 1992. During the same period, the temperature decreased only slowly from 7.2 to 6.0 × 10⁶ K. Using recent results of NLTE modeling of prominence-like plasmas, we also derive the emission measure of cool H loops and discuss their temperature and ionisation degree. During two hours of H observations (11–13 hours after the flare) the averaged emission measure does not show any significant change, though the amount of visible cool material decreases and the volume of the loops increases. The emission measure in H, after correction for the Doppler-brightening effect, is slightly lower than in soft X-rays. Since the hot plasma seems to be more spatially extended, we arrive at electron densities in the range n _infe ^supho n _infe ^supcool 2 × 10¹⁰ cm^–3 at the time of the H observations.These results are consistent with the post-flare loop model proposed by Forbes, Malherbe, and Priest (1989). The observed slow decrease of the emission measure could be due to an increase of the volume of the loops and a gradual decrease of the chromospheric ablation driven by the reconnection, which seems to remain effective continuously for more than 16 hours. The cooling time for hot loops to cool down to 10⁴ K and to appear in H would be only a few minutes at the beginning of the gradual phase but could be as long as 2 hours at the end, several hours later.     

Multi-thermal observations of newly formed loops in a dynamic flare

The dynamic flare of 6 November, 1980 (max 15:26 UT) developed a rich system of growing loops which could be followed in H for 1.5 hr. Throughout the flare, these loops, near the limb, were seen in emission against the disk. Theoretical computations of deviations from LTE populations for a hydrogen atom reveal that this requires electron densities in the loops close to, or in excess of 10¹² cm ^-3. From measured widths of higher Balmer lines the density at the tops of the loops was found to be 4 x 10¹² cm ^-3 if no non-thermal motions were present, or 5 × 10¹¹ cm ^-3 for a turbulent velocity of ~ 12 km s ^-1.It is now general knowledge that flare loops are initially observed in X-rays and become visible in H only after cooling. For such a high density, a loop would cool through radiation from 10⁷ to 10⁴ K within a few minutes so that the dense H loops should have heights very close to the heights of the X-ray loops. This, however, contradicts the observations obtained by the HXIS and FCS instruments on board SMM which show the X-ray loops at much higher altitudes than the loops in H. Therefore, we suggest that the density must have been significantly lower when the loops were formed and that the flare loops were apparently both shrinking and increasing in density while cooling.NAS/NRC Research Associate, on leave from CNIE, Argentina.Operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation. Partial support for the National Solar Observatory is provided by the USAF under a Memorandum of Understanding with the NSF.     

3-D Magnetic Field Configuration Late in a Large Two-Ribbon Flare

We present H and coronal X-ray images of the large two-ribbon flare of 25–26 June, 1992 during its long-lasting gradual decay phase. From these observations we deduce that the 3-D magnetic field configuration late in this flare was similar to that at and before the onset of such large eruptive bipolar flares: the sheared core field running under and out of the flare arcade was S-shaped, and at least one elbow of the S looped into the low corona. From previous observations of filament-eruption flares, we infer that such core-field coronal elbows, though rarely observed, are probably a common feature of the 3-D magnetic field configuration late in large two-ribbon flares. The rare circumstance that apparently resulted in a coronal elbow of the core field being visible in H in our flare was the occurrence of a series of subflares low in the core field under the late-phase arcade of the large flare; these subflares probably produced flaring arches in the northern coronal elbow, thereby rendering this elbow visible in H. The observed late-phase 3-D field configuration presented here, together with the recent sheared-core bipolar magnetic field model of Antiochos, Dahlburg, and Klimchuk (1994) and recent Yohkoh SXT observations of the coronal magnetic field configuration at and before the onset of large eruptive bipolar flares, supports the seminal 3-D model for eruptive two-ribbon flares proposed by Hirayama (1974), with three modifications: (1) the preflare magnetic field is closed over the filament-holding core field; (2) the preflare core field has the shape of an S (or backward S) with coronal elbows; (3) a lower part of the core field does not erupt and open, but remains closed throughout flare, and can have prominent coronal elbows. In this picture, the rest of the core field, the upper part, does erupt and open along with the preflare arcade envelope field in which it rides; the flare arcade is formed by reconnection that begins in the middle of the core field at the start of the eruption and progresses from reconnecting closed core field early in the flare to reconnecting opened envelope field late in the flare.     

