Force-free magnetic fields with singular current density surfaces and their stability

Starting from Bernstein's principle of magnetohydrodynamic energy, a general analysis is presented for the stability of a kind of 1-D force-free magnetic fields with singular current density surfaces and a single parameter in cylindrical coordinates. It is found that in the parameter space of this kind of force-free magnetic fields there simultaneously exist stable and unstable regions. Their stability is solely determined by the radial distribution of the magnetic pitch in the neighborhood of the cylinder axis, and is independent of the presence of singular current density surface at the boundary of the field.     

Observational evidence for solar coronal decimetric radio pulsations with very short periods

Using the decimetric (700–1500 MHz) radio spectrometer and the synchronous observational system with high temporal resolution at four frequencies (1420, 2130, 2840 and 4260 MHz) of Yunnan Observatory, two rare events were observed on 2001 June 24 and 1990 July 30. The former was a small radio burst exhibiting pulsations with short periods (about 29, 40 and 100 ms) in the impulsive phase. The latter was a large radio burst, which at 2840 MHz produced radio pulsations with period of about 30 ms. This paper focuses on pulsations with very short periods in the range of 29–40 ms. The mechanism of generation of such pulsations may be modulation of radio radiation by the periodic trains of whistler packets originating in unstable regions of the corona. Alternatively, these pulsations can be attributed to wave-wave non-linear interactions of electrostatic upper hybrid waves driven by beams of precipitating electrons in flaring loops.     

The magnetic field strength and energy flux of energetic electrons in a microwave burst source region

The observations of a microwave burst with multiple impulses on 1993 Oct 2, 073940–074100 UT are analysed. This event consists of multiple impulses superimposed on a slowly varying burst background. Our formula for coronal magnetic field diagnostics was used here for the first time to derive the field strength and information on the energetic electrons. The results are: 1) The mean spectral index of the impulsive component in the optically thin part is less than that of the slow background by 1 (a harder spectrum). The mean brightness temperature at 19.6 GHz of the former is 6 times that of the latter. 2) The mean magnetic strengths of the impulse and slow burst regions are 158 G and 531 G, respectively. The time variation in the slow burst region is saddle-shaped, being 50% lower in the middle than at the beginning and end. 3) The column density NL and number density N of energetic electrons in the impulsive component are 4% and 8% of those of the slow component, but the energy flux and emission coefficient are 100% and 800% greater. The two components appear to be produced by two different electron groups with different energy distributions in two different regions.     

细磁通量管运动的特征

从细磁通量管运动方程组导出了特征速度、特征线及其相容关系。这些结果是用特征线法研究细磁通量管运动的基础，也是正确提出定解问题的依据。表征细磁通量管横向波传播的特征速度与管内流动的ＡｌｆｖｅｎＭａｃｈ数有关。当管内流速超过ｋｅｌｖｉｎ－Ｈｅｌｍｈｏｌｔｚ不稳定性临界值时，不存在横向波模式。     

The Gnevyshev-Ohl rule for physical parameters of the solar magnetic field: The 400-year interval

We consider a number of questions pertaining to the famous Gnevyshev-Ohl rule. We discuss various formulations of the rule and show that it is not violated in its exact formulation in the last pair of 11-year cycles 22 and 23. The rule has been found to hold not only for statistical indices of solar activity but also in the context of physical parameters of the solar magnetic field: the sunspot magnetic flux and the open magnetic flux. We have established that the hypothesis by Usoskin et al. (2001) about the “loss“ of one cycle at the end of the 18th century allows the Gnevyshev-Ohl rule, which regulates the behavior of physical parameters of the solar magnetic field, to be made universal, without any exceptions, at least in the last 400 years. Thus, in fact, we can talk about the Gnevyshev-Ohl law of the long-term dynamics of the solar magnetic field, a law that holds at both normal and extreme levels of solar activity.     

