Formation of current helicity and emerging magnetic flux in solar active regions

Mon. Not. R. Astron. Soc. 326, 57±66 (2001) Formation of current helicity and emerging magnetic flux in solar active regions Hongqi Zhang w Beijing Astronomical Observatory, National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012, China Accepted 2000 November 17. Received 2000 November 1; in original form 2000 June 2 ABSTRACT This paper aims to study the properties of the current helicity in solar active regions. The current helicity provides different information relative to the magnetic helicity and has a simple relationship with the magnetic energy in the approximation of the force-free field. For example, we analyse the active region (NOAA 7321) which was a newly emerging delta active region in 1992 October. It provides good evidence for the development of the magnetic chirality in the solar active regions. From a series of photospheric-vector magnetograms and corresponding soft X-ray images, it is found that the newly emerging magnetic flux associates the current helicity from the subatmosphere in the active regions with the redistribution of the current helicity density in the upper atmosphere, i.e. it provides observational evidence that flux and helicity emerge together. Key words: Sun: magnetic fields. 1 INTRODUCTION The study of the magnetic (current) helicity in the solar atmosphere is an important project. It relates to the generation of the magnetic field from the subatmosphere and the solar activity on the solar surface. The trans-equatorial sign role of the magnetic (current) helicity in the solar active regions was discovered by Seehafer (1990). He found that the most active regions have negative magnetic (current) helicity in the northern hemisphere and positive magnetic helicity in the southern hemisphere. More recently, Martin, Bilimora & Tracada (1993) showed that in the northern hemisphere most large quiescent filaments are dextral, while in the southern hemisphere they are sinistral. The relationship between the electric current helicity in solar active regions and the solar activity cycle was presented by Bao & Zhang (1988) and Zhang & Bao (1998). It is normally believed that the magnetic field forms near the bottom of the convection zone and emerges at the solar surface where it forms solar active regions. The observational current helicity in the active regions, which is inferred by the photospheric-vector magnetograms, probably comes from the emergence of pre-twisted magnetic ropes in the subatmosphere or the linkage of a different magnetic field, and so on, near the solar surface. However, until now it has not been very clear whether magnetic helicity comes up into the solar atmosphere together with new magnetic flux or whether the flux comes up with no helicity and gets the helicity later, for instance through the action of twisting or shearing motion on the already emerged magnetic field. Thus the study of the magnetic chirality in active regions w E-mail: zhq@sun10.bao.ac.cn becomes an important project. The photospheric-vector magnetic field brings some information on the generation of the magnetic field from the subatmosphere. A possible way to solve this question is to follow the evolution of the photospheric-vector magnetic field in the individual active regions, in order to analyse the possible development of the magnetic shear and the relationship between it and the current helicity, i.e. detailed observations are needed to decide whether or not the magnetic flux comes pretwisted. As the total photospheric current helicity density cannot be inferred by the photospheric-vector magnetograms if one rejects more assumptions, the different current helicity parameters [such as B k 7 B k and a(introduced from the force-free field) etc.] have be used to analyse the magnetic chirality in the active regions. Thus, the comparison between the different current helicity parameters also becomes important and necessary. In this paper, we will analyse the formation of the non-potential magnetic field from a series of photospheric-vector magnetograms in emerging flux regions. We will compare the photosphericvector magnetic field with the morphological configuration of solar X-ray images in the analysis of the spatial configuration of the magnetic field. This is useful in enabling us to understand the basic properties of the magnetic chirality in active regions. We will also present the configuration of the electric current helicity and the relationship it has with the non-potential magnetic field in active regions. 2 DEFINITION OF MAGNETIC HELICITY Helicities are topological measures of the structural complexity of the corresponding fields (Moffatt 1978; Berger & Field 1984; q 2001 RAS

