Magnetic topologies in the solar corona due to four discrete photospheric flux regions

Many dynamic phenomena in the solar corona are driven by the complex and ever-changing magnetic field. It is helpful, in trying to model these phenomena, to understand the structure of the magnetic field, i.e. the magnetic topology. We study here the topological structure of the coronal magnetic field arising from four discrete photospheric flux patches, for which we find that seven distinct, topologically stable states are possible; the changes between these are caused by six types of bifurcation. Two bifurcation diagrams are produced, showing how the changes occur as the relative positions and strengths of the flux patches are varied. A method for extending the analysis to higher numbers of sources is discussed.     

Magnetic domain structures and stray fields of individual elongated magnetite grains revealed by magnetic force microscopy (MFM)

In order to clarify the relationship between microscopic and macroscopic magnetic features of a rock, we applied magnetic force microscopy (MFM) as a local probe on a sample with an intense natural remanent magnetisation, a norite from Heskestad, Norway. We studied in detail seven magnetite (Fe₃O₄) exsolution lamellae, five of them were about 30 μm long and a few micrometers wide, two were significantly shorter; all were located in their natural host, a grain of clinopyroxene. By combining MFM images of surface magnetisation with information about shape observed with optical microscopy (OM), the internal domain structure was determined for individual grains. In general, the lamellae were pseudo-single-domain grains with open-flux domain magnetisations parallel to their long axes. The domain sizes were, in cross-section, on the order of a micrometer for the longer lamellae and about 300 nm for the short lamellae. By increasing the separation between the MFM probe and the exposed end of the lamellae, information could be obtained about the decrease in stray fields for the individual grains. Close to the lamellae, stray fields were significant even for grains with multiple domains. The largest fields were found above the largest domains. A separation of approximately one domain width was found to be a characteristic distance, where stray fields from adjacent domains begin to cancel one another.     

Modelling of magnetic data for scaling geology

Interpretation of magnetic data can be carried out either in the space or frequency domain. The interpretation in the frequency domain is computationally convenient because convolution becomes multiplication. The frequency domain approach assumes that the magnetic sources distribution has a random and uncorrelated distribution. This approach is modified to include random and fractal distribution of sources on the basis of borehole data. The physical properties of the rocks exhibit scaling behaviour which can be defined as P(k) = Ak^?β, where P(k) is the power spectrum as a function of wave number (k), and A and β are the constant and scaling exponent, respectively. A white noise distribution corresponds to β = 0. The high resolution methods of power spectral estimation e.g. maximum entropy method and multi‐taper method produce smooth spectra. Therefore, estimation of scaling exponents is more reliable. The values of β are found to be related to the lithology and heterogeneities in the crust. The modelling of magnetic data for scaling distribution of sources leads to an improved method of interpreting the magnetic data known as the scaling spectral method. The method has found applicability in estimating the basement depth, Curie depth and filtering of magnetic data.     

New energy and helicity bounds for knotted and braided magnetic fields

In this article we present a review of some of the author's most recent results in topological magnetohydrodynamics (MHD), with an eye to possible applications to astrophysical flows and solar coronal structures. First, we briefly review basic work on magnetic helicity and linking numbers, and fundamental relations with magnetic energy and average crossing numbers of magnetic systems in ideal conditions. In the case of magnetic knots, we focus on the relation between their groundstate energy and topology, discussing the energy spectrum of tight knots in terms of ropelength. We compare this spectrum with the one given by considering the bending energy of such idealized knots, showing that curvature information provides a rather good indicator of magnetic energy contents. For loose knots far from equilibrium we show that inflexional states determine the transition to braid form. New lower bounds for tight knots and braids are then established. We conclude with results on energy-complexity relations for systems in presence of dissipation.     

Geoefficiency of solar eruptive events

The sources of geomagnetic disturbances during 1999–2003 are discussed. The relation between geomagnetic activity and the rate of coronal mass ejections (CMEs), their parameters, and the dynamics of solar photospheric magnetic fields is considered. It is shown that during the reorganization of unipolar regions of the photospheric magnetic field, the number of CMEs increases and their parameters change. The geomagnetic disturbance level also increases in these periods.     