The time-delayed solar cycle luminosity modulation by sub-surface magnetic flux tubes

In order to explore the mechanism of the solar cycle luminosity change observed by the Active Cavity Radiometer Irradiance Monitor (ACRIM) I experiment on board of the spacecraft Solar Maximum Mission, we examined running mean time profiles of the daily ACRIM data from the declining phase of solar cycle 21 to the rising phase of solar cycle 22. By comparing them with those of the daily sunspot number, integrated surface magnetic field flux, integrated He I 10830 Å line equivalent width data, and two kinds of data sets of the daily integrated Ca II K line index as indices of the surface magnetic activities, we found (i) that the running mean time profiles of the six independent data sets have several peaks and valleys in common in one solar cycle with time intervals on the order of a few hundreds of days, and (ii) that the peaks and valleys of the ACRIM data profiles followed the peaks and valleys of all the other five indices of the surface activities by 40 to 60 days. This time delay phenomenon suggests (i) that the luminosity modulation was not directly caused by dark and bright features of the surface magnetic activities that the other five indices represent, and (ii) that the missing sunspot radiative flux which was blocked by sub-surface magnetic flux tubes of sunspots and sunspot groups should be re-radiated 40 to 60 days after the surface emergence of the magnetic flux tubes. The concept of the time delay resolves the enigma of the missing sunspot radiative flux and the enigma of the ACRIM experiment that the luminosity dropped when a sunspot or a sunspot group appeared on the surface while the yearly mean of the luminosity decreased and increased along with the decrease and increase of the yearly sunspot number of the 11-year solar cycle. A model of the mechanism to understand these phenomena is presented and its application to other stars is suggested.     

The rise of twisted magnetic flux tubes

Sunspots are caused by the eruption of magnetic flux tubes through the solar photosphere: current theories of the internal magnetic field of the Sun suggest that such tubes must rise relatively unscathed from the base of the convection zone. In order to understand how the structure of the magnetic field within a buoyant flux tube affects its stability as it rises, we have considered the quasi-two-dimensional rise of isolated magnetic flux tubes through an adiabatically stratified atmosphere. The magnetic field is initially helical; we have investigated a range of initial field configurations, varying the distribution and strength of the twist of the field.     

Properties of flux tubes and the relation with solar irradiance variability

At the solar surface the magnetic field is bundled into discrete elements of concentrated flux, often referred to as magnetic flux tubes, which cover only a small fraction of the solar surface. Flux tubes span a whole spectrum of sizes, ranging from sunspots to features well below the best currently obtainable spatial resolution. Whereas sunspots have been well studied, our knowledge of the true brightness of small-scale magnetic features is hampered by the insufficient spatial resolution of the observations. A better understanding of the thermal and magnetic properties of these small-scale features, however, is crucial for an understanding of (climate-relevant) long-term solar irradiance variations.     

Magnetosonic waveguide model of solar wind flow tubes

We consider solar wind flow tubes as a magnetosonic wave-guide. Assuming a symmetric expansion in edges of slab-modelled wave-guide, we study the propagation characteristics of magnetosonic wave in the solar wind flow tubes. We present the preliminary results and discuss their implications.     

On the possibility of investigation of the magnetic field structure in subphotospheric layers of the Sun according to observations of sunspot torsional oscillations

A method of investigation of the magnetic field structure in subphotospheric layers of the Sun has been developed. The method is based on observations of the torisonal oscillations of single sunspots. Characteristics of the torsional oscillations have been obtained from observations of the longitudinal magnetic field and radial velocities of seven single sunspots in the photospheric line Fe I λ5253 Å. The parameters of the torsional oscillations and magnetic tubes in the deep layers have been determined. The radius of the cross section of a magnetic flux tube forming a sunspot is greatest near the Sun’s surface and is approximately equal to the radius of a sunspot umbra. Down to the deeper layers, it decreases quite quickly. The longitudinal electric current appearing in the magnetic tube changes direction. The typical time of the current changes is determined by the period of the torsional oscillations. The intensity of the longitudinal magnetic field in the tube increases with depth. The Alfven wave velocity averaged over the length of a magnetic tube is tens or hundreds of times less than this velocity in a sunspot umbra. It decreases with an increase in the period of oscillations. A decrease in the Alfven wave velocity leads to an increase in the twisting angle of magnetic field lines.     

The variation of the angle between the magnetic and rotation axes in a collapsing star

We derive the formula for the variation of the magnetic axis in a collapsing oblique rotator. Our results of calculation show that the case of the magnetic axis coincident with the rotation axis is unstable, and the angle between the two axes will grow on any small perturbation.     

