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We investigated the complex subsurface magnetic rope structure of a super-active region NOAA 10488. With the set of twisted magnetic loop, knot and bifurcate configuration ,we could explain the complicated flux emerging, developing and disappearing by following Tanaka model (Tanaka, 1991). Based on Huairou photospheric vector magnetograms, we calculated the current helicity and found the dominant helicity sign is positive. We deduced that the whole active region might be one twisted magnetic rope.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html
The continuum energy distributions of R127 and R110 in the outburst phase are fitted by use of a optically envelope model. Both stars show two peaks in the continuum energy distributions in which one lies in the short-wavelength range (near 1250Å) and the other in the optical band. We suggest that the fluxes in the UV and optical bands may have different origins: the UV flux comes from the central star and the optical flux comes from the expanded optically envelope. We construct such a model for LBVs with the use of two LTE atmosphere models with different temperatures, and find it to be in satisfactory agreement with the observed spectral energy distributions of R127 and R110.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html
We analyze the formation process of delta configuration in some well-known super active regions based on the photospheric vector magnetogram observations. It is found that the magnetic field in the initial developing stage of some delta active regions shows the potential-like configuration in the solar atmosphere, the magnetic shear develops mainly near the magnetic neutral line with the magnetic islands of opposite polarities, and the large-scale photospheric twisted field forms late gradually. Some results are obtained: (1) The analysis of magnetic writhe of whole active regions cannot be limited in the strong field of sunspots, because the contribution of the fraction of decayed magnetic field is non-negligible. (2) The magnetic model of kink magnetic ropes, proposed to be generated in the sub-atmosphere, is not consistent with the evolution of large-scale twisted photospheric transverse magnetic field and the relationship with magnetic shear in some delta active regions completely.
The photospheric current helicity density is a quantity reflected the local twisted magnetic field and relates to the remain of transfered magnetic helicity in the photosphere, even if the mean current helicity density brings the general chiral property in a layer of solar active regions. As the emergence of new magnetic flux in active regions, the changes of photospheric current helicity density with the injection of magnetic helicity into the corona from the sub-atmosphere can be detected. Because the injective rate of magnetic helicity and photospheric current helicity density contain the different means in the solar atmosphere, the injected magnetic helicity probably is not proportional to its remain (current helicity density) in the photosphere. A evidence is that the rotation of sunspots does not synchronize with the twist of photospheric transverse magnetic field in some active regions (such as, delta active regions) completely, as one believes that the rotation of sunspots reflects the magnetic one and connects with the injection of magnetic helicity. They represent different aspects of magnetic chirality. The synthetical analysis of the observational magnetic helicity parameters actually provides a relative complete picture of magnetic helicity and its transfer in the solar atmosphere.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html
Coronal heating is an important problem in solar physics. With the development of highly qualified instruments, such as TRACE, SOHO and Yohkoh, more and more observations about coronal loops have been obtained. The coronal loops' heating, being an important ingredient of coronal heating, has been paid particular attentions recently. But there are still some key issues about the structure and mechanism of the loops' heating unresolved. In this paper, after a brief review on the latest progress in both observations and modeling of coronal loops, we emphatically discuss the heating of hydrostatic loops and hydrodynamic loops based on the 1D model. The prospect of the subject is presented.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html
Coronal mass ejections (CME) from the solar corona are the most spectacular phenomena of solar activity. Solar physicists are tried to relate CME with other forms of solar activities. CMEs are the result of a large scale rearrangement of solar magnetic field and they are often observed as an eruption of twisted magnetic fields from the solar atmosphere. SOHO/LASCO detected (http://cdaw.gsfc.nasa.gov/CME_list) more than 7500 CMEs during 1996-2003 June. The catalog contains all the CMEs with primary characteristics e.g. linear speed, central position angle, and the angular width. We will use these characteristics to study the variations of CME within these periods. The period starts from the sunspot minimum to entire sunspot maximum range where the solar activity is high. Solar proton events ($E>10MeV$) were collected from NOAA website (http:/www.lep.gsfc.nasa.gov/waves) of the associated CMEs with halo CMEs. We find from CMEs data that the occurrence of average CME rate is 121.51 per month during June 1999 to June 2003 (sunspot maximum range) whereas the occurrence of average CME rate is 41.24 per month during January 1996 to May 1999 (sunspot minimum range), although during the year 1996 (when the average sunspot number is 8.6 per month) occurrence of average CME rate is 18.16 per month. The CME occurrence rate is also correlated with the sunspot numbers with high statistically significant level. The CME number is highest in 2002 but CME is higher in 2000 than in 2001. There is an overall similarity between sunspot number and CME rates but there are differences particularly from June 1999 which is the beginning of the sunspot maximum range. The CME rate peaks in September 2001 to October 2002, which is about 1.25 year after the sunspot maximum. Similarly the average speed of CME at the time of sunspot maximum range and sunspot minimum range are 575 km/sec. and 266 km/sec. respectively. This means that the average speed of CME increases from 1996 to June 2003. The CME speed is also correlated with the sunspot numbers with less