58 H. Zhang Figure 1. Two kinds of basic configuration of the magnetic field, corresponding to the linkage (left) and twist (right) of the lines of force in the active regions. Seehafer 1990). The helicity of magnetic fields may be characterized by several different parameters. The magnetic helicity density h m ˆ A B, with A the vector potential for magnetic field B (i.e. B ˆ 7 A, which measures the chirality of magnetic lines of force. The total magnetic helicity in a volume V is H m ˆ A B d 3 x; 1 V which may not be conserved when finite resistivity is present (Berger & Field 1984). However, such magnetic helicity cannot be measured in the solar atmosphere as yet. The current helicity density h c (where h c ˆ B 7 B is another important physical quantity for measuring the magnetic field in the solar atmosphere. If the magnetic field is not completely parallel to its vector potential, we can define 7 A ˆ ba D; 2 where D is a perpendicular vector to A. We can then obtain h c ˆ b 2 h m 7b A D f D 7 A: where f (D) is a function of the vector D; f D ˆbD 7 D: This means that the relationship between the magnetic and current helicities is complex. We notice that only if 7 A is parallel to A does the relationship of both helicity densities become simple, and both helicity densities constantly show the same sign. According to definition (Berger & Field 1984; Berger 1986), the magnetic helicity can be separated into two kinds. One is the self-helicity, which relates to the magnetic flux tubes that are twisted themselves. This helicity may be used to analyse the twisted magnetic flux loops. The other is the mutual helicity, which relates to the different magnetic flux tubes linked to each other. As the helicity contains both, the total helicity can be written in the form H m ˆ TF 2 2LF 1 F 2 ; where the T is the twisted number of magnetic flux F and L is the linkage number of different magnetic fluxes F 1 and F 2. These relate to two basic spatial configurations of the magnetic field systems in the solar active regions, shown in Fig. 1. The similar case can also be used in the analysis of the current helicity. Now we consider two thin, untwisted, isolated, linked, closed current loops (labelled 1 and 2), as shown in Fig. 2; the electric current is assumed to vanish outside these current loops. In the case of two linked current loops, the current helicity H c ˆ H c1 H c2 : We show that if V completely encloses the two current loops, H c1 ˆ V B 7 B d3 x provides a measure of their linkage. The differential element of volume for each current loop is d 3 x ˆ dl ds where dl is an element of length along the loop and ds is the 3 4 5 surface cross-section of the current loop. For a thin, untwisted current loop, both dl and ds are parallel to the direction of the electric current, so B 7 B d 3 x ˆ B 7 B dl ds ˆ B dl7 B ds; so that H c1 ˆ Figure 2. Two linked, untwisted, closed electric current loops. c1 s1 B dl7 B ds: We recall that the current through a surface s is defined as I ˆ c= 4p Š s7 B ds and can also be expressed as I ˆ c= 4p Š lb dl; where l is the contour following the perimeter of s. The current I 1 ˆ c= 4p Š s17 B ds is invariant along c1. If we neglect the coefficient c/(4p), we can obtain H c1 ˆ I 1 B dl ˆ I 1 I 2 : 8 c1 From symmetry, it is seen that H c2 ˆ I 1 I 2 also. Hence, the current helicity of two lined, thin, untwisted current loops is H c ˆ 2I 1 I 2 : 9 Similar to equation (5), the general total current helicity can be written in the form, H c ˆ TI 2 2LI 1 I 2 ; where I, I 1 and I 2 are the electric current systems. 6 7 10 3 OBSERVATIONAL EVIDENCE OF THE MAGNETIC CHIRALITY Although the determination of the real total current helicity is a complex problem in the solar atmosphere, the marks of the current helicity in the photosphere can be detected by the photosphericvector magnetograms. We can analyse the distribution of the current helicity density and its evolution in the photosphere.

