Exact static equilibrium of vertically oriented magnetic flux tubes

A method is prescribed for generating exact solutions of magnetostatic equilibrium describing a cylindrically symmetric magnetic flux tube oriented vertically in a stratified medium. Given the geometric shape of the field lines, compact formulae are presented for the direct calculation of all the possible distributions of pressure, density, temperature and magnetic field strength compatible with these field lines under the condition of static equlibrium. The plasma satisfies the ideal gas law and gravity is uniform in space. A particular solution is obtained by this method for a medium sized sunspot whose magnetic field obeys the similarity law of Schlüter and Temesváry (1958). With this solution, it is possible for the first time to illustrate explicitly the confinement of the magnetic field of the cool sunspot by the hotter external plasma in an exact relationship involving both magnetic pressure and field tension as well as the support of the weight of the plasma by pressure gradients. It is found that the cool region of the sunspot is not likely to extend much more than a few density scale heights below the photosphere. The sunspot field approaches being potential in the neighbourhood of the photosphere so that the Lorentz force exerting on the photosphere is less than what the magnetic pressure would suggest. This accounts for how the sunspot field can be confined in the photosphere where its magnetic pressure is often observed to even exceed the normal photospheric pressure. The energy mechanism operating in the sunspot and the question of mechanical stability are not treated in this paper.Normally at Lau Kuei Huat (Singapore) Private Limited, 55 Shipyard Road, Singapore 22, Singapore.     

Flare build-up in low-lying magnetic loops

B. C. Low's study on non-linear force-free magnetic field is extended in an effort to explain the preflare low-lying magnetic loops observed by Skylab. Using Low's method of analytical continuation, a revised boundary-value problem is solved analytically. It is shown that high magnetic loops will evolve into low-lying ones when both the shear angle between field line and the neutral line increases with time and the foot-points of the field lines close upon the neutral line. The density, temperature and electric current density are high in these lowlying loops, thus providing conditions for flare (especially proton flare) build-up.     

Including stereoscopic information in the reconstruction of coronal magnetic fields

We present a method to include stereoscopic information about the three-dimensional structure of flux tubes into the reconstruction of the coronal magnetic field. Due to the low plasma beta in the corona we can assume a force-free magnetic field, with the current density parallel to the magnetic field lines. Here we use linear force-free fields for simplicity. The method uses the line-of-sight magnetic field on the photosphere as observational input. The value of is determined iteratively by comparing the reconstructed magnetic field with the observed structures. The final configuration is the optimal linear force-free solution constrained by both the photospheric magnetogram and the observed plasma structures. As an example we apply our method to SOHO MDI/EIT data of an active region. In the future it is planned to apply the method to analyse data from the SECCHI instrument aboard the STEREO mission.     

The rotation of the solar atmosphere

A model of the solar atmosphere is presented in which we discuss the conservation of angular momentum for the two basic states in which the solar gas can be: namely, either confined by closed field lines or outflowing along open magnetic field lines. It can be shown that the boundary conditions are in general different for these two cases. From this we obtain the results that in the closed configuration the gas can corotate at the solar surface with the magnetic field lines and its angular velocity will then increase with height, whereas for a gas flowing along an open field line the angular velocity will decrease. An exception to the latter case can be found where the open magnetic field lines are strongly nonradial and where the density is a slowly varying function of radius. In such regions the angular velocity may initially increase with height, reach a maximum and then decrease.Kitt Peak National Observatory Contribution No. 439.Operated by The Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.     

Electron reflectometry in the martian atmosphere

The technique of electron reflectometry, a method for remote estimation of planetary magnetic fields, is expanded from its original use of mapping crustal magnetic fields at the Moon to achieving the same purpose at Mars, where the presence of a substantial atmosphere complicates matters considerably. The motion of solar wind electrons, incident on the martian atmosphere, is considered in detail, taking account of the following effects: the electrons' helical paths around the magnetic field lines to which they are bound, the magnetic mirror force they experience due to converging field lines in the vicinity of crustal magnetic anomalies, their acceleration/deceleration by electrostatic potentials, their interactions with thermal plasma, their drifts due to magnetic field line curvature and perpendicular electric fields and their scattering off, and loss of energy through a number of different processes to, atmospheric neutrals. A theoretical framework is thus developed for modeling electron pitch angle distributions expected when a spacecraft is on a magnetic field line which is connected to both the martian crust and the interplanetary magnetic field. This framework, along with measured pitch angle distributions from the Mars Global Surveyor (MGS) Magnetometer/Electron Reflectometer (MAG/ER) experiment, can be used to remotely measure crustal magnetic field magnitudes and atmospheric neutral densities at ∼180 km above the martian datum, as well as estimate average parallel electric fields between 200 and 400 km altitude. Detailed analysis and full results, concerning the crustal magnetic field and upper thermospheric density of Mars, are left to two companion papers.     