significant level than the average rate of CME occurrence. The maximum monthly average speed is about 677.3 km/sec. at the time of April 2001, which is about 5 months earlier than the second sunspot maximum. From the preliminary list of halo CME events from SOHO/LASCO during January 1996 to June 2003 we find that the occurrence rate of average halo CME events during January 1996 to May 1999 is about 1.10 per month whereas during June 1999 to June 2003 is about 4.00 per month, during the year 1996 only two halo CMEs is occurred. We also find that the average speed of halo CME events during sunspot minimum range is 838 km/sec, whereas average speed of the halo CME events during sunspot maximum range is 1000 km/sec. Although during the year 1996 the average speed of halo CME events is 451 km/sec. From the characteristics of halo CMEs in years we find that the number of halo CME increases from 1996 to 2001 and the number of halo CME is maximum in the year 2001, after that number of halo CME decreases. In the 23rd solar cycle maximum solar activity occurred during June to September 2001 we call the time as 2nd sunspot maximum time. We also find that number of high speed ($>1000\,km/sec.$) halo CME is highest during 2nd sunspot maximum range (i.e., during 2001-2002). We find from the halo CME data that average halo CME speed increases from 1996 to 1998 and then decreases from 1998 to 2000 and again increases from 2000 to 2003 and we expect that the average speed of halo CME will decrease after 2003. We find 78 solar proton events ($E >10MeV$) from CME and about 43 of them are from halo CME during 1996 to 2003. We noticed that the maximum solar proton events occurred at the second sunspot maximum, which is occurred after $1\frac12$ sunspot maximum in the 23rd solar cycle. We find there exist 5 phases of solar proton events ($E >10MeV$) data in the 23rd solar cycle. The first phase is at the sunspot minimum, 2nd phase is after two years from the sunspot minimum, 3rd phase is at the time of sunspot maximum and 4th phase occurs just one and half year (usually it is about 2/3 years) after the sunspot maximum and 5th phase occurs 2/3 years before the sunspot minimum. We find six solar proton events ($E >10MeV$) data within 1999 to 2003 with 12900 to 31700 pfu which produced strong geomagnetic storms and all of them are very high-speed halo CME. It is known that very fast CMEs $(V_{p}> 1000$km/sec.) are capable of causing extremely intensive geomagnetic storm when $D_{st} $ index ${<}\,{ -}300nT$. We find that there is a significant correlation between the speed of the CME and solar proton events ($E>10MeV$) data. Solar radius measurement at Rio de Janeiro from 1997-2000 shows that the solar radius varies in phase with the solar cycle. Astrolabes of Antalya, Rio de Janeiro and Santiago suggest that the solar radius varies in phase with the solar cycle. From the detection of solar radius variations with MDI on board SOHO it is found that the solar radius increases with the number of sunspots[l]. It appears that solar radius variation and solar neutrino flux variation with the solar cycle is due to the variation of solar core pulsations and is mainly responsible for the variation of CME and its speed that is in phase with the solar cycle. We suggest that the above-mentioned characteristics are interrelated and that a pulsating solar core may be their common origin [2].To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html
Observations of the low solar corona, in particular in the EUV, are an effective means of identifying the solar sources of coronal mass ejections (CMEs). SOHO/EIT, with its continuous 24 hours per day coverage, is well suited to perform this task. Source regions and start times of frontside full and partial halo CMEs (that may be geoeffective) can thus be determined. The most frequent EUV signatures of CMEs are coronal dimmings. EIT waves, eruptive filaments and post-eruption arcades are also reliable signatures. Frontside halo CMEs with source regions close to the solar disc center have the strongest chance to hit the Earth. The inspection of the EIT data together with photospheric magnetograms may give an idea about the ejected interplanetary flux rope magnetic field and, in particular, about the presence or absence of southward (geoeffective) field. If a source region is situated close to the solar limb, the corresponding CME also may be geoeffective, as the CME-driven shocks have large angular extent. In this case the storm can be produced by the sheath plasma behind the shock, provided it contains strong enough southward interplanetary magnetic field. Some implications for the operational space weather forecast are discussed. EIT and LASCO are capable to identify the solar sources of the most of geomagnetic storms. In some cases, however, the identification is uncertain, so the observations by the future STEREO mission will be needed for the investigation of similar events.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html
Large Solar Energetic Particles (SEPs) are closely associated with coronal mass ejections (CMEs). The significant correlation observed between SEP intensity and CME speed has been considered as the evidence for such a close connection. The recent finding that SEP events with preceding wide CMEs are likely to have higher intensities compared to those without was attributed to the interaction of the CME-driven shocks with the preceding CMEs or with their aftermath. It is also possible that the intensity of SEPs may also be affected by the properties of the solar source region. In this study, we found that the active region area has no relation with the SEP intensity and CME speed, thus supporting the importance of CME interaction. However, there is a significant correlation between flare size and the active region area, which probably reflects the spatial scale of the flare phenomenon as compared to that of the CME-driven shock.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html
This book describes the two main applications of plasma physics, laboratory research on thermonuclear fusion energy and plasma-astrophysics of the solar system, stars, accretion discs, etc., from the single viewpoint of magnetohydrodynamics (MHD). This provides effective methods and insights for the interpretation of plasma phenomena on virtually all scales, ranging from the laboratory to the Universe. The key issue is understanding the complexities of plasma dynamics in extended magnetic structures.