日冕物质抛射的能量来源

观测表明, 日冕物质抛射（ＣＭＥ） 伴随着闭合磁场形成开放的过程理论研究指出, 磁场在ＣＭＥ 过程中起主导作用, 而且对应于相同的边界条件, 开放场中储存的磁能最多一个系统如何能在向外输送能量的同时增加自身的能量？ 本文就该问题进行了讨论     

Results on 3-D solar magnetic field,observations and models

This review presents some of the new developments in the understanding of coronal magnetic fields in flares and coronal mass ejections. The modelling of the coronal magnetic field based on observed photospheric field permits to understand the location of energy release. Various flare observations are consistent with a model where magnetic reconnection occurs between two magnetic fields of different connectivity. Because magnetic helicity is almost conserved, the stored energy cannot be fully released in confined flares. The corona gets rid of the helicity injected by the convection zone only by ejecting part of the magnetic field. A severe physical constraint (open-field limit) on these ejections has been firmly established for force-free fields. It is, however, possible to open partially the field or to eject a twisted flux-tube keeping the energy of the field behind the open-field limit. New results show that in simply connected fields this happen after a finite time without loss of equilibrium, while in more complex topology a loss of equilibrium can still be present.     

Evolution of Magnetic Fields in Galaxies with Spiral Structure

We present simulations of the 3D nonlinear induction equation in order to investigate the temporal evolution of large-scale magnetic fields in spiral galaxies. Our model includes differential rotation, ambipolar diffusion and, based on small-scale turbulence, eddy diffusivity and the tensorial -effect with magnetic feedback. The nonaxisymmetric spiral pattern and – if considered – the vertical stratification of the galaxy are represented in its density and turbulence profile. Neglecting vertical stratification the lifetime and geometry of an initial magnetic field depend on the correlation time of interstellar turbulence _corr . Short correlation times increase the lifetime of the initial magnetic field, but the field is rapidly wound up. Its pitch-angles develop to zero. The magnetic field has disappeared after at most 1 to 1.5 Gyr. A resonance like phenomenon is found by tuning the pattern velocity of the galactic spiral. The simulations then show an exceptional amplification of the magnetic field in the case that the pattern speed and a magnetic drift velocity have similar values. Considering a vertical stratification we achieve sufficiently long living grand-designed magnetic fields excited by dynamo action. The behaviour and geometry of the resulting field is again significantly influenced by the correlation time _corr . Small values of _corr lead to axisymmetric fields with small pitch-angles and field-concentration between the spiral arms. Increasing the correlation time the solutions show larger pitch-angles; and depending on very large correlation times the galactic dynamo rather generates fields clearly within the spiral arms and having a bisymmetric structure.     

Numerical simulations of MHD dynamos

The generation of magnetic fields in space plasmas and in astrophysics is usually described within the framework of magnetohydrodynamics. Turbulent helical flows produce magnetic fields very efficiently, with correlation length scales larger than those characterizing the flow. Within the context of the solar magnetic cycle, a turbulent dynamo is responsible for the so-called alpha effect, while the Omega effect is associated to the differential rotation of the Sun.We present direct numerical simulations of turbulent magnetohydrodynamic dynamos including two-fluid effects such as the Hall current. More specifically, we study the evolution of an initially weak and small-scale magnetic field in a system maintained in a stationary regime of hydrodynamic turbulence, and explore the conditions for exponential growth of the magnetic energy. In all the cases considered, we find that the dynamo saturates at the equipartition level between kinetic and magnetic energy, and the total energy reaches a Kolmogorov power spectrum.     

地球附近第23太阳活动周磁云和非磁云ICME的对比统计

行星际日冕物质抛射（ICME）,作为影响地球空间天气的重要源头之一,根据其磁场结构特点可分为磁云（MC）和非磁云ICME两个子集.本文对第23周的磁云和非磁云ICME结构及其地磁效应进行对比统计研究.第23周ICME事件总数为317个,其中磁云占ICME比例为33.75%,非磁云ICME占66.25%.统计结果表明,非磁云ICME数与太阳黑子数呈现出非常好的正相关性,而磁云与太阳黑子数的这种相关性并不明显.相反,磁云占ICME的比率与太阳黑子数呈现出一定的反相关性.对磁云与非磁云ICME引起的地磁暴的比较研究表明：磁云及其鞘区引发的地磁暴平均水平要高于非磁云ICME及其鞘区.磁云和非磁云ICME的磁场强度、南向磁场强度和传播速度整体上都随地磁暴水平提升而增加.对磁云与非磁云ICME参数的进一步对比分析表明,磁云及其鞘区的平均磁场强度和南向磁场分量平均值都明显要比非磁云ICME的大;而二者的等离子体温度、密度和速度平均值相差并不明显.     