Electrostatic instability excited by an electron beam trapped in the magnetic mirror of the magnetosphere

A dispersion relation which takes into account the nonuniformity of the magnetic field as well as the plasma density along the field lines is obtained for an electrostatic wave propagating parallel to the magnetic field. This dispersion relation is solved for a particular case in which a group of electrons with a monochromatic distribution in magnetic moment is mixed with a low energy plasma. Such electrons are shown to excite ion acoustic waves carried by the low-energy plasma component near multiples of the bounce frequency of these electrons. The theoretical results are applied to explain electrostatic oscillations with a period of approximately fifty seconds observed in the high energy electron fluxes at synchronous altitude.     

The structure of the white-light corona and the large-scale solar magnetic field

The large-scale density structure of the white-light solar corona has been compared to the organization of the solar magnetic field as identified by the appearance of neutral lines in the photosphere in order to examine whether any consistent relationship exists between the two. Data from the High Altitude Observatory's Mk-III K-coronameter have been used to describe the coronal density structure, and observations from several sources, beginning with observations from the University of Hawaii Stokes Polarimeter have been used to establish the magnetic field distribution. Stanford magnetograms as well as the neutral line inferred from potential field models have also been examined. During the period covering Carrington rotations 1717 to 1736 brightness enhancements in the low corona tend to lie over the global neutral sheet identified in the photospheric magnetic field. The brightest of these enhancements, however, are associated with neutral lines through active regions. These associations are not 1-1, but do hold both in stable and evolving conditions of the corona. We find a significant number of long-lived neutral lines, including filaments seen in H, for which there are not coronal enhancements.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

On the stability of twisted magnetic fields

The stability of helical magnetic fields is investigated when fluid motions are present along the lines of force. The general dispersion relation is obtained and some limiting cases are examined. It is established that the configuration can be unstable when the velocity field exceeds a certain critical value. This result is to be compared with the case when the helical fields confined by a rigid boundary are stable when the energy density in the velocity field is at least equal to that of the magnetic field.     

The conditions for the existence of the electric field opposite to the current along the magnetic field lines in the thin plasma

The flow of the current along the magnetic field lines in the thin plasma directed opposite to the electric field is considered. The particles moving to the equatorial plane are supposed to have mirror points above the region of absorption (the ionosphere) and the particles moving to the ionosphere are supposed to have mirror points below the region of absorption. The current, therefore, flows. The functions of the distribution of the electrons and ions are considered to be mono-energetic. The energies of the electrons and the ions and their densities on the boundary of absorption are estimated for the potential difference and for the current density which are typical for the auroral field lines.     

关于日冕中稳恒态磁流体力学流动的一个定理

本文报告了在日冕或其他天体物理环境中，沿磁力线流动的稳恒态磁流体力学流动的一个定理和一个重要关系。它们是利用宏观动能密度对磁能密度的比例导出的。     

太阳多极活动区中的磁重联、剪切低磁弧内的强电流和冕穴结构

探讨了复杂磁结构上空日冕物理状态与磁剪切的关系．结果表明在强磁场的磁中性线上方磁剪切会引起具有强电流和较强等离子体压力的低磁弧．这可解释Ｙｏｈｋｏｈ 卫星的观测结果     

A self-consistent model of the magnetosphere with centrifugal wind,I

Under the purely centrifugal approximation (gravity and pressure force are neglected), stellar magnetospheres are classified into three main types of different physical properties in the two-dimensional parameter space. They are characterized essentially by the strength of the magnetic field and the plasma density, at the base of the magnetosphere. Among the three types, the type II magnetosphere has moderate surface densities for a given field strength, and is expected to possess a centrifugal wind blowing across the magnetic field lines without affecting them appreciably. Such a situation may be realized through a modification of the electric field from that under the ideal-MHD condition, owing to the inertia of a plasma. In order to illustrate this mechanism, the type II magnetosphere is taken up for a numerical simulation. The effect of artificial viscosity is avoided by integrating the characteristic equations for both components of the plasma, instead of solving the fluid equations directly. Our model reproduces a disk-like outflow of the centrifugal wind across the magnetic field lines which are closed through the equatorial plane.     

Adiabatic motion of an electron bunch in the magnetosphere

The motion of a space-limited energetic electron bunch injected along geomagnetic field lines is studied. Dimensions of a bunch moving in a weakly inhomogeneous medium are shown to change so that a product of the bunch and background densities divided by a square of the magnetic field appears to be an adiabatic invariant. The bunch decelerates when its density tends to the background electron density.     

