On practical representation of magnetic field

Various manners of determination of a magnetic field are reviewed briefly from the standpoint of practicality and uniqueness. Then a practical representation of magnetic fields in terms of a class of force-free magnetic field is described. The proposed scheme is based on the physical consideration that in the chromosphere and lower corona a quasistatic magnetic field must be nearly force-free and that for the class of force-free magnetic field, i.e., ×B=B with = constant, the magnetic field can be determined uniquely from the observed distribution of the vertical component of a magnetic field. The applicability of the representation is demonstrated by examples and the limitations are discussed.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Magnetic reconnection in a high-temperature plasma of solar flares

Simple self-consistent models for non-neutral current sheets are considered. Characteristics of high-temperature turbulent current sheets (HTCS) with a small transverse component of magnetic field are determined for conditions in the solar corona. The energy output of such an HTCS is much larger than that of a neutral sheet. This makes it possible to consider the HTCS as an energy source not only in long-lived X-ray loops but also in flaring loops during the not or main phase of a flare. In this case, the magnetic reconnection velocity agrees with the observed velocity of the loop rise. Thus, these phenomena can be interpreted as a result of magnetic reconnection, for example, between new flux emerging from under the photosphere and an old magnetic field.The role of a longitudinal magnetic field in a current sheet is less important for HTCS. As a result of the compression of a longitudinal field, there appears an electric current circulating around the sheet. This current may induce strong Joule heating, if the compression is large. This additional heating is realized because of the annihilation of the main component, not the longitudinal component of magnetic field. The effect is small for HTCS, but may be significant for preflare current sheets.     

Force-free equilibrium at magnetic neutral points

It is shown that, at neutral points of force-free magnetic fields, the electric current density must vanish. This property is independent of whether the neutral points are isolated or (e.g.) fill lines or surfaces. One implication is the fact that in a cold pressureless plasma the formation of neutral current sheets cannot be adiabatically slow. The field-line topology in the neighbourhood of neutral points is discussed. At neutral points of force-free magnetic fields in general three constant- surfaces, defined by the equation ×B=B, with the same value of intersect orthogonally. If, during a time-development, the magnetic field gradient matrix B _i/x _j becomes singular at a neutral point, the field topology can change qualitatively — in general connected with the merger of two or more neutral points into one and/or the splitting up of one neutral point into several others. This can be interpreted as implying the transition from a quasi-static evolution to a dynamical state in which magnetic energy is released.     

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.     

Multiple moving magnetic structures in the solar corona

We report the study of moving magnetic structures inferred from the observations of a moving type IV event with multiple sources. The ejection contains at least two moving radio emitting loops with different relative inclinations. The radio loops are located above multiple H flare loops in an active region near the limb. We investigate the relationship between the two systems of loops. The spatial, temporal and geometrical associations between the radio emission and near surface activities suggest a scenario similar to coronal mass ejection (CME) events, although no CME observations exist for the present event. From the observed characteristics, we find that the radio emission can be interpreted as Razin suppressed optically thin gyrosynchrotron emission from nonthermal particles of energy 100, keV and density 10²–10⁵ cm^–3 in a magnetic field 2 G.     

Shear angle of magnetic fields

In this paper we introduce a new parameter, the shear angle of vector magnetic fields, , to describe the non-potentiality of magnetic fields in active regions, which is defined as the angle between the observed vector magnetic field and its corresponding current-free field. In the case of highly inclined field configurations, this angle is approximately equal to the angular shear, , defined by Hagyardet al. (1984). The angular shear, , can be considered as the projection of the shear angle, , on the photosphere. For the active region studied, the shear angle, , seems to have a better and neater correspondence with flare activity than does . The shear angle, , gives a clearer explanation of the non-potentiality of magnetic fields. It is a better measure of the deviation of the observed magnetic field from a potential field, and is directly related to the magnetic free energy stored in non-potential fields.     