Radio Emission from Galactic Disks

This paper gives a short overview of the observational results on galactic magnetic fields. Interstellar magnetic fields, as deduced from multi-frequency polarization observations, show a well-ordered structure largely following the spiral arms. In some galaxies an axisymmetric spiral pattern dominates (the field being directed inwards), while others exhibit a dominant bisymmetric spiral field or mixed modes, as predicted from non-linear dynamo theory. As long as star formation activity is low, the magnetic fields are rather regular. Strong star formation leads to turbulent cloud motions and supernova explosions, which tangle the field, so that the radio emission is only weakly polarized. As a consequence the highest fractional polarizations and polarized intensities at centimeter wavelengths are found in interarm regions. At decimeter wavelengths, galactic disks become optically thick for polarized emission. In NGC 6946 the regular field is concentrated in narrow magnetic arms located in between the optical spiral arms. The field cannot simply be frozen into the gas and oriented by a density-wave flow. A galactic dynamo may provide a stable spiral pattern of the field, but non-axisymmetric models are still being developed.     

Convective dynamos with intermediate and strong fields

Abstract

The weak-field Benard-type dynamo treated by Soward is considered here at higher levels of the induced magnetic field. Two sources of instability are found to occur in the intermediate field regime M ～ T ^1/12, where M and T are the Hartmann and Taylor numbers. On the time scale of magnetic diffusion, solutions may blow up in finite time owing to destabilization of the convection by the magnetic field. On a faster time scale a dynamic instability related to MAC-wave instability can also occur. It is therefore concluded that the asymptotic structure of this dynamo is unstable to virtual increases in the magnetic field energy.

In an attempt to model stabilization of the dynamo in a strong-field regime we consider two approximations. In the first, a truncated expansion in three-dimensional plane waves is studied numerically. A second approach utilizes an ad hoc set of ordinary differential equations which contains many of the features of convection dynamos at all field energies. Both of these models exhibit temporal intermittency of the dynamo effect.     

Geomagnetic activity and wind velocity during the Maunder minimum

Following a given classification of geomagnetic activity, we obtained aa index values for the Maunder minimum (1645–1715). It is found that the recurrent and fluctuating activities were not appreciable and that the shock activity levels were very low. The aa index level was due almost entirely to the quiet days. Calculated average solar-wind velocities were 194.3 km s^–1 from 1657 to 1700 and 218.7 km s^–1 from 1700 onwards. Also, the coronal magnetic field magnitude and southward interplanetary magnetic field component Bz were lower. It is concluded that the nearly absent levels of geomagnetic activity during this period were due to lower coronal and Bz magnetic field magnitudes as well as to the continuous impinging on the Earth of a slow wind.     

The emergence of braided magnetic fields

We study the emergence of braided magnetic fields from the top of the solar interior through to the corona. It is widely believed that emerging regions smaller than active regions are formed in the upper convection zone near the photosphere. Here, bundles of braided, rather than twisted, magnetic field can be formed, which then rise upward to emerge into the atmosphere. To test this theory, we investigate the behaviour of braided magnetic fields as they emerge into the solar atmosphere. We compare and contrast our models to previous studies of twisted flux tube emergence and discuss results that can be tested observationally. Although this is just an initial study, our results suggest that the underlying magnetic field structure of small emerging regions need not be twisted and that braided field, formed in the convection zone, could suffice.     

Two examples of spectral approach to source depth estimation in gravity and magnetics

Fourier transformation of gravity and magnetic anomalies from space to the frequency domain provides aready method for source depth estimation since progressively deeper sources are indicated by the lower frequency components of an anomaly. Two examples are presented here to demonstrate the efficacy of this approach. One example pertains to the interpretation of vertical intensity magnetic anomalies over a layered ultramafic body for estimating the thickness of relatively non-magnetic layer in it and map the dispositions of the layers. The other example is the estimation of crustal thickness in the Indian region from the Bouguer anomaly map. The spectral method is shown, by these two examples, to provide a rapid and elegant tool for the source depth estimation for magnetic and gravity data.     