Study of the post-flare loops on 29 July 1973

Bright and dark curvilinear structures observed between the two major chromospheric ribbons during the flare of 29 July 1973 on films from the Big Bear Solar Observatory are interpreted as a typical system of coronal loops joining the inner boundaries of the separating flare ribbons. These observations, made through a 0.25 Å H filter, only show small segments of the loops having Doppler shifts within approximately ± 22 km s^–1 relative to the filter passband centered at H, H -0.5 Å or H +0.5 Å. However, from our knowledge of the typical behavior of such loop systems observed at the limb in H and at 5303 Å, it has been possible to reconstruct an appoximate model of the probable development of the loops of the 29 July flare as they would have been viewed at the limb relative to the position of a prominence which began to erupt a few minutes before the start of the flare. It is seen that the loops ascended through the space previously occupied by the filament. On the assumption that H fine structures parallel the magnetic field, we can conclude that a dramatic reorientation of the direction of the magnetic field in the corona occurred early in the flare, subsequent to the start of the eruption of the filament and prior to the time that the H loops ascended through the space previously occupied by the filament.     

Coronal bright points at 6 cm wavelength

We report the results of the first observations of solar coronal bright points at 6 cm wavelength using the Very Large Array (VLA), with a spatial resolution of 1.2. The maximum brightness temperature of the sources observed is 3 × 10⁴ K with a mean value of 1 × 10⁴ K (above the quiet Sun value). The lifetime of most sources is between 5 and 20 min. The average diameter of the sources is about 5–15 arc. The sources are gaussian-like near the footpoint of miniature loops and they appear in groups. The observations indicate that significant fluctuations in the brightness temperature (sometimes quasi-periodic) and in the spatial extents of these sources can occur over periods of a few minutes.On leave from Beijing Observatory, Beijing, Peoples Republic of China.     

Lyman continuum observations of solar flares

A study is made of Lyman continuum observations of solar flares, using data obtained by the Harvard College Observatory EUV spectroheliometer on the Apollo Telescope Mount. We find that there are two main types of flare regions: an overall mean flare coincident with the H flare region, and transient Lyman continuum kernels which can be identified with the H and X-ray kernels observed by other authors. It is found that the ground level hydrogen population in flares is closer to LTE than in the quiet Sun and active regions, and that the level of Lyman continuum formation is lowered in the atmosphere from a mass column density m 5/sx 10^–6 g cm^–2 in the quiet Sun to m 3/sx 10^–4 g cm^–2 in the mean flare, and to m 10^–3g cm^–2 in kernels. From these results we derive the amount of chromospheric material evaporated into the high temperature region, which is found to be - 10¹⁵g, in agreement with observations of X-ray emission measures. A comparison is made between kernel observations and the theoretical predictions made by model heating calculations, available in the literature; significant discrepancies are found between observation and current particle-heating models.     

Kinematical analysis of flare spray ejecta observed in the corona

The mass ejection event on 17 January 1974 was a classsic spray associated with a flare from an over the limb region. The structure of the accompanying coronal transient was typical of well-observed mass ejections, with coronal loops and a forerunner racing ahead of the rising prominence. Observations in H, soft X-ray, white light and radio wavelengths allowed us to track both cool (T _e10⁴ K) and hot (T _e>10⁶ K) material from limb de-occultation to 6R . We determined the kinematics and thermodynamics of the internal material, and the overall mass and energy budget of the event. The majority of the mass and energy was linked with coronal material, but at least 20% of the ejected mass originated as near-surface prominence material. We conclude that the upper part of the prominence was being continuously heated to coronal temperatures as it rose through the corona. Above 2R nearly all of the material was completely ionized. The primary acceleration of the prominence occurred below 3.5 × 10⁴ km with all of the material exhibiting constant velocity above 1.5R . We found evidence that a moving type IV burst, indicative of strong magnetic fields, was associated with the upper part of the prominence. Our observations suggest that both the cool and hot material were acted upon by a similar, continuous force(s) to great heights and over a long time interval. We find that the observations are most consistent with magnetic propulsion models of coronal transients.     

Relation between cool and hot post-flare loops of 26 June 1992 derived from optical and X-ray (SXT-Yohkoh) observations

We have analyzed the physical conditions of the plasma in post-flare loops with special emphasis on dynamics and energy transport using SXT-data (hot plasma) and optical ground-based data from Pic du Midi, Wrocaw, and Ondejov (cool plasma). By combining the H observations with the SXT images we can understand the relationship between cool and hot plasmas, the process of cooling post-flare loops and the mechanism which maintains the long duration of these loops. Using recent results of NLTE modeling of prominence-like plasmas, we derive the emission measure of cool H loops and this gives us a realistic estimate of the electron density (2.2 × 10¹⁰ cm^–3). Then, by comparing this emission measure with that of hot loops derived from SXT data, we are able to estimate the ratio between electron densities in hot and cool loops taking into account the effect of geometrical filling factors. This leads to the electron density in hot loops 7 × 10⁹ cm^–3. We also derive the temperature of hot X-ray loops ( 5.5 × 10⁶ K), which, together with the electron density, provides the initial values for solving the time-dependent energy balance equation. We obtain the cooling times which are compared to a typical growth-time of the whole loop system ( 2000 s). In the legs of cool H loops, we observe an excess of the emission measure which we attribute to the effect of Doppler brightening (due to large downflow velocities).     