Solar chromospheric magnetic fields in active regions inferred by monochromatic images of the Stokes' parameterV of the Hβ line

A series of H chromospheric magnetograms was obtained at various wavelengths near the line center with the vector video magnetograph at Huairou Solar Observing Station as a diagnostic of chromospheric magnetic structures. The two-dimensional distribution of the circular polarization light of the H line with its blended lines at various wavelength in active regions was obtained, which consists of the analyses of Stokes' profileV of this line. Due to the disturbance of the photospheric blended line Fei 4860.98 for the measurement of the chromospheric magnetic field, a reversal in the chromospheric magnetograms relative to the photospheric ones occurs in the sunspot umbrae. But in the quiet, plage regions, even penumbrae, the influence of the photospheric blended Fei 4860.98 line is not obvious. As regards the observation of the H chromospheric magnetograms, we can select the working wavelength between -0.20 and -0.24 from the line core of H to avoid the wavelengths of the photospheric blended lines in the wing of H.After the spectral analysis of chromospheric magnetograms, we conclude that the distribution of the chromospheric magnetic field is similar to the photospheric field, especially in the umbrae of the sunspots. The chromospheric magnetic field is the result of the extension of the photospheric field.     

Динамические равновесные плазменные конфигуации и физика магнитосферы

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Метагалактические протоны сверхвысоких энергий

, . 2.7°- . . . E3×10¹⁹ (1.6) .     

EUV emission,filament activation and magnetic fields in a slow-rise flare

The evolution of coronal and chromospheric structures is examined together with magnetograms for the 1B flare of January 19, 1972. Soft X-ray and EUV studies are based on the OSO-7 data. The H filtergrams and magnetograms came from the Sacramento Peak Observatory. Theoretical force-free magnetic field configurations are compared with structures seen in the soft X-ray, EUV and H images. Until the flare, two prominent spots were connected by a continuous dark filament and their overlying coronal structure underwent an expansion at the sunspot separation rate of 0.1 km s^–1. On January 19, the flare occurred as new magnetic fields emerged at 10¹⁹ Mx h^–1 beneath the filament, which untwisted and erupted as the flare began. The pre-flare coronal emissions remained unchanged during the flare except for the temporary addition of a localized enhancement that started 5 min after flare onset. EUV lines normally emitted in the upper transition region displayed a sudden enhancement coinciding in time and location with a bright H point, which is believed to be near the flare trigger or onset point. The EUV flash and the initial H brightening, both of which occurred near the center of the activated filament, were followed by a second EUV enhancement at the end of the filament. The complete disruption of the filament was accompanied by a third EUV enhancement and a rapid rise in the soft X-ray emission spatially coincident with the disappearing filament. From the change of magnetic field inferred from H filtergrams and from force-free field calculations, the energy available for the flare is estimated at approximately 10³¹ erg. Apparently, changes in the overlying coronal magnetic field were not required to provide the flare energy. Rather, it is suggested that the flare actually started in the twisted filament where it was compressed by emerging fields. Clearly, the flare started below the corona, and it appears that it derived its energy from the magnetic fields in or near the filament.NCAR is sponsored by NSF.     

The proton-proton reaction and related reactions in an intense magnetic field

The reaction rates for the proton-proton reaction and the related electron capture reaction in a strongly magnetized relativistic electron gas of arbitrary degree of degeneracy are computed. The proton-proton reaction rates are unaffected by the presence of the magnetic field for field strengths up to the critical valueH _q =m ² c ³/e=4.414×10¹³G. For fields greater thanH _q , the proton-proton reaction rates are enhanced linearly with (=H/H _q ).The PeP reaction is investigated in detail for a wide range of temperatures, densities and magnetic field strengths that are of interest. The main results are as follows: In the non-degenerate regime the reaction rates are significantly reduced for high temperatures (T ₉5) and low fields (1). For instance, _pep(H)=0.04 _pep(O) at =10^–3,T ₉=10. For relatively high fields (>1) and low temperatures (T ₉2), the reaction rates are enhanced approximately linearly with . In the complete degenerate regime the reaction rates are reduced up to one-third of the field-free value for moderate densities (₆/_e10). At high densities (₆/_e10) the reaction rates are unaffected by the magnetic field.     

