However, in the most of the solar atmosphere the magnetic fields are believed to be responsible for passive bottling the plasma in particular magnetic structure with the gravity playing role on the longer sizes/time scales. It is generally assumed that plasma transport is highly non-isotropic, being very efficient along the field lines (this processes being rapid, because information is transmitted along the flux tubes at the Alfven speed) and (in comparison) nearly completely prohibited across. The condition of plasma being frozen-into the field is expected to be valid about everywhere in the visible portion of the atmosphere, with the importance of the magnetic forcing growing in regions of lower plasma b (b - gas-to-magnetic pressure). Flux freezing in the coronal plasma is relaxed when local field gradients become sufficiently steep: the magnetic field then changes its topology, and releases energy by reconnection events. Transition from the dominance of gas pressure (b > 1) to magnetic field pressure (b < 1) occurs within the observed layers (transition region). In a picture shared at present by the most of researches, so called magnetic funnels are rooted in the network elementary magnetic flux-tubes. They are rapidly widening to fill the whole space in the corona. In order to understand the emissivity observed in lines formed below 10⁵K, Dowdy et al. (1986) and Peter (2002) postulate presence of closed loop-like structures below these magnetically open funnels (cf. Figure 1). Without the magnetic field, the temperature of the atmosphere would become more or less horizontally uniform within minutes.

With the inhomogeneous magnetic field present, its concentrations would diffuse across plasma in time scale comparable to the age of the Sun only. This picture usually standing behind ''classical'' thinking of basic atmospheric structuring, certainly does not constitute a generally valid description for most (any?) of the phenomena observed in the solar atmosphere. In numerous cases rather fast (even timescales of activity cycle are fast for typical magnetic diffusion times) reconfiguration (as deduced from the observed changes of the morphology) is observed. This necessitates corresponding changes of the (directly invisible) pattern of currents contributing to the magnetic field. Some of the field lines of such time-varying magnetic configurations are distinctive by their brightness reflecting enhanced plasma densities. An outstanding problem is our lack of understanding about how the Sun chooses different field lines to populate with plasma - a kind of evaporation scenario might be in work - see the discussion later on. In the present study we pop up selected images of solar structures where the emission patterns particularly well indicate for specific organization of links in the corona. These patterns, however complicated by themselves, reveal to us some internal order, in the sense that the overall complexity of the structures may be broken up into segments similar in shape, but different in size. These elementary structures - building blocks - appear to be replicated and linked in a self-organized manner over few orders of sizes. These we call stages. The tiniest of them are seen at the present observational limit of ~ tens of kilometers in the photosphere. The largest observed structures: stramers and CMEs extend well into the interplanetary space filled with the solar wind, for many solar radii outwards.

2  The Images

Figure 5: Evolution of the X-ray morphology of the C9.1 long duration limb flare as seen using Al12 Yohkoh SXT filters on 29 November 1992. On the upper GOES plot, the times of images are indicated.

In the image sequence seen in Figure 5, the evolution of the ''loop-summit'' kernel shows its rise (phases a-c) most probably due to the upward force exerted on it by a system of up-winded loops crossing at the kernel. The kernel appears to split during the decay phase (d-e) together with the formation of the visible arcade. In frame (f), a loop like connection is formed between these two kernels (sketched) with the arms (rooted in these edge kernels) going far away (also drawn in frame (h).

Another example shown here has been observed by SXT on 21 September 1999 and its evolution is presented in Figure 6. Here also, kernel rise is observed (a-b), splitting into two (b-c), this time more vertical (in projection). The up-winded arms become filled with plasma, probably drawn from the kernel itself (e-g). The formation of ''hanging arcade'' with the bright edge kernels is seen around (g-h) with subsequent relaxation at (i). At this late phase down- and up-winding arms cross, as is schematically drawn on top.

Figure 6: Evolution of the X-ray morphology of the C7 gradual rise and fall limb flare as seen using Al Yohkoh SXT filters on 21 September 1999. On the GOES plot, the times of images are indicated.