Evaluating Mean Magnetic Field in Flare Loops

We analyze multiple-wavelength observations of a two-ribbon flare exhibiting apparent expansion motion of the flare ribbons in the lower atmosphere and rising motion of X-ray emission at the top of newly-formed flare loops. We evaluate magnetic reconnection rate in terms of V _r B _r by measuring the ribbon-expansion velocity (V _r) and the chromospheric magnetic field (B _r) swept by the ribbons. We also measure the velocity (V _t) of the apparent rising motion of the loop-top X-ray source, and estimate the mean magnetic field (B _t) at the top of newly-formed flare loops using the relation 〈V _t B _t〉≈〈V _r B _r〉, namely, conservation of reconnection flux along flare loops. For this flare, B _t is found to be 120 and 60 G, respectively, during two emission peaks five minutes apart in the impulsive phase. An estimate of the magnetic field in flare loops is also achieved by analyzing the microwave and hard X-ray spectral observations, yielding B=250 and 120 G at the two emission peaks, respectively. The measured B from the microwave spectrum is an appropriately-weighted value of magnetic field from the loop top to the loop leg. Therefore, the two methods to evaluate coronal magnetic field in flaring loops produce fully-consistent results in this event.     

Magnetic diffusion and flare energy buildup

Photospheric motion shears or twists solar magnetic fields to increase magnetic energy in the corona, because this process may change a current-free state of a coronal field to force-free states which carry electric current. This paper analyzes both linear and nonlinear two-dimensional force-free magnetic field models and derives relations of magnetic energy buildup with photospheric velocity field. When realistic data of solar magnetic field (B ₀ 10³ G) and photospheric velocity field (v _max 1 km s^–1) are used, it is found that 3–4 hours are needed to create an amount of free magnetic energy which is of the order of the current-free field energy. Furthermore, the paper studies situations in which finite magnetic diffusivities in photospheric plasma are introduced. The shearing motion increases coronal magnetic energy, while the photospheric diffusion reduces the energy. The variation of magnetic energy in the coronal region, then, depends on which process dominates.     

The stationary post-flare arch of May 21/22, 1980

On May 21/22, 1980 the Hard X-Ray Imaging Spectrometer aboard the SMM imaged an extensive coronal structure after the occurrence of a two-ribbon flare on May 21, 20:50 UT. The structure was observed from 22:20 UT on May 21 until its disappearence at 09:00 UT on May 22.At 22:20 UT the brightest pixel in the arch was located at a projected altitude of 95 000 km above the zero line of the longitudinal magnetic field. At 23:02 UT the maximum of brightness shifted to a neighbouring pixel with approximately the same projected altitude. This sudden shift indicates that the X-ray structure consisted of (at least) two separate arches at approximately the same altitude, one of which succeeded the other as the brightest arch in the structure at 23:02 UT.From 23:02 UT onwards the maximum of brightness did not change its position in the HXIS coarse field of view. With a spatial resolution of 32 this places an upper limit of 1.1 km s^-1 on the rise velocity of the arch. Thus, contrary to a similar arch observed on November 6/7, where rise velocities of the order of 10 km s^-1 were measured in the same phase of development, the May 22 arch was a stationary structure at an altitude of 145000 km.The following values were estimated for the physically relevant quantities of the May 21/22 arch at the time of its maximum brightness (23:00 UT): temperature T 6.3 × 10⁶ K, electron density n _e 1.1 × 10⁹ cm^-3, total emitting volume V 5 × 10²⁹ cm³, energy density 2.9 erg cm^–3, total energy contents E 1.4 × 10³⁰ erg, total mass M 9 × 10¹⁴ g.The top of the arch was observed at 145 000 km altitude within 1.5 hr after the flare occurrence. Since it seems unlikely that the structure already existed prior to the flare at 20:50 UT, the arch must have risen to its stationary position with an average velocity exceeding 17 km s^–1 (possibly much faster). We speculate that the arch was formed very fast at the flare onset, when (part of) the active region loop system was elevated within minutes to the observed altitude.     

Electron–Whistler Interaction in Coronal Loops and Radiation Signatures

Interaction of the 30–300 keV electrons with whistlers in solar coronal loops is studied using a quasi-linear approach. We show that the electron–whistler interaction may play a dominant role in the formation of fast electron spectra within the solar flare loops with the plasma temperature 10⁷ K and plasma density 10¹¹ cm^–3. It is found that Landau damping of whistlers provides weak and intermediate pitch-angle diffusion regimes of fast electrons in coronal loops. The level of whistler turbulence in the weak diffusion regime under flare conditions is estimated as 10^–7 of the energy density in the thermal particles. The `top – footpoint' relations between the hard X-ray flux densities and spectra are derived. The reason for a `broken' spectrum of the flare microwave emission is discussed.     