Current helicity in solar active regions 59 Oct. 25, 01:07 Oct. 25, 05:41 Oct. 26, 01:38 3.1 Evolution of the photospheric magnetic field For the analysis of the development of the magnetic chirality, as an example, we firstly illustrate the emergence of magnetic flux forming a new active region (NOAA 7321) from 1992 October 25 to November 1, observed at the Huairou Solar Observing Station at Beijing Astronomical Observatory. The preliminary analysis on the relationship between the emerging magnetic flux and the electric current in this region was made by Zhang (1995). This emerging flux region (EFR) was born on 1992 October 23 and gradually formed a new delta active region (NOAA 7321). In Fig. 3, we show the vector magnetograms resolved for a 1808 ambiguity of the transverse field in AR 7321 on 1992 October 25± 27. The tilt angle of the magnetic axis of the main poles of this active region relative to the solar equator is about 608. The magnetic flux of this active region emerged rapidly, as the main poles of opposite polarity moved away at a speed of about 0.4 km s 21 on 1992 October 25. The transverse components of the magnetic field gradually became parallel to the magnetic neutral line in the middle of the active region. On October 26 and 27, the shear of the transverse field increased near the magnetic neutral line and the total flux of the longitudinal field also increased. We also notice that in the northern side of the magnetic main pole of negative polarity and in the southern side of the magnetic main Oct. 27, 02:53 Figure 3. Vector magnetograms resolved in the 1808 ambiguity of transverse fields in the active region (NOAA 7321) observed on 1992 October 25±27. The solid (dashed) contours correspond to positive (negative) fields of ^50, 200, 1000, 1800, 3000 Gauss. North is at the top and east is at the left of the diagram. pole of positive polarity, the transverse magnetic field extends out and almost keeps the basic configuration of the potential field. Amounts of magnetic flux emerged mainly near the magnetic neutral line between the magnetic main poles (S and N) of opposite polarities (Zhang 1995). A similar case was demonstrated by Zhang & Song (1992). The magnetic shear in the emerging flux region is normally caused by the emergence of the small-scale magnetic flux of opposite polarity. The two-dimensional singular points of the magnetic field, inferred by the photospheric-vector magnetograms on October 27 in the active region, were analysed by Wang, Wang & Qiu (1999). The magnetic connectivity of the transverse field provides the vestige of the topology of the magnetic lines of force in (or above) the photosphere. These provide a basic morphology of the formation of the twisted magnetic field in the active region.> 3.2 Current helicity parameters B k 7 B k and a We notice that the current helicity density can be written as the sum of two parts: h c ˆ B k 7 B k B ' 7 B ' : 11 The first term on the right-hand side of equation (11) is observable, and can be inferred by photospheric-vector magnetograms (Abramenko, Wang & Yurchishin 1996). However, the

60 H. Zhang Oct. 25, 01:07 Oct. 25, 05:41 Oct. 26, 01:38 second term is difficult to obtain as one rejects more assumptions, because no observational data of the vector magnetic field in the other layers of the solar atmosphere is available. If one neglects the second term (the combined one between the transverse magnetic field and transverse current in the current helicity) on the right-hand side of equation (11), one can analyse the chirality of the magnetic field near the areas where the longitudinal component of the magnetic field and electric current are more dominant than the transverse ones. It is important to provide the basic property of the twisted magnetic field near strong magnetic poles in the active regions, because one normally believes that the magnetic poles extend vertically upwards from the deep atmosphere (Lites & Skumanish 1990). The observational part of the current helicity density is B y h c obs ˆ B k 7 B k ˆ B z x 2 B x : 12 y The derivatives are approximated by a four-point differencing scheme; the current helicity is computed at each intersection of four magnetogram pixels and the calculated helicity is smoothed to eliminate the small-scale fluctuation of the observed data (Wang, Xu & Zhang 1994). Fig. 4 shows the distribution of the current helicity parameter Oct. 27, 02:53 Figure 4. The electric current helicity parameter B k 7 B k in