The book starts with an exposition of the elements of plasma physics, followed by an in-depth derivation of the MHD model. By means of the conservation laws, different model problems for laboratory and astrophysical plasmas are formulated. The spectral theory of MHD waves and instabilities is then developed in analogy with quantum mechanics. The centrepiece is the analysis of inhomogeneous plasmas with intricate spectral structures that provide a unified view of waves and instabilities in plasmas as different as tokamaks and coronal flux tubes. This is illustrated by the magnetic structures and dynamics observed in the solar system, and analysed in detail for cylindrical flux tubes. Advanced chapters on wave damping and resonant heating expose the wonderful interplay of physics and mathematics.
In order to provide the student with all the tools that are necessary to understand plasma dynamics, the classical MHD model is developed in great detail without omitting steps in the derivations. The necessary restriction to ideal dissipationless plasmas, in static equilibrium and with inhomogeneity in one direction, is more than compensated by the insight gained in the intricacies of magnetized plasmas. With this objective the size of the original manuscript, including advanced topics of magnetohydrodynamics, became impractical so that we decided to split it into two volumes.
In this chapter we will make an excursion to the vast territory of magnetic structures and dynamics of the different plasmas encountered in the solar system, in particular the Sun and the planetary magnetospheres. While laboratory plasma confinement for the eventual goal of energy production also provides a rich diversity of magnetic structures, their topology and dynamics is always constrained by the presence of a fixed set of coils with programmed currents that should control the spatial and temporal behaviour of the magnetic fields. The reason is clear: for the success of thermonuclear energy production, plasma dynamics and complexity are not really desired. The best thing would be to extract energy from a plasma that just sits quietly inside a toroidal vessel and the engineering approach to plasma confinement is to try to approach this ideal as closely as possible. The history of thermonuclear fusion research demonstrates impressive progress along this line but also the immense obstacles, due to complex plasma dynamics, that have to be overcome. In astrophysical plasmas, on the other hand, no such human engineering constraints exist: plasmas and their associated magnetic structures appear to be almost free to exhibit the bewildering variety of different dynamics that are observed on virtually all length and time scales.
Space missions in the second part of the twentieth century have played an important role in demonstrating the different magnetic structures and dynamics of plasmas in the solar system.
The dynamics of magnetically confined plasmas, as exploited in laboratory nuclear fusion research and observed in astrophysical systems, is essentially of a macroscopic nature so that it can be studied in the fluid (MHD) model introduced in Chapter 2. The ‘derivation’ of the MHD equations in Chapter 3 provided indications about the range of validity and the limitations of the equations. In the present chapter, we will develop the MHD model for the interaction of plasma and magnetic field in detail and, thus, obtain a powerful ‘picture’ for the dynamics of the mentioned plasmas.
Recall from the introduction of Chapter 3 that the equations of magnetohydrodynamics can be introduced either by just posing them as postulates for a hypothetical medium called ‘plasma’ or by the much more involved procedure of averaging the kinetic equations. Whereas Chapter 3 was mainly concerned with the second method, in the present chapter we exploit the first method: we simply pose the equations and use physical arguments and mathematical criteria to justify the result. We continue the exposition of Section 2.4.1, where we already encountered the relevant equations.
Postulating the basic equations
The ideal MHD equations describe the motion of a perfectly conducting fluid interacting with a magnetic field. Hence, we need to combine Maxwell's equations with the equations of gas dynamics and provide equations describing the interaction.
First, consider Maxwell–s equations, already encountered in Chapters 2 and 3.