Observations of preburst heating and magnetic field changes in a coronal loop at 20 cm wavelength

The Very Large Array (VLA) has been used at 20 cm wavelength to study the evolution of a burst loop with 4 resolution on timescales as short as 10 s. The VLA observations show that the coronal loop began to heat up and change its structure about 15 min before the eruption of two impulsive bursts. The first of these bursts occurred near the top of the loop that underwent preburst heating, while the second burst probably occurred along the legs of an adjacent loop. These observations evoke flare models in which coronal loops twist, develop magnetic instabilities and then erupt. We also combine the VLA observations with GOES X-ray data to derive a peak electron temperature of T _e = 2.5 × 10⁷ K and an average electron density of N _e 1 × 10¹⁰ cm^–3 in the coronal loop during the preburst heating phase.     

Multiple loop activations and continuous energy release in the solar flare of June 15, 1973

The spatial and temporal evolution of the high temperature plasma in the flare of 1973 June 15 has been studied using the flare images photographed by the NRL XUV spectroheliograph on Skylab.The overall event involves the successive activations of a number of different loops and arches bridging the magnetic neutral line. The spatial shifts and brightenings observed in the Fe xxiii–xxiv lines are interpreted as the activation of new structures. These continued for four or five minutes after the end of the microwave burst phase, implying additional energy-release unrelated to the nonthermal phase of the flare. A shear component observed in the coronal magnetic field may be a factor in the storage and release of the flare energy.The observed Fe xxiii–xxiv intensities define a post-burst heating phase during which the temperature remained approximately constant at 13 × 10⁶ K while the Fe xxiv intensity and 0–3 Å flux rose to peak values. This phase coincided with the activation of the densest structure (N _e = 2 × 10¹¹ cm^–3). Heating of higher loops continued into the decay phase, even as the overall temperature and flux declined with the fading of the lower Fe xxiv arches.The observed morphology of individual flaring arches is consistent with the idea of energy release at altitude in the arch (coincident with a bright, energetic core in the Fe xxiv image) and energy flow downward into the ribbons. The Doppler velocity of the Fe xxi 1354 Å line is less than 5 km s^–1, indicating that the hot plasma region is stationary.The relation of this flare to the larger class of flares associated with filament eruptions and emerging magnetic flux is discussed.     

On the inability of magnetically constricted transition regions to account for the 105 to 106 K plasma in the quiet solar atmosphere

Although back conduction from the corona has been shown to be inadequate for powering EUV emission below T 2 × 10⁵ K, it is thought to be adequate in the temperature range 2 × 10⁵ K < T < 10⁶ K. No models to date, however, have included the large magnetic constriction which should occur in the legs of coronal loops where conductive transition regions, hitherto thought to contain the bulk of the plasma in this higher temperature range, are located. On the basis of fine scale magnetograms, Dowdy et al. (1986) have estimated that these magnetic flux tubes are constricted from end to end by an areal factor of approximately 100. Furthermore, on the basis of simple steady-state conductive models, Dowdy et al. (1985) have shown that the large constriction can inhibit the conductive flow of heat by an order of magnitude. We are thus led to re-examine static models of this region of the atmosphere which incorporate not only conduction and radiation but also the effects of large magnetic constrictions. We find that the structure of this plasma depends not only on the magnitude of the constriction but also on the tube's shape.Our results show that no model with a constriction of order 100 can simultaneously (a) produce the variation of differential emission measure with temperature derived from measured line intensities and (b) satisfy the observed constraint (Reeves, 1976) that EUV emission from below T 7 × 10⁵ K be confined to the supergranular network, covering no more than 0.45 of the solar surface. The failure of the models suggests that the bulk of the 10⁵–10⁶ K plasma in the quiet solar atmosphere is not in transition region structures, but is instead magnetically isolated from the corona and heated internally. Even though the transition region component of 10⁵–10⁶ K plasma in the legs of coronal loops should exist, it comprises only a small fraction of the total 10⁵–10⁶ K plasma and, hence, produces only a small fraction of the observed EUV emission from this temperature range.We also find that for any permitted tube shape, constriction factors of order 100 reduce the coronal conductive energy losses to the transition region to a value which is less than a third of the value for an unconstricted field, i.e., to less than 2 × 10⁵ erg cm ^–2 s ^–1. In particular, if the magnetic geometry of the upper transition region is extremely concave (i.e., horn-shaped geometry with most of the areal divergence near the hot end), then a constriction of order 100 results in a conductive loss of less than 1 × 10⁴ erg cm^–2 s^–1 and, hence, much less than the coronal radiative energy loss. For such geometries, the constriction in the magnetic field hence provides an effective thermal insulation of the corona from the cooler parts of the solar atmosphere.Presidential Young Investigator.