the active region (NOAA 7321) during 1992 October 25±27, and the size of the maps is the same as Fig. 3. The solid (dashed) contours indicate the positive (negative) regions of the current helicity distribution of ^0.0025, 0.01, 0.025, 0.05, 0.09, 0.15 G 2 m 21. The arrows mark the transverse magnetic field. B k 7 B k inferred by the vector magnetic field in the active region (NOAA 7321). If it is compared with the distribution of the corresponding magnetogram, we can find that the opposite signs of the current helicity exist in the same main magnetic poles in the active region, and the sign of the current helicity does not change. The intensity of the current helicity parameter B k 7 B k in the solar photosphere increased over the period October 25±27. The mean intensities of the current helicity parameter B k 7 B k for the areas of B k. 250 G in Fig. 4 at 01:07 and 05:41 ut on October 25, 01:28 ut on October 26 and 02:53 ut on October 27 are 2.6, 4.7, 8.5 and 7.2 respectively (the unit is 10 22 G 2 m 21 ). We can infer that the helicity in most areas of the active region is positive. This means that the current helicity density increases in the photosphere with the emerging magnetic flux in the active region. On 1992 October 27, the total intensity of the current helicity parameter B k 7 B k in the photosphere was 5:3 10 10 G 2 m (in unit height) and was larger than the normal active regions (Zhang & Bao 1998). From letting B ˆ Bb; where b is a unit vector along the direction of the magnetic field, the current helicity density may be written in the form (Zhang & Bao 1999) h c ˆ ab 2 ; 13

Current helicity in solar active regions 61 Oct. 25, 01:07 Oct. 25, 05:41 where a ˆ b 7 b: 14 The term a is a factor reflecting the helicity of the unit magnetic field. In the approximation of the force-free field, the a-factor can be obtained by the formula a ˆ 7 B k B k B 2 k Oct. 26, 01:38 ˆ B y x 2 B x y =B z : 15 We display the a-factor in the areas where the longitudinal magnetic field is larger than 250 G, in the active region NOAA 7321, shown in Fig. 5. Even through, the most information of the a-factor in the active region can be found. This approximation can probably be used to analyse the photospheric strong magnetic field in active regions (Canfield et al. 1993), but has failed in some of areas in the active region because the gas pressure is not negligible relative to the magnetic pressure (Zhang 1997). If the deviation from the force-free field is not obvious in the active regions, it can be used to analyse the distribution of the photospheric magnetic helicity density. The current helicity density in the photosphere inferred by equation (13) has the same sign distribution with a in the approximation of the force-free field. The mean current helicity densities (ab 2 ) for the areas of B k. 250 G at 01:07 and Oct. 27, 02:53 Figure 5. The a-factor of the force-free field in the areas where the longitudinal field is larger than 250 G in the active region (NOAA 7321) during 1992 October 25±27; the size of the maps is the same as Fig. 3. The solid (dashed) contours indicate the positive (negative) a-factor distribution of ^0.25, 1.0, 2.5, 5., 10.0, 15.0 (10 27 M 21 ). The others are the same as Fig. 4. 05:41 ut on October 25, 01:28 ut on October 26 and 02:53 ut on October 27 in the active region NOAA 7321 are 3.1, 6.7, 15.6 and 14.4 respectively (the unit is 10 22 G 2 m 21 ). The current helicity density h c ˆ ab 2 shows a similar tendency to increase with B k 7 B k : On the other hand, as we pay attention to the a-factor of the active region in the photosphere, we can find that the density of the a-factor did not change significantly on October 26 and 27. Wang & Wang (1998) found that in the active region NOAA 7321 the a-factor tends to retain its sign and a slow growth speed. The mean a values for the areas of B k. 250 G at 01:07 and 05:41 ut on October 25, 01:28 ut on October 26 and 02:53 ut on October 27 in Fig. 5 are 3.2, 5.6, 6.6 and 7.0 respectively (the unit is 10 28 m 21 ). This means that in the emergence of new magnetic flux in the active region the degree of twisting in the magnetic lines of force does not change significantly, except in the initial stage of the magnetic shear in the active region on October 25. As we compare the distribution of the a-factor with B k 7 B k in the photosphere, we find that both the parameters also show the same sign distribution, but the a-factor brings more information on the highly sheared magnetic field (such as near the magnetic neutral line) and also no real information on B ' 7 B ' : The resolution of the 1808 ambiguity of the highly sheared transverse magnetic field normally is difficult in areas near the magnetic neutral lines in the flare-producing active regions. The

