Electric fields in coronal magnetic loops

We analyze spectra taken with the 40 cm coronograph at Sacramento Peak Observatory, for evidence of Stark effect on Balmer lines formed in coronal magnetic structures. Several spectra taken near the apex of a bright post-flare loop prominence show significant broadening from H₁₀ to the limit of Balmer line visibility in these spectra, at about H₂₀ The most likely interpretation of the increasing width is Stark broadening, although unresolved blends of Balmer emissions with metallic lines could also contribute to the trend. Less significant broadening is seen in 3 other post-flare loops, and the data from 5 other active coronal condensations observed in this study show no broadening tendency at all, over this range of Balmer number. The trend clearly observed in one post-flare loop requires an ion density of n _i ? 2 × 10¹² cm^?3, if it is to be explained entirely as Stark effect caused by pressure broadening. But mean electron densities measured directly from the Thomson scattering at λ3875 in the same SPO spectra, yield n _e ? 3?7 × 10¹⁰ cm^?3 for the same condensations observed within that loop. Comparison of this evidence from electron scattering, with densities derived from emission measures and line-intensity ratios, argues against a volume filling factor small enough to reconcile the values of n _i and n _e derived in this study. This discrepancy leads us to suggest that the Stark effect observed in these loops, and possibly also in flares, could be caused by macroscopic electric fields, rather than by pressure broadening. The electric field required to explain the Stark broadening in the brightest post-flare loop observed here is approximately 170 V cm^?1. We suggest an origin for such an electric field and discuss its implications for coronal plasma dynamics.     

Thermal equilibria of coronal magnetic loops

Equations of thermal equilibrium along coronal loops with footpoint temperatures of 2 × 10⁴ K are solved. Three fundamentally different categories of solution are found, namely hot loops with summit temperatures above about 4 × 10⁵ K, cool loops which are cooler than 8 × 10⁴ K along their whole length and hot-cool loops which have summit temperatures around 2 × 10⁴ K but much hotter parts at intermediate points between the summit and the footpoints. Hot loops correspond to the hot corona of the Sun. The cool loops are of relevance for fibrils, for the cool cores observed by Foukal and also for active-region prominences where the magnetic field is directed mainly along the prominence. Quiescent prominences consist of many cool threads inclined to the prominence axis, and each thread may be modelled as a hot-cool loop. In addition, it is possible for warm loops at intermediate summit temperatures (8 × 10⁴K to 4 × 10⁵ K) to exist, but the observed differential emission measure suggests that most of the plasma in the solar atmosphere is in either the hot phase or the cool phase. Thermal catastrophe may occur when the length or pressure of a loop is so small that the hot solution ceases to exist and there are only cool loop solutions. Many loops can be superimposed to form a coronal arcade which contains loops of several different types.     

Energy equilibrium in coronal magnetic loops -reinvestigated

Temperature distribution in cylindrically symmetric coronal magnetic loops has been reinvestigated under various conditions: (a) loop with the pressure varying along the radial distance, and (b) loop with constant pressure, for cooler apex loops and hotter apex loops. This work is reinvestigation of our previous work published inAstrophysics and Space Science (Chandra and Prasad, 1993b).     

The structure of coronal magnetic loops

We present here a model, based on observations, for the magnetic-field equilibrium of a cool coronal loop. The pressure structure, taken from the Harvard/Skylab EUV data, is used to modify the usual force-free-field form in quasi-cylindrical symmetry. The resulting field, which has the same direction but different strength, is calculated and its variation displayed. Finally, localized interchange stability is evaluated and discussed, as the first step in a subsequent complete magnetohydrodynamic-stability analysis.     

The structure of coronal magnetic loops

We present the second part of a complete theory for the plasma and field structure of a cool coronal arch, corresponding to those observed in the EUV from Skylab. The global magneto-hydrodynamic (MHD) stability of a previously described equilibrium-loop model is evaluated, and compared with that of an unmodified ambient force-free field. The influence of the photospheric boundary condition is also evaluated, producing a specification of stability limits which depend on the relative field and plasma pressures and scale widths. The resulting restrictions on the allowable field configuration of a coronal loop are then compared with observed values. The implications of this general method for deducing small-scale coronal magnetic-field structure from the measured plasma profile of an emissive feature are also described.     