An example for solar flares caused by magnetic field non-equilibrium

Using a photospheric magnetogram of the solar activity complex HR 16862, 16863, 16864 at the end of May 1980 as boundary data a sequence of three-dimensional force-free magnetic fields with spatially constant ( defined by the equation × B = B) is calculated, including numerical field-line tracing. The field is assumed not to be frozen-in and ¦¦, which is a measure of the magnetic free energy, is assumed to increase with time due to some dynamo mechanism. Variation of , starting from = 0, produces a catastrophe-like change of the topology of a field-line system corresponding to an arch filament system connecting the leading spot of HR 16863 with the trailing spot of HR 16862. This topological change is interpreted as causing a series of large homologous flares with synchronous flaring in the two spots. The catastrophe-like behaviour of the field topology is attributed to the nonlinear field-line equations.     

X-ray and Hα observations of a filament-disappearance flare: An empirical analysis of the magnetic field configuration

A flare event occurred which involved the disappearance of a filament near central meridian on 29 August 1973. The event was well observed in X-rays with the AS & E telescope on Skylab and in H at BBSO. It was a four-ribbon flare involving both new and old magnetic inversion lines which were roughly parallel. The H, X-ray, and magnetic field data are used to deduce the magnetic polarities of the H brightenings at the footpoints of the brightest X-ray loops. These magnetic structures and the preflare history of the region are then used to argue that the event involved a reconnection of magnetic field lines rather than a brightening in place of pre-existing loops. The simultaneity of the H brightening onsets in the four ribbons and the apparent lack of an eruption of the filament are consistent with this interpretation. These observations are compared to other studies of filament disappearances. The preflare structures and the alignment of the early X-ray flare loops with the H filament are consistent with the schematic picture of a filament presented first by Canfield et al. (1974).     

Constraints of the neutrino magnetic moment from white dwarf cooling

The neutrino magnetic moment provides an additional energy emission in stars. It will accelerate the white dwarf cooling process and reduce the life time of the white dwarf, but it causes a conflict with the observation. We use observational constraints to derive an upper limit for the neutrino magnetic moment: 4.0×10^–12 _B      

Возникновение полярных и экваториальных конденсаций В плазме вБлизи переменного магнитного диполя

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The motion of a plasma in the time-dependent dipole magnetic field is considered. It is shown that the increase of the magnetic moment of the dipole (for example, as the result of the explosion of a magnetic star) leads to the concentration of a plasma in the polar regions. Likewise, a decrease of the magnetic moment (contraction of a star) would lead to the concentration of surrounding plasma in the equatorial plane. This process may be of importance in astrophysics and, particularly, in the dynamics of nebulae and non-stationary star envelopes.

     

Равновесие, устойчивость и эволюия вращающегося замагниченного газового диска

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The exact solutions for the equilibrium of rotating gaseous disk with poloidal magnetic field are obtained. The stability of the disk with respect to uniform expansion and contraction is investigated by means of the variational principle. It is shown that if the equilibrium is determined by gravitational and magnetic forces only, the disk is in neutral equilibrium with respect to perturbations of the form r=r. The instability to short-waves perturbations is studied by the quasi-classical method. The analysis shows that if the magnetic field isH>2G, where is the surface density, then these perturbations are stabilized. The configurations of the electrical field induced by the rotation of magnetized disk are found. In conclusion, the questions of the evolution of the disk are discussed in connection with the quasar model when pulsar-like radiation is taken into account.

     

About the motion of a heavy flexible string attached to the satellite in the central field of attraction

The motion of a heavy inextensible flexible string attached to the satellite in the central gravitational field is discussed. It is supposed that the mass of the string is infinitesimally small compared to the mass of the satellite and hence it does not affect the latter's motion. Under the assumption that the satellite moves along the Keplerian elliptical orbit (in particular circular orbit), the relative motion of the string is investigated. It has been shown that the motion of the flexible string is unstable which is stable in the case of a solidified string.