62 H. Zhang Figure 6. The sunspot (left) and soft X-ray (right) images on October 26 (top) and 27 (bottom) in the active region NOAA 7321. magneto-optical effect is another notable problem for the measurement of transverse magnetic field near centre of the sunspots where the field is strong and with the smaller inclination of the magnetic field to the line of sight (Landolfi & Landi Degl'Innocenti 1982). The observational error (about 108 for the Huairou Magnetograph) of the azimuthal angles of the transverse field, caused by the magneto-optical effect, probably causes a change of the observed mean current helicity value, but it does not significantly change the basic information of the current helicity in the active region (Bao et al. 2000; Zhang 2000). 4 FORMATION OF MAGNETIC CHIRALITY 4.1 Configuration of soft X-ray images Fig. 6 shows sunspot and soft X-ray images on 1992 October 26 and 27 in the active region NOAA 7321 obtained by the Soft X-ray Telescope on board the Yohkoh satellite. It can be found that the basic configuration of the soft X-ray loops in the active region changed significantly. If compared with the vector magnetograms in Fig. 3, we can see that the bright loops on October 26 correspond to the magnetic main poles of opposite polarities. It can be inferred that the magnetic field likes the potential one above the photosphere. However, on October 27, the configuration of the loops is different from that on October 26 and shows more of a tendency towards the highly sheared photospheric transverse magnetic field. This is probably caused by the emergence of a non-potential field from the lower atmosphere and the rearrangement of the basic topological magnetic field in the corona. 4.2 Configuration of magnetic chirality The development of the magnetic shear with the emerging active region was discussed by Wang et al. (1994). If we compare the evolution of the current helicity parameter B k 7 B k on the different days shown in Fig. 4, the significant change of the current helicity density in the photosphere can be found. The mean growing-rate of the photospheric current helicity parameter B k 7 B k is about 1:5 10 5 G 2 ms 21 in the active region NOAA 7321, during the period 1992 October 24±27. The force-free model of the magnetic field is a powerful tool for analysing the spatial static state of the magnetic field above the photosphere. By comparing the configuration of soft X-ray images from 1992 October 26 and 27 in Fig. 6, we can show the spatial configuration of the magnetic lines of force above the photosphere extrapolated by the approximation of the linear force-free field in the active region NOAA 7321 in the top and side-on view (see Figs 7 and 8). We can see that the approximation of the potential field a ˆ 0 from October 26 in Fig. 7 is basically consistent with the distribution of the soft X-ray loops above the photosphere in the active region, although the highly sheared magnetic field forms near the magnetic neutral line. The approximation of the force-free field

Current helicity in solar active regions 63 a ˆ 0:45 unit ˆ 1 10 000 km Š observed on October 27 is used in Fig. 8. The distributions of the magnetic lines of force in both days are roughly consistent with that of the soft X-ray loops in the active region. It is evident that the formation of the large-scale sheared magnetic field is delayed more in the corona than that in the photosphere. The emerging magnetic flux changes the preexisting potential-like configuration of the magnetic field to the non-potential one in the active region. As we study the variation of the current helicity by using Faraday's law B = t ˆ 2c7 E, the evolution of the current helicity density can be derived; h c ˆ 22c7 E 7 B 2 c7 7 E BŠ: 16 t This shows a similar form to the magnetic helicity density obtained by Berger & Field (1984), h m t ˆ 22cE B 2 c7 E A fb ; 17 Figure 7. The distribution of the magnetic lines of force above the photosphere on 1992 October 26 in the active region NOAA 7321 in (top) the top and (bottom) the side-on views. The short bars and thick dashed lines mark the photospheric transverse magnetic field and magnetic neutral lines respectively.