It appears from these and many other flare sequences studied that edge loop-top kernels are the root-points for the other (magnetic) connections. One of the most striking for us pattern of such magnetic rooting ''via kernels'' is shown in Figure 7. Here is seen in more details the transition of a longer structure connecting the opposite polarity regions of the atmosphere with the short, arcade-like bright emission patches at the foot-points. On the enlarged sequence, taken with cadence of few seconds, the root-points (circles) are seen to jump from one to the other side of this footpoint arcade, as the event evolve, with the corresponding change of the brightness of the longer interconnecting loop. This may indicate that the interconnecting loop is actually composed of two near-parallel threads, rooted to a pair of edge kernels of the foot-point arcade.

Figure 7: Left: The overlay of deconvolved SXT Al01 image (gray scale - dark indicates higher X-ray intensity) with the white light (SXT sensor) contour image. The SXT image represents the plasma being at the temperature above ~ 2 MK. The iso-contours indicate the umbrae locations. Deconvolved X-ray image represents the mean of 10 exposures taken over the period 15:20:57 UT - 15:22:20 UT on 11 July 1992 when the flare (prominent double loop) was in progress. Heavy line marks the ''neutral line'' shape as derived from the Marshall vertical magnetic field component. Right: Nine consecutive deconvolved SXT Be119 images (column order) for the indicated ''foot-point'' region of this flare. The size of individual sub-frame is 24.5 arcsec ×24.5 arcsec).

Even more illustrative in the context of ''rooting'' are images of protuberances, especially these, being ''in eruption'' where the expansion enlarges the substructures sometimes many times allowing to see them as through the magnifying glass. An example is presented in Figure 8. Here, the cool plasma resumes shapes of multiple nested arches, showing beautifully the sequence of ''rooting'' for at least three adjoining stages. It would be impossible to model this field line configuration by means of potential/force-free extrapolations from the photosphere. A particularly interesting feature is the splitting of the higher stage structures into branches at the endpoints (see magnified portions). Similar split-end branches are observed by TRACE as presented recently by Aschwanden and Title, (2004). The authors comment that the structures presented follow along dome-like and canopy-like configurations.

Figure 8: A small limb prominence about 50000 km high observed on 7 December 1970, showing the characteristic vertical structure which remains static while material flows downs through the magnetically defined filamentary tubes. These tubes are apparently ''anchored'' in the spine of the ''lower stage'' structure. The joints are presumably the plasma kernels where the magnetic field lines of the tube merge through the field lines of the spine. Picture was taken in Ha line. Enlarged are three regions in the picture showing the basic structures in more details. Courtesy: Sacramento Peak Observatory, John W. Evans Solar Facility (http://nsosp.nso.edu/esf/pics.html). Similar split-end branches are observed by TRACE (right two panels).

Figure 9: Left: Thin dark features in active region 10030 on 15 July 2002. For detailed description see Scharmer et. al., 2002. Right: Images of a solar active region taken on 24 July 2002 near the eastern limb of the Sun at heliographic coordinates S15 E53. The limb is towards the top of the image. The tick marks are 1000 km apart. The smallest resolvable features in the image are less than 100 km in size.

Figure 10: Upper row: Part of an MDI magnetogram and a co-aligned part of a simultaneous TRACE filtergram (right, from Rutten, 1999: Figure 1). Lower row: Part of a high-resolution (0.2 arcsec) G-band filtergram (bandpass 10 Å FWHM) from a sequence taken by R.A. Shine with the SVST and simultaneous Ca II K filtergram (bandpass 3 Å FWHM) of the same area (left, from Rutten, 1999: Figure 6).

So we conclude at this point that recent observations support the view of plasma being organized into systems of tiny canopies (arcades) of fluxropes joining opposite magnetic elements, as soon as they became visible from outside. Such organization is probably possible through establishing magnetic contacts across the arcade summits. This process involves the formation of turbulent kernels (of the cross-section < 100 km) at the photospheric level.