西安市道路灰尘磁学特征及其对环境的响应

西安市道路表面灰尘样品的环境磁学研究显示磁化率(χ)、非磁滞磁化率（χ_ARM）以及饱和等温剩磁（SIRM）均比较高,表明样品中磁性矿物含量较高.其中磁化率（χ）主要受人类活动强度影响,而非磁滞磁化率（χ_ARM）及饱和等温剩磁（SIRM）则由人为活动强度和磁性矿物种类共同决定.κ-T曲线以及等温剩磁（IRM）获得曲线显示样品中磁铁矿和磁赤铁矿等亚铁磁性矿物占主导,并可能含有少量的单质铁,其相对含量与人类活动种类有关：与单纯的交通排放及冶金活动相比,密集的人群流动可带来更多的单质铁矿物.磁畴图谱显示磁性矿物粒径变化不大,以准单畴及多畴颗粒等粗颗粒为主,明显大于成土作用形成的磁性颗粒.综合磁性矿物含量种类以及粒径可辨别污染及污染来源,提供污染监测的磁学手段,并初步进行污染来源划分.     

Solar-terrestrial storms of October 2003. 2. Five-phase dynamics of the substorm of October 28–30

The assumption that a solar-heliospheric storm has five phases is formulated based on the storm that occurred in October 2003. The first phase: slow (between solar rotations) convergent motions of photospheric sources of large-scale open solar fields (LOFs) with generation of active regions (ARs) between these fields. The second phase: magnetic energy pumping with adjustment of zero lines of the photospheric magnetic field in AR to the configuration of the LOF sector (subsector) boundaries. The third phase: AR destabilization with ordering of the complex of sporadic phenomena near ARs parallel to the zero line and fragments of the nearest LOF boundary. The fourth phase: propagation of disturbances in the near-Sun space with ordering relative to the LOF boundaries. The fifth phase: propagation of a coronal mass ejection (CME) in the inner heliosphere in the case when the axial axis of a magnetic cloud in CME is parallel to the LOF boundary and to the zero line in AR. Original results of LOF modeling and a number of substantial results of the known advanced studies of individual aspects of this storm are used to justify this dynamics as applied to the storm of October 28–30. Specific contents and features of each storm phases are presented. The specific feature of the first phase, responsible for the storm space-time scales and intensity, consisted in the displacement of the entire LOF negative magnetic flux (～5 × 10²² μs) from the north pole to the south with flowing around a midlatitude obstacle and with zonal convergent motions of LOF. The assumption of the AR configuration adjustment (the second phase) and ordering of disturbances (the third–five phases) during this storm near the subsector boundary between LOFs of identical polarity has been confirmed. It is noted that the pulse phase of the AR 0486 flare, coronal waves, and dimmings along the subsector boundary and the southwestern LOF “dam” joining ARs 0486 and 0484 (superposition of the third and fourth phases) originated almost simultaneously. The two-component disturbance structure is confirmed: halo-type CME with the axis along the LOF subsector boundary and a bright local ejection of magnetic plasma from the region above the southwestern LOF dam.     

A class of analytic solutions of the magnetic force-free field equations

Abstract

Formation of electric current sheets in the corona is thought to play an important role in solar flares, prominences and coronal heating. It is therefore of great interest to identify magnetic field geometries whose evolution leads to variations in B over small length-scales. This paper considers a uniform field B ₀[zcirc], line-tied to rigid plates z = ±l, which are then subject to in-plane displacements modeling the effect of photospheric motion. The force-free field equations are formulated in terms of field-line displacements, and when the imposed plate motion is a linear function of position, these reduce to a 4 × 4 system of nonlinear, second-order ordinary differential equations. Simple analytic solutions are derived for the cases of plate rotation and shear, which both tend to form singularities in certain parameter limits. In the case of plate shear there are two solution branches—a simple example of non-uniqueness.     

Towards the interpretation of Uranus's eccentric magnetic field

Abstract

Coriolis forces stimulate dynamo action in a rapidly-rotating fluid by promoting complexities in the pattern of fluid motions, notably departures from symmetry about the axis of rotation. This pattern and its time variations determine the instantaneous form and temporal behaviour of the magnetic field so produced. Instantaneous magnetic fields will usually exhibit in their broad-scale features approximate alignment with the rotation axis. This is borne out by observations of the magnetic fields of the Earth, Jupiter and Saturn, and it is likely on general grounds that Neptune will be found to have an aligned magnetic field. But, as is shown by laboratory and theoretical studies of thermal convection in rapidly-rotating fluids, for some ranges of rotation speed, rate of heating, etc. certain patterns can occur which in electrically-conducting fluids would produce magnetic fields exhibiting departures from alignment with the rotation axis, which instantaneously could be quite pronounced but would average out to very small values over sufficiently long periods of time. These findings indicate obvious strategies for theoretical studies towards the interpretation of Uranus's eccentric magnetic field (which need not invoke departures from axial symmetry in the thermal, mechanical or electrical boundary conditions of the dynamo region within the planet) and for further observational studies.