64 H. Zhang where f is the scalar potential. As the volume V is fixed, one can integrate equation (16) over V, where S is the surface of V, tofind that dh c dt ˆ 22c 7 E 7 B d 3 x 2 c 7 E BŠ ds: V S 18 It is found that the current helicity is not conserved. If the ideal Ohm's law applies, then E ˆ 2 1/c = V B Š: We can find that the time variation of the current helicity depends on the twisted motion and variation of the magnetic field. From the second term { S 7 V B BŠ ds} in equation (18), it is found that the emergence of sheared magnetic flux in the solar surface actually reflects the transport of the current helicity density from the interface, such as the solar photosphere or subatmosphere. Moreover, the equivalent evolution of the electric current helicity also can be described by the form of the electric current systems in the solar atmosphere in equation (10). By comparing this with equations (2)±(4), one can probably obtain the conclusions that the similar conservation property of the current helicity relative to the magnetic helicity can be restricted in the approximation of the linear force-free field and that a stays constant. In the approximation of the force-free magnetic field in equation (13), we find that the change of the current helicity density obviously relates to that of the force-free factor and the magnetic energy density. The ratio between the current helicity Figure 8. The distribution of the magnetic lines of force above the photosphere on 1992 October 27 in the active region NOAA 7321 in (a) the top and (b) the side-on views. The short bars and thick dashed lines mark the photospheric transverse magnetic field and magnetic neutral lines respectively.

Current helicity in solar active regions 65 Figure 9. The topological change of the magnetic field above the photosphere in the active region on 1992 October 26 (left) and 27 (right) in the top (top) and side-on (bottom panel) views in the active region. The dashed lines mark the magnetic lines of force before the reconnection of the field. The thick arrow shows the moving direction of the emerging magnetic flux. and magnetic energy can be written in the form R ˆ Hc ˆ vb 7 B d3 x W m v B2 =8p d 3 x ˆ 8p vab2 d 3 x ˆ 8p a; v B2 d 3 x 19 where aå is the mean force-free factor. If the magnetic field in the active region does not significantly change, we can analyse the evolution of the current helicity density in the photosphere by that of the a-factor only (Pevtsov, Canfield & Metchalf 1994). However, the change of the magnetic field intensity is an important index in most of the active regions, such as emerging flux regions. This means that we also need information on the magnetic field to analyse the development of the photospheric current helicity density in the active region. From the above analysis of the photospheric-vector magnetograms and the corresponding current helicity in the active region NOAA 7321, the possible formation model of the photospheric current helicity shows the combination between the emergence of magnetic-flux arranged abnormal polarities and pre-existing magnetic field in the active region. The study of the magnetic helicity is a complex problem, because one can only obtain h m ˆ B2 20 a in the approximation of the linear force-free field (Pevtsov, Canfield & Metchalf 1995), where B and a are observable in the photosphere. It is found that the magnetic helicity density has the same sign distribution as a, but normally one cannot obtain the simple conclusion that the mean magnetic helicity density has the same sign as the mean a-value on the solar surface, because the weak a-areas, which may have the opposite sign to the mean a-value, have been amplified in the calculation. This means that the observational study of the magnetic helicity in the solar atmosphere is much more difficult than the study of the current helicity, even in the photosphere. During the development of the new active region (NOAA 7321), some flares occurred near the highly sheared magnetic neutral line in the active region (Zhang 1995; Liu et al. 1998; Wang et al. 1998). Liu et al. (1998) provided a good consistence between the extrapolated photospheric magnetic field in the high solar atmosphere in the approximation of the force-free field model and the distribution of the soft X-ray loops observed on 1992 October 27. On 1992 November 2, the large, soft X-ray flare-loops were observed from the side-on point of view as the active region rotated near the western solar limb (Ichimoto et al. 1993), and it can be inferred that footpoints of the cusp flareloops observed on November 2 were located at the magnetic main poles of opposite polarity in the active region (Sakurai 1994). It is evident that a large amount of emerging magnetic lines of force significantly change the configuration of the magnetic field above the photosphere, which triggers the reconnection of the large-scale magnetic field (i.e. the flares). A possible change of the magnetic field, caused by the emerging magnetic flux near the middle of active region, is shown in Fig. 9. One believes that the morphology of soft X-ray images reflects the configuration of the magnetic field in Fig. 6 and considers the curvature of the magnetic lines extrapolated by the force-free field in Figs 7 and 8. The rough conservation of the magnetic helicity probably exists in the rapidly reconnected process of the magnetic field above the photosphere (Berger & Field 1984) and the topology of the magnetic field changes to a relatively simple form. It is noticed that the approximation of the force-free field normally is correct in the solar corona. This means that in the upper atmosphere, the electric current is roughly parallel to the magnetic lines of force. The topological change of magnetic lines of force in the solar corona probably reflects the electric current change and gives some information on the current helicity. However, this approximation probably does not always hold in the lower solar atmosphere. The change of the current helicity density in the photosphere during solar flares was demonstrated by Bao et al. (1999), which provides a real trace of the change of current helicity above the photosphere.