How does one know whether a dynamical system is stable or not? Consider the well-known example of a ball at rest at the bottom of a trough or on the top of a hill (Fig. 6.1). There is a position (indicated by the full circle) where the potential energy W due to gravity has an extremum W0. Displacing the ball slightly to a neighbouring position (at the open circle) results in either a higher or a lower potential energy W1. This corresponds to a stable system in the first case (W1 > W0) and an unstable system in the second case (W1 < W0).
Already at this stage some important observations can be made, viz.:
(a) We have tacitly assumed that the constraining surface is curved, i.e. either convex or concave, so that there is a position of rest, which is called the equilibrium position. In this case, one may rescale the potential energy such that the equilibrium state corresponds to W0 = 0, and W1 becomes the potential energy of the displacement, which is called the perturbation.
(b) If the constraining surface is flat and inclined, the system is not in equilibrium and the ball simply rolls along the plane. This lack of equilibrium, when W has no extremum, should be well distinguished from neutral or marginal stability, when W1 = W0. The latter situation occurs when the surface is horizontal, so that the value W = 0 may be assigned to both W0 and W1.
Under ordinary circumstances, matter on Earth occurs in the three phases of solid, liquid, and gas. Here, ‘ordinary’ refers to the circumstances relevant for human life on this planet. This state of affairs does not extrapolate beyond earthly scales: astronomers agree that, ignoring the more speculative nature of dark matter, matter in the Universe consists more than 90% of plasma. Hence, plasma is the ordinary state of matter in the Universe. The consequences of this fact for our view of nature are not generally recognized yet (see Section 1.3.4). The reason may be that, since plasma is an exceptional state on Earth, the subject of plasma physics is a relative latecomer in physics.
For the time being, the following crude definition of plasma suffices. Plasma is a completely ionized gas, consisting of freely moving positively charged ions, or nuclei, and negatively charged electrons. In the laboratory, this state of matter is obtained at high temperatures, in particular in thermonuclear fusion experiments (T ∼ 108 K). In those experiments, the mobility of the plasma particles facilitates the induction of electric currents which, together with the internally or externally created magnetic fields, permits magnetic confinement of the hot plasma. In the Universe, plasmas and the associated large-scale interactions of currents and magnetic fields prevail under much wider conditions.
In Chapters 7 and 9, the MHD spectral analysis of an ideal plasma with inhomogeneities in one spatial direction led to singular second order differential equations for the plasma displacement in the direction of inhomogeneity: Eqs. (7.91) and (9.31). The two singularities of these equations give rise to two continuous parts of the MHD spectrum, as demonstrated in Section 7.4 for slab geometry and in Section 9.2.2 for cylindrical geometry. It was shown that the eigenfunctions corresponding to these Alfvén and slow magneto-sonic continua possess non-square integrable tangential components leading to extreme anisotropic behaviour. Clearly, this has a dramatic effect on the dynamical behaviour of inhomogeneous plasmas. In the present chapter, we will discuss the consequences of these continuous spectra for the dynamical response of an inhomogeneous plasma slab or cylinder to periodic, multi-periodic, or random external drivers. This will lead to the concepts of resonant absorption of waves and phase mixing of neighbouring magnetic field lines.
Resonant ‘absorption’ (or ‘dissipation’) and phase mixing are fundamental properties of MHD waves that are studied in many different plasma systems. These phenomena affect the dynamics of plasma perturbations significantly and often dominate the energy conversion and transport in inhomogeneous plasmas. Since they are basic to MHD wave heating and acceleration of plasmas, they deserve special attention. In fact, since all plasmas occurring in nature are – to a higher or lower degree – inhomogeneous and since waves can be excited easily in plasmas, resonant absorption and phase mixing frequently occur.
There are basically two ways of introducing the equations of magnetohydrodynamics:
(a) pose them as reasonable postulates for a hypothetical medium called ‘plasma’;
(b) derive them by appropriate averaging of kinetic equations.
Our approach, starting with Chapter 4, is mainly along the lines of the first method, pioneered by Grad [98, 32] in a series of lecture notes, using physical arguments and mathematical criteria to justify the results. In this chapter, the main steps of the second method will be discussed and shown to be somewhat unsatisfactory since they involve a number of approximations that are often difficult to justify. The reason for going through this analysis anyway is that it provides understanding of the domain of validity of the MHD description and that it indicates what kind of modifications are in order when this description fails.
Mathematically inclined readers may skip this digression, where most results from kinetic theory are not derived but simply stated, and continue reading with Chapter 4. Also, the serious student of magnetohydrodynamics is advised to turn to a detailed study of the present chapter only after a first reading of Chapters 4–11 on basic MHD since the level of this chapter is essentially that of the advanced theory, but it has been placed here because this is where it logically belongs.
We give a ‘derivation’ of the MHD equations by averaging the kinetic equations for plasmas.