Electron acceleration by electric fields near the footpoints of current-carrying coronal magnetic loops

We analyze the electric fields that arise at the footpoints of a coronal magnetic loop from the interaction between a convective flow of partially ionized plasma and the magnetic field of the loop. Such a situation can take place when the loop footpoints are at the nodes of several supergranulation cells. In this case, the neutral component of the converging convective flows entrain electrons and ions in different ways, because these are magnetized differently. As a result, a charge-separating electric field emerges at the loop footpoints, which can efficiently accelerate particles inside the magnetic loop under appropriate conditions. We consider two acceleration regimes: impulsive (as applied to simple loop flares) and pulsating (as applied to solar and stellar radio pulsations). We have calculated the fluxes of accelerated electrons and their characteristic energies. We discuss the role of the return current when dense beams of accelerated particles are injected into the corona. The results obtained are considered in light of the currently available data on the corpuscular radiation from solar flares.     

Modelling coronal magnetic fields

The hairy ball model of coronal magnetic fields has a spherical source surface separating potential and radial magnetic fields. In the present model the source surface is chosen such that the wind speed equals the Alfvénic speed at selected points on the source surface. Results have been obtained for a dipole base field and an isothermal corona.Proceedings of the 14th ESLAB Symposium on Physics of Solar Variations, 16–19 September 1980, Scheveningen, The Netherlands.     

Stability of siphon flow in coronal magnetic loops

Plasma siphon flow with velocities up to 100 km/s have been observed in coronal magnetic loops. We discuss the stability of this siphon flow using slab and cylinder models. We calculate numerically the dispersion relation and obtain the rate of growth of instability and the frequency of perturbing waves. Our main conclusions are that magnetic field is a stabilizing factor and that flow velocity is a de-stabilizing factor. We discuss the question whether stationary, high-velocity siphon flow can exist in coronal magnetic loops.     

Thermal condensations in coronal magnetic fields

Conditions under which cool condensations can form in the solar corona are investigated using the powerful phase plane method to analyse the energy and hydrostatic balance equations. The importance of the phase plane approach is that the conclusions deduced are not sensitive to the actual choice of boundary conditions adopted which only determine the actual contour. The importance of heating variations and area divergence are studied as well as the influence of gravity for their effect on the formation of cool condensations. The cool temperature at which optically thin radiation and heating balance is important and the links with other cool solutions are mentioned.     

A class of force-free magnetic fields for modeling pre-flare coronal magnetic configurations

Three-dimensional, quasi-static evolutions of coronal magnetic fields driven by photospheric flux emergence are modeled by a class of analytic force-free magnetic fields. Our models relate commonly observed photospheric magnetic phenomena, such as the formation and growth of sunspots, the emergence of an X-type separator, and the collision and merging of sunspots, to the three-dimensional magnetic fields in the corona above. By tracking the evolution in terms of a continuous sequence of force-free states, we show that flux emergence and submergence along magnetic neutral lines in the photosphere are essential processes in all these photospheric phenomena. The analytic solutions we present have a parametric regime within which the magnetic energy attained by an evolving force-free field may be of the order of 10³⁰ ergs to several 10³¹ ergs, depending on the magnetic environment into which an emerging flux intrudes. The commonly used indicators of magnetic shear in magnetogram interpretation are discussed in terms of field connectivity in our models. It is demonstrated that the crossing angle of the photospheric transverse magnetic field with the neutral line may not be a reliable indicator of the magnetic shear in the coronal field above, due to the complexity of three-dimensionality. The poorly understood constraint of magnetic-helicity conservation on the availability of magnetic free energy for a flare is briefly discussed.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

A model of interplanetary and coronal magnetic fields

A model of the large-scale magnetic field structure above the photosphere uses a Green's function solution to Maxwell's equations. Sources for the magnetic field are related to the observed photospheric field and to the field computed at a source surface about 0.6 R above the photosphere. The large-scale interplanetary magnetic field sector pattern is related to the field pattern at this source surface. The model generates magnetic field patterns on the source surface that compare well with interplanetary observations. Comparisons are shown with observations of the interplanetary magnetic field obtained by the IMP-3 satellite.     

Ray-type spectra of plasma turbulence in coronal magnetic loops

The problem of stationary spectra of Langmuir, l, and electromagnetic, t, waves excited in a magnetic trap (loop) by a group of suprathermal electrons, whose velocity distribution includes a loss cone, is considered. Within the framework of weak turbulence theory, accurate spectra of l- and t-waves are found. These spectra have the form of thin rays in wavevector space. Forms of plasma emission radio lines of a homogeneous source near the plasma frequency and its second harmonic are determined.     