66 H. Zhang 5 RESULTS After the analysis, the main results are as follows. (i) The current helicity is observable in the solar atmosphere. It is not conservative and probably changes with the evolution of the magnetic field. The relationship between the current helicity and magnetic helicity is usually complex. The current helicity shows a relatively simple relationship with the a-factor and the magnetic energy in the approximation of the force-free field. (ii) The formation of the current helicity of the active region in the solar surface is connected with the newly emerging magnetic flux. The increase of the helicity density around the main magnetic poles is continuously contributed to by a series of emerging flux with opposite polarity arrangement. This means that the topological change of the current chirality in the solar surface is probably brought up from the sub-atmosphere. ACKNOWLEDGMENTS HZ is grateful to staff at Huairou Solar Observing Station for their support in these observations. This research was supported by the Chinese Academy of Sciences and the National Science Foundation of China. REFERENCES Abramenko V. I., Wang T. J., Yurchishin V. B., 1996, Sol. Phys., 168, 75 Bao S. D., Zhang H. Q., 1998, ApJ, 496, L43 Bao S. D., Zhang H. Q., Ai G. X., Zhang M., 1999, A&AS, 139, 311 Bao S. D., Pevtsov A. A., Wang T. J., Zhang H. Q., 2000, Sol. Phys., 195, 75 Berger M. A., Field G. B., 1984, J. Fluid Mech., 147, 133 Berger M. A., 1986, Geophys. Astrophys. Fluid Dyn., 34, 265 Canfield R. C. et al., 1993, ApJ, 411, 362 Ichimoto K. et al., 1993, in Sakurai T., Hirayama T., Ai G., Proc. II Japan± China Seminar on Solar Physics, NAOJ, 151 Landolfi M., Landi Degl'Innocenti E., 1982, Sol. Phys., 78, 355 Lites B. W., Skumanich A., 1990, ApJ, 348, 747 Liu Y., Akioka M., Yan Y. H., Ai G. X., 1998, Sol. Phys., 177, 395 Martin S. f., Bilimora R., Tracada P. W., 1993, BAAS, 25, (3), 1217 Moffatt H. K., 1978, Magnetic Field Generation in Electrically Conducting Fluids. Cambridge Univ. Press, Cambridge Pevtsov A. A., Canfield R. C., Metchalf T. R., 1994, ApJ, 425, L117 Pevtsov A. A., Canfield R. C., Metchalf T. R., 1995, ApJ, 440, L109 Sakurai T., 1994, in Enome S., Hirayama T., eds, Proc. Kofu Symp., New Look at the Sun with Emphasis on Advanced Observations of Coronal Dynamics and Flares, NRO Report No. 360, NAOJ, 363 Seehafer N., 1990, Sol. Phys., 125, 219 Wang T. J., Xu A. A., Zhang H. Q., 1994, Sol. Phys., 155, 9 Wang T. J., Qiu J., Zhang H. Q., 1998, A&A, 336, 359 Wang T. J., Wang H. N., 1998, Astrophys. Rep. Special Issue, No. 4, Beijing Astron. Obs., Beijing, p. 62 Wang T. J., Wang H. N., Qiu J., 1999, A&A, 342, 854 Zhang H. Q., 1995, A&A, 304, 541 Zhang H. Q., 1997, A&A, 324, 713 Zhang H. Q., 2000, Sol. Phys., 197, 235 Zhang H. Q., Song M. T., 1992, Sol. Phys., 138, 69 Zhang H. Q., Bao S. D., 1998, A&A, 339, 880 Zhang H. Q., Bao S. D., 1999, ApJ, 519, 876 This paper has been typeset from a TEX/L A TEX file prepared by the author.