The density and magnetic field of the dense cores of the molecular cloud L 1630

The density and magnetic field strength of the dense cores in the Orion B molecular cloud are derived from the observed radius and FWHM line width based on the model of a uniformly magnetic sphere. We obtain the average magnetic field strength of 110μG and the average density of 8 × 10⁴/cm³ for the 39 cores, which agree closely with the observations. The method for deriving the density and magnetic field strength is applicable to the cores with R>0.2pc.     

The effect of magnetic field morphology on the structure of massive IRDC clumps

Infrared dark clouds (IRDCs) have dense elongated clumps and filaments with the favorable viewing condition of being on the near-side of a bright mid-infrared background. The clumps usually have multiple cores around the center. In this work, we study the effect of magnetic field morphology on the structure of massive IRDC clumps. To achieve this goal, we consider an axisymmetric isothermal oblate IRDC clump, embedded into a constant external magnetic field. We assume a polynomial function for the magnetic field morphology inside the clump. We use the numerical iterative methods to solve the equations: the successive over-relaxation method to find the magnetic and gravitational fluxes, and then the biconjugate gradient method to find the optimized values of mass and current densities. The results show that the IRDC clump will be very elongated along the perpendicular direction of the external magnetic field lines. Also, the assumption of choosing of a polynomial function for the magnetic field morphology leads to the formation of dense regions around the center. The greater the density of the central region, the larger the density of these dense regions and the closer to the center. The presence of these dense regions can lead to the formation of cores at these points.     

Magnetic field dragging and the vertical structure of thin accretion discs

The presence of an imposed vertical magnetic field may drastically influence the structure of thin accretion discs. If the field is sufficiently strong, the rotation law can depart from the Keplerian one. We consider the structure of a disc for a given eddy magnetic diffusivity but neglect details of the energy transport. The magnetic field is assumed to be in balance with the internal energy of the accretion flow. The thickness of the disc as well as the turbulent magnetic Prandtl number and the viscosity, α , are the key parameters of our model. The calculations show that the radial velocity can reach the sound speed for a magnetic disc if the thickness is comparable to that of a non-magnetic one. This leads to a strong amplification of the accretion rate for a given surface density. The inclination angle of the magnetic field lines can exceed the critical value 30° (required to launch cold jets) even for a relatively small magnetic Prandtl number of order unity. The toroidal magnetic fields induced at the disc surface are smaller than predicted in previous studies.     

The structure of coronal arcades and the formation of solar prominences

The temperature and density are obtained for coronal plasma in thermal and hydrostatic equilibrium and located in a force-free magnetic arcade. The isotherms are found to be inclined to the magnetic field lines and so care should be taken in inferring the magnetic structure from observed emission.When the coronal pressure becomes too great, the equilibrium ceases to exist and the material cools to form a quiescent prominence. The same process can be initiated at low heating rates when the width or shear of the arcade exceeds a critical value.We suggest that the prominence should be modelled as a dynamic structure with plasma always draining downwards. Material is continually sucked up along field lines of the ambient arcade and into the region lacking a hot equilibrium, where it cools to form new prominence material.     

Computation of inner coronal magnetic fields from longitudinal field components on a spherical photosphere

A method is developed which for a certain day permits the approximate calculation of closed small and large scale magnetic field lines. From the photospheric longitudinal components of the magnetic field measured at this day normal components are derived taking into account the curvature of the solar surface. The magnetic fields are assumed to be potential or force-free fields.The method is applied to observations of September 5 and September 7, 1973. The projected magnetic field lines are compared with the loop structures which are visible in XUV pictures taken on these days. In the cases where no good agreement could be obtained for potential fields, force-free fields are calculated and fitted to the observed structures.     

The coronal and interplanetary magnetic fields at the time of the solar eclipse of 7 March, 1970

The magnetic field in the outer corona and in interplanetary space has been calculated from the photospheric magnetic fields measured around the time of the 7 March, 1970 eclipse. The field-line maps are compared with eclipse photographs showing coronal structures out to about 12 r . The projected field lines as well as the observed streamers appear straight. This is caused by the rapid expansion of the outer corona and is not an indication of corotation. The calculations show that the angular velocity of the coronal plasma decreases rapidly with distance.The relation between magnetic fields and density enhancements is discussed. The field strength in the photosphere seems to determine the amount of mechanical heating of the lower corona. The density structure higher up in the corona will, however, depend decisively on the topology of the field, particularly on whether we are on open or closed field lines, and not simply on field strength.The calculations show a sector structure of the interplanetary field, which agrees well with spacecraft observations. Also the magnitudes of the observed and calculated interplanetary field agree after the Mt. Wilson magnetograph data have been corrected to account for the temperature and saturation effects in the spectral line Fei 5250 Å.On leave from the Astronomical Observatory, Lund, Sweden.The National Center for Atmospheric Research is sponsored by the National Science Foundation.