Figure 11: Observation of the large system of transient structure seen on 14 April 2000. The line drawn on an enlargement, represents a direct link between plasmas originating from active regions on both hemispheres. Envisaged stretching of the supporting magnetic field line is indicated (http://lasco-www.nrl.navy.mil/images/000714_c2eit_sm.gif).

As a consequence of looking through many of images similar to those shown above, we came to the idea of hierarchical model of organization of links in the solar atmosphere. Description of this model in more details we start with the summary of properties of its basic constituting structure.

3  Basic structure

Figure 12: Proposed hierarchical structure of magnetic links in the visible atmosphere. The basic structure consists of kernels located along the arcade summits. The most active are the edge kernels within each arcade. The links to larger scale structures occur through edge kernels. Magnetic tension is represented by arrows.

In this model, we propose that the corona consists of numerous interlinked basic structures: ''spiders''. Within the body of elementary ''spider'' a number of distinctive plasma kernels and links between them are present: legs are linking to lower structures (their kernels), arms to upper. There may be many legs in the spider (more in the smaller structures) and usually less (two) arms linking to the kernels of the structure above. Down-links provide rooting to below (eventually to magnetic elements) while up-links introduce upward stress (eventually through links to solar wind). The other, more detailed properties of the spiders are listed below.

1. Turbulent kernels at the edges of the spider are the most distinguished. They are the regions where links from ''above'' are rooted. Edge kernels are places of efficient reconnection, where the energy stored in stressed magnetic configuration is disposed off most efficiently.

2. Active kernels at the edge of the arcade are the locations of direct joints of the spider with the overlying higher structures. In this way the hierarchy is build-up: legs (loop roots) of a higher structures are anchored in the edge kernels of the lower structures.

3. Individual spider ''limbs'' are going mostly downwards. Opposite limbs form classical arcade-like structures, with the spine (arcade channel) running immediately below the loop summits. Legs originating from edge kernels are usually the best seen as they provide the most direct contacts from regions of efficient energy deposition. They connect with denser kernels below, providing channels for filling the edge kernels with plasma (through a kind of evaporation process - between kernels). Following filling of the entire spider depends on efficiency of horizontal links along the arcade channel.

4. Turbulent kernels (secondary) can be seen everywhere along the arcade. Links between them and the edge kernels allow for some plasma and energy transport ''across'' the arcade. Secondary kernels are the roots of arcade rays (''downflows to arcade'') seen sometimes on the TRACE and (overexposed) SXT images and form the end-points of ''draperies'' (see Figure 8).

5. Secondary kernels constitute the plasma source for down-flows through associated arcade legs. The entire spider plasma may eventually drain through them. This persistent downflows are easy to observe in EUV and visible spectra.

6. Kernels are the primary locations where reconnection takes place at the realistic rates. The reconnection rate depends most probably on the tension of magnetic stresses within the kernel. Increased magnetic stresses are balanced by higher gas pressure inside the kernel.

7. A hard X-ray sources are located along the arms going up from the edge kernels at its surface (its transition region).

8. The overall structure is globally stretched outwards due to interaction with the fast solar wind. This stretching is ''transported'' down within the hierarchy, with the most of stress occurring at the edge joints.

9. Owing to its frequent (overwhelming) presence everywhere in the atmosphere, spider may presumably represent a stable somewhat relaxed configuration of the magnetized rotationally stressed system. In this case the spider configuration might represent the low energy quasi-steady-state arrangement.

As concerns the plasma condition inside the turbulent kernel, we refer to the model presented by Jakimiec et al., (1998). For more details see also http://solarmuri.ssl.berkeley.edu/~hhudson/cartoons/thepages/Jakimiec.html.

Figure 13: Simplified configuration of magnetic fiels in hierarchical model in the lower and upper corona.

Within the hierarchical equatorial structure, 6 - 7 distinct stages can be identified. Each of the stages may relate to particular solar phenomenon. In Table 1, we name and list these stages and present their basic properties.