The betatron effect in collapsing magnetic traps

We consider the question of how the betatron effect affects the particle acceleration in a magnetic trap with a rapidly decreasing length. We show that the additional increase in energy caused by the betatron acceleration as the trap contracts is exactly offset by the decrease in the time of particle confinement in the trap, because the loss cone becomes larger during the contraction. As a result, the particle energy at the time of escape from the trap remains the same as that in a collapsing trap without contraction. We estimate the Alfvén-pumping efficiency in a collapsing trap in connection with the problem of particle acceleration in solar flares. The additional energy acquired by particles from magnetic-field oscillations is shown to be negligible. We discuss the possible observational manifestations of the betatron effect in solar flares.     

Fractal properties of solar magnetic fields

We study the spatial properties of solar magnetic fields using data from the Solar Vector Magnetograph of the Marshall Space Flight Center (MSFC) (FeI 5250.2 Å) and SOHO/MDI longitudinal magnetic field measurements (Ni 6767.8 Å) (96-min full-disk maps). Our study is focused on two objects: the fractal properties of sunspots and the fractal properties of the spatial magnetic field distribution of active and quiet regions considered as global structures. To study the spatial structure of sunspots, we use a well-known method of determining the fractal dimension based on an analysis of the perimeter—area relation. To analyze the fractal properties of the spatial magnetic field distribution over the solar surface, we use a technique developed by Higuchi. We have revealed the existence of three families of self-similar contours corresponding to the sunspot umbra, penumbra, and adjacent photosphere. The fractal coefficient has maxima near the umbra—penumbra and penumbra—photosphere boundaries. The fractal dependences of the longitudinal and transverse magnetic field distributions are similar, but the fractal numbers themselves for the transverse fields are larger than those for the longitudinal fields approximately by a factor of 1.5. The fractal numbers decrease with increasing mean magnetic field strength, implying that the magnetic field distribution is more regular in active regions.     

Converging and diverging convection around axisymmetric magnetic flux tubes

A numerical model of idealized sunspots and pores is presented, where axisymmetric cylindrical domains are used with aspect ratios (radius versus depth) up to 4. The model contains a compressible plasma with density and temperature gradients simulating the upper layer of the Sun's convection zone. Non-linear magnetohydrodynamic equations are solved numerically and time-dependent solutions are obtained where the magnetic field is pushed to the centre of the domain by convection cells. This central magnetic flux bundle is maintained by an inner convection cell, situated next to it and with a flow such that there is an inflow at the top of the numerical domain towards the flux bundle. For aspect ratio 4, a large inner cell persists in time, but for lower aspect ratios it becomes highly time dependent. For aspect ratios 2 and 3 this inner convection cell is smaller, tends to be situated towards the top of the domain next to the flux bundle, and appears and disappears with time. When it is gone, the neighbouring cell (with an opposite sense of rotation, i.e. outflow at the top) pulls the magnetic field away from the central axis. As this happens a new inner cell forms with an inflow which pushes the magnetic field towards the centre. This suggests that to maintain their form, both pores and sunspots need a neighbouring convection cell with inflow at the top towards the magnetic flux bundle. This convection cell does not have to be at the top of the convection zone and could be underneath the penumbral structure around sunspots. For an aspect ratio of 1, there is not enough space in the numerical domain for magnetic flux and convection to separate. In this case the solution oscillates between two steady states: two dominant convection cells threaded by magnetic field and one dominant cell that pushes magnetic flux towards the central axis.     

Time-dependent interaction of granules with magnetic flux tubes

The time-dependent interaction of the granulation velocity field with a magnetic flux tube is investigated here. It is seen that when a magnetic field line is displaced normal to itself so as to simulate thebuffeting action of granules, a flow of gas is initiated along the field. By choosing a lateral velocity field which is consistent with observations of granules, it is found that the resulting gas motion is a downward flow with a velocity compatible with the observed downflow in isolated photospheric flux tubes. It is therefore proposed that the observed photospheric downflow is a manifestation of the interaction of granules with flux tubes.     

行星际磁通量绳尺度及能量研究

行星际磁通量绳是太阳风中一种重要的磁结构.从1995-2001年的Wind卫星的观测资料中认证了144个行星际磁通量绳.其时间尺度介于几十分钟到几十小时之间,其空间尺度呈现连续分布.通过估算磁通量绳单位长度的能量和总能量发现:磁通量绳的能量分布和耀斑的类似都呈现很好的幂率谱.通过讨论行星际磁通量绳和太阳活动爆发的关系,建议所有的小、中、大尺度通量绳都直接起源于太阳上的爆发,和磁云对应于通常的日冕物质抛射一样,中、小尺度的通量绳对应相对较小的日冕物质抛射.