The solar-surface boundary conditions of coronal magnetic loops

The dynamical properties of a realisticthermal-structure interface between a coronal loop and the chromosphere/photosphere are investigated by numerical simulations using acoustic and Alfvénic excitations. These properties are relevant to the end conditions seen by coronal MHD perturbations (e.g., waves or instabilities), in the absence of much slower energetics effects. Analytic studies of coronal-loop hydromagnetics have often made simplifying assumptions about the boundary conditions at the loop base in order to make their calculations tractable. However, in the presence of a transition region and chromosphere with rapidly varying plasma conditions, it is not clear how valid these heuristic assumptions are. In this study, we find that the discontinuous fluid-density model approximately represents the reflection/ transmission scaling with respect to varying transition-region density and temperature (i.e., dynamic impedance) ratios, although it does not quantitatively predict the chromospheric response to wave-like coronal activity. This disagreement is partially due to the finite width of the corona-to-photosphere transition.     

A model for elemental coronal flux loops

The photosphere possesses many small, intense patches of magnetic flux. Each of these patches (or sources) is connected magnetically through the corona to several sources of opposite polarity. An elemental flux loop consists of all of the flux joining one such source to another. We find that each source is connected to twenty other sources, on average, and that the typical flux and diameter of elemental loops in the corona are 10¹⁶ Mx and 200 km; there are approximately 17 separators for each source. We also model a typical large-scale coronal loop consisting of many elemental loops and determine its complex internal topology. Each upright null lies at the end of about 22 separatrices, which tend to be clustered together in trunk-like structures, analogous to river-valleys in a geographical contour map. Prone nulls correspond to saddle points, while their spines are analogous to watersheds.     

XUV observations of coronal magnetic fields

Spectroheliograms obtained with the Naval Research Laboratory's Extreme Ultraviolet Spectrograph (S082A) on Skylab are compared with Kitt Peak National Observatory magnetograms. A principal result is the characteristic reconnection of flux from an emerging bipolar magnetic region to previously existing flux in its vicinity. Examples of the disappearance of magnetic flux from the solar atmosphere are also shown. The results of a particularly simple, potential field calculation are shown for comparison with the Skylab observations.     

The evolution of coronal magnetic fields

Slow photospheric motions can produce flow speeds in the corona which are fast enough to violate quasi-static evolution. Therefore, high-speed flows observed in the corona are not necessarily due to a loss of equilibrium or stability. In this letter we present an example where the flow speed increases indefinitely with, height, while the coronal magnetic energy increases quadratically with time.     

Representations of coronal magnetic fields including currents

Solar Physics - Coronal electric currents are superposed on the calculated large-scale current-free (potential) magnetic field of the solar corona and the new magnetic configurations are mapped....     

The orientation of pre-transient coronal magnetic fields

Loop-like white light coronal transients are generally believed to be nearly planar sheets which are thin compared to the loop extent; however, this picture may be questioned since virtually no observations (of the more than 100 transient events observed during 1973–74 Skylab period) show such loops edge-on. From the group of transient events studied by Munro etal. (1979) for which definite surface associations exist, we find loop transients are strongly correlated with filament regions where the filament axis was oriented north-south. From direct soft X-ray observations of an expanding arch, the possible identification of the soft X-ray signature of footpoints of transient loops, and monochramatic observations of low coronal loops, we infer that loop-like coronal transients have their origin in low-lying coronal loops nearly co-planar with the north-south aligned filament axis. The situation with respect to non-loop events is less clear; such events apparently often arise from more complex filament geometries. Possible reasons for the preference of transients to arise from north-south filament-oriented regions are discussed.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Stereoscopic determination of the three-dimensional geometry of coronal magnetic loops

The three-dimensional shape of coronal magnetic loops is restored from extreme ultraviolet (XUV) images of the Sun (Skylab mission 3, 1973) by using the perspective effect due to the solar rotation. An original method is developed which only depends on the assumption that the magnetic structures under consideration are (at least geometrically) stable within the time interval used for restoration. Large scale loops interconnecting different active regions are studied by applying this method. They are found to lie approximately in planes inclined from the local vertical. Generally these loops are asymmetric, i.e. their apices are shifted toward one of the footpoints. This tendency is also confirmed by the computation of coronal magnetic fields based on the photospheric magnetic data.On leave from Observatoire de Paris-Meudon, 91190 Meudon, France.     

Thermal equilibria of coronal magnetic loops with non-constant cross-sectional area

Equations of thermal equilibrium along coronal loops are solved in the absence of gravity but where the cross-sectional area changes along the loop. The footpoint temperature is assumed to be 2 × 10⁴ K. Several fundamental types of solution are found, namely hot loops, cool loops, hot-cool loops (where the footpoints and summits are cool but the intermediate parts are hotter) and warm loops (cool along most of their lengths except the summits). On increasing the cross-sectional area the summit temperature generally increases slightly except for warm loops where no increase in temperature is recorded and hot-cool loops where a dramatic increase in summit temperature may occur. The cool and hot-cool loops may model elementary fibril structures within prominences.