In the turbulent kernel, magnetic field is very complicated, with the magnetic field lines strongly braided, like in skein. This effectively isolates the kernel from the surrounding atmosphere allowing it to resume symmetric shape. The plasma contained in the kernel is compressed. The only transport is allowed along those few field lines which escape outside through legs and arms. Those escaping field lines provide links to the other kernels. The filling factor in the kernel is expected to be nearly one, dropping dramatically at the edges. One can think of a bunch of magnetic field lines which emerge from particular kernel with a given mass, volume and temperature. Through each emerging field line, a stretching force (magnetic tension) acts on the entire kernel. Kernel's position and dynamics result from the balance of all such forces and the gravity. If those forces are not balanced, entire kernels may move respective each other in a complicated way. For those pairs being directly linked, this relative motion may result in acceleration/deceleration (heating/cooling) of the particles fixed to connecting field lines. Magnetic mirroring of particles trapped in the portion of ''local atmosphere'' between linked kernels is easy to imagine. The hard X-rays may came as a result of the precipitation of accelerated particles escaping from the loss cone and penetrating the surface of an associated denser kernel. This might be an equivalent of the classical scenario of high energy particles penetrating the dense transition region of a classical loop. The role of the photosphere is resumed in this case by the dense plasma contained in the kernel, and the propagation of accelerated particles takes place along the arm(s) connecting the kernel to the other one in a hierarchical system. Inside the kernel, the conditions are expected to be close to thermal, but not necessarily isothermal as the heating rate might be distributed within the kernel in many ways. Plasma flows between kernels may also take place provided necessary pressure and/or potential energy differences exist along interconnecting channels. This flows may lead to a slow filling of the spider system through the chain of most active kernels along the way to the tiniest one linked directly to dense plasma in the photospheric magnetic element. This staged filling may be taught as a counterpart of classical evaporation.

4  The Hierarchy

Following our earlier considerations (Sylwester and Sylwester, 1998a, Sylwester, 1999), we postulate here that most of the corona is organized in a hierarchical net of magnetic links extending from the levels just below the photosphere up to the interplanetary space. This concept, illustrated in Figure 12 is extended to links between the magnetically closed portion of the solar atmosphere (forming one equatorial hierarchical system) and the regions of fast solar wind originating from coronal holes in Figure 13.

As concerns dynamics, the reconfiguration of stage I structures is the fastest with the typical correlation times of minutes. On the largest scale, typical life-time of a global configuration constitute a fraction of solar cycle. Constant reconfiguration is however a basic property of the entire structure.

At any time, reconnection simplify the magnetic configuration in some kernels braking some links, and creating new interconnections, the plasma contained spreads along the field lines. A new kernels are created as the new magnetic flux emerge from below. Some field lines, closing within the structure, those close to the envelope current sheet recombine to fast solar wind gaining tension from the solar wind plasma expanding into heliosphere. This picture, if real, elucidate that the plasma system (under the envelope) undergoing constant stresses is in a chaotic transient equilibrium state (self-organized criticality) like in a sandpile. The smallest disturbance (recombination - tether-cutting) may lead to catastrophic energy release (flare, CME) involving a part (up to total) of the energy contained in stressed system. Smaller, of local importance, energy releases (micro-flares, chromospheric explosions, various brightenings etc.) are much more common (power law with the exponent ~ 2, Hughes et. al., 2003), like in any self-organized system in the critical equilibrium.

The solar atmosphere can easily be imagined as the forced system where solar magnetic fields are subject to permanent stress from below (due to convective motions in photosphere) and above (large scale reconfigurations on the closed/open field boundaries). If such description is indeed appropriate for the solar atmosphere, the consequences of such a system of self-organized links are far-reaching.

One may ask: Single loops are generally well seen - don't they? This is easy to imagine that one of the edge kernels is dominant, filing preferentially only one side of the spider. In this case a structure resembling a single loop would be seen, except with the brighter thermal kernel at the summit - just the picture observed by SXT.

5  Summary and Conclusions