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Influence du champ magnétique terrestre sur le mouvement d'un satellite autour de son centre de gravité

Résumé On étudie l'effet du champ magnétique terrestre sur le mouvement d'un satellite autour de son centre de gravité. Le satellite possède une symétrie dynamique et un moment magnétique propre dirigé suivant l'un des axes principaux d'inertie; le champ magnétique terrestre est assimilé au champ d'un dipôle dont les pôles coïncident avec les pôles terrestres. On néglige les perturbations de la trajectoire du satellite qui est supposée circulaire. La position du satellite par rapport à son centre de gravité est repérée dans un système d'axes lié au plan de l'orbite et le mouvement est décrit à l'aide des angles d'Euler , , . La symétrie sphérique et le choix du moment magnétique sur l'un des axes d'inertie permettent d'éliminer l'angle .La solution pour et peut se développer en séries de puissance d'un petit paramètre . Les séries convergent pour ||<1.Lorsque le moment magnétique est faible on la rotation du satellite rapide, est faible. Les développements sont calculés effectivement jusqu'à ².La comparaison des résultats avec l'intégration numérique du système d'équations différentielles est satisfaisante.

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The effect of the Earth's magnetic field on the motion of a satellite around its centre of mass is investigated. The satellite is assumed to be dynamically symmetric and to be magnetized in the same direction as that of a principal axis. The Earth's magnetic field is assumed to be a dipole field whose poles coincide with the rotation poles of the Earth. The satellite's orbit is circular and perturbations are neglected. The position of the satellite with respect to its centre of mass is given with respect to a coordinate system fixed in the orbital plane and the motion is described by Euler's angles , , . The spherical symmetry and the coincidence of the magnetic moment with a principal axis allow one to eliminate the angle .The solution for and , can be expanded in power series for small parameter .The series converge for <1. is small for a small magnetic moment or a high angular velocity of the rotating satellite. The terms of the expansion of the series are calculated up to ².The comparison of the results with those obtained by numerical integration of the differential equation is satisfactory.

     

Hydrogen and helium spectra in large magnetic fields

The energy levels and wave functions of hydrogen and helium atoms in the presence of large (10⁷G) magnetic fields are found by assuming that the eigenvalues and eigenvectors may be approximated by those of a truncated Hamiltonian matrix. In these atoms, fields of this size produce, in addition to the usual Paschen-Back effect, a quadratic Zeeman effect. This contributes an upward shift to the energy of all levels, which at sufficiently high fields dominates the Paschen-Back splitting.The behavior of a number of eigenvalues and wave functions as a function of magnetic field is presented. The effects of the field on the wavelengths and strengths of the components of H and the helium lines 4471, 4026 and 4120 as well as the forbidden 4025 are examined. In hydrogen the lines are split into components attributed to the now nondegenerate transitionsnlm _lnlm_l. In helium forbidden lines are excited, which may develop strengths larger than those of the allowed lines.     

Vector magnetic field evolution,energy storage,and associated photospheric velocity shear within a flare-productive active region

The evolution of vector photospheric magnetic fields has been studied in concert with photospheric spot motions for a flare-productive active region. Over a three-day period (5–7 April, 1980), sheared photospheric velocity fields inferred from spot motions are compared both with changes in the orientation of transverse magnetic fields and with the flare history of the region. Rapid spot motions and high inferred velocity shear coincide with increased field alignment along the B _L= 0 line and with increased flare activity; a later decrease in velocity shear precedes a more relaxed magnetic configuration and decrease in flare activity. Crude energy estimates show that magnetic reconfiguration produced by the relative velocities of the spots could cause storage of 10³² erg day^–1, while the flares occurring during this time expended 10³¹ erg day^–1.Maps of vertical current density suggest that parallel (as contrasted with antiparallel) currents flow along the stressed magnetic loops. For the active region, a constant-, force-free magnetic field (J = B) at the photosphere is ruled out by the observations.Presently located at NASA/MSFC, Huntsville, Ala. 35812, U.S.A.