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Quantum Locking and the Meissner Effect Lead to the Origin and Stability of the Saturn Rings System

It is demonstrated how superconducting iced particles of the protoplanetary cloud of Saturn are coming to magnetic equator plane and create the stable enough rings disk. There are two steps. First, after appearance of the Saturn magnetic field due to Meissner phenomenon, all particles orbits are moving to the magnetic equator plane. Finally they become distributed as rings and gaps like iron particles around magnet on laboratory table. And they are separated from each other by the magnetic field expelled from them. It takes up to few tens of thousands years with ten meters rings disk thickness. Second, because of quantum locking all particles become to be locked within magnetic well at the magnetic equator plane due to Abrikosov vortex for superconductor. Finally each particle is locked within three-dimensional magnetic well. It works even when particles have small fraction of superconductor. During the rings evolution some contribution to the disk also could come from the colli-sion-generated debris of the current moon, coming meteorites and from the geysers like it happened due to magnetic coupling of Saturn and Enceladus. The rings are relict of the early days of the magnetic field of Saturn system.


Introduction
Since 1610 when Galileo Galilei discovered such a nice and attractable space planetary structure there has not been yet complete understanding of the Saturn rings origin and age. There are three version of this process. Two of them have very close ideas of the gravity defragmentation when massive object was tidally disrupted when passing nearby Saturn [1] [2]. It was postulated that the rings particles can be collision-generated debris of this massive object. One well-developed theory is saying that an asteroid was destroyed coming to the Roche zone [1].
This approach was criticized because it does not have conformation of Cassini probe due to the fact that iced particles of the rings do not have iron which is contained in the asteroid matter. Note that metal matter of asteroid as a heavy part may disappear by going to the Saturn by gravity. Later theory suggested a Titan-sized satellite was destroyed by passing Saturn as it migrates inward towards Saturn [2]. Here it is not clear well where the core of it disappeared.
Also we could not consider both theories as eventually completed. Because, for example, they could not explain particles separation, thin width and sharp edges of the rings, why rings exist only for the planets behind the asteroid belt, electromagnetic phenomena of the rings, spokes in the B ring, and other phenomena.
There is no yet clear answer about the age of the rings formation. It remains a mystery. First idea was that they were as old as the Saturn system. Then after measurements of meteoroid flux into the Saturn system from Cassini's dust-counting instrument since the spacecraft arrived at Saturn in 2004, Kempf and colleagues showed that the still-bright rings collect too much dust pollution to have maintained their youthful shine for billions of years [3]. Authors concluded the ice of the rings should be far dirtier than it was if it had been gathering space dust during 4 billion years and rings disk may be much younger than Saturn system itself.
But when the Cassini spacecraft sent back the clearest images yet of Saturn's rings, M. Hedman and P. Nicholson [4] have received a totally new understanding of what is the matter of the B ring system of Saturn. After studying photos images, they came to the conclusion that the most striking B ring of Saturn's demonstrates for the observer an optical illusion. The mass of the B ring is only from one-half to one-seventh of the previously existing assessment. Those measurements reveal that the B ring, which makes up 80 percent of the total ring mass, is about 0.4 times that of Saturn's moon Mimas. In fact, B ring of Saturn contain three times less matter than previously thought. "The best analogy of this situation with B ring of Saturn is something like a fog over the meadow may seem less transparent and empty, than a water-filled pool, which has a much higher density than the fog" (P. Nicholson). And authors conclude that rings are much younger.
For example the guess of L. Esposito is that a single moon about half the mass of Mimas was ripped up around 200 million years ago [5]. It means Saturn's rings are surprisingly young and may be from shredded moons. Also more detailed discussion about age and fate of Saturn rings was presented J. Henry [6]. It looks like the best answer of the problem with the ring origin and age is given by the title of the paper written by P. Estrada, R.H. Durisen and J.N. Cuzzi: "After V. V. Tchernyi (Cherny), A. Yu. Pospelov International Journal of Astronomy and Astrophysics the Cassini grand finale, is there a final consensus on ring origin and age?" [7].
We have noted that all discussed above models of the origin and age of Saturn rings are based on classical understanding of the gravitational defragmentation of the massive body [13]. But both above theories do not allow a single common position of the physical concept in order to extend our understanding of many experimentally observed effects of the rings. And there has not been yet a clear explanation why and how particles rotating around Saturn on chaotic orbits within protoplanetary cloud coming to the equator rings disk and are held inside of it for a long time.
Our third version of the rings origin is also related to the Safronov theory of planet formation and it is based on the evolution of the protoplanetary cloud [13]. At the beginning of the process of formation of the rings system all iced particles are rotating around Saturn on chaotic orbits inside the protoplanetary cloud in accordance with the Kepler's law. After appearance of the magnetic field of Saturn all iced particles start to interact with it. The question is how all orbits of the particles may come to the equatorial plane of Saturn. If we are able to find answer to this question so it means that particles of the rings have approximately the same age as the age of the magnetic field of the Saturn, and the rings disk particles are relict of the early days of the Saturn system magnetic field.
In order to solve problem of the Saturn rings origin we suggested that iced particles of the rings may possess electromagnetic quality of superconductor [4]- [23]. The reason for this suggestion is existence of magnetic field of Saturn and low temperature in it vicinity. Electromagnetic simulation has demonstrated that during some time after appearance of the Saturn magnetic field, all the chaotic orbits of the superconducting particles of the protoplanetary cloud will go to the magnetic equator plane where the magnetic energy has a minimum value. For Saturn magnetic equator is almost coincident with the geographical equator. Finally particles become distributed as rings and gaps like iron particles around magnet on laboratory table. And particles are separated from each other by the magnetic field expelled from them. Surprisingly, assuming Saturn's rings contain superconducting matter many difficulties in understanding the nature of the rings can find simple explanations [24]- [36]: origin, evolution, and dynamics of the rings As we can see it already, the data of the Cassini mission once again confirms importance of electromagnetic interactions and the correctness of the conclusion of H. Alfven that the "solar system history is recorded in the Saturn rings structure" [37]. And it becomes to be a physical reality of our electromagnetic model to extend common understanding of the Saturn rings origin. At the same time we still have some questions about stability of the rings disk, it thickness and time of creation. Below we try to provide some additional information related to solution of these problems. Now we are going to add our consideration of the Saturn rings origin going to the quantum understanding of the superconductivity of iced particles and influence of it on the stability of the rings disk.

Discussion about Electromagnetism and Quantum Phenomenon of the Superconductor Related to Solution of the Proposed Problem
An interesting idea of the rings formation is coming from the general electromagnetic theory physics when we notice the similarity of the picture of the Saturn rings to the picture when iron particles creates dense and rarefied regions in a nonuniform magnetic field near by the magnet on laboratory table (please, see Figure 1).
The question is how we can get the same good looking structure for the rings  [41]. Recently also team of physicists has found the small amounts of superconducting materials might be relatively common in meteorites [42].
Recently was demonstrated an important fact that even small amount of superconducting matter may hold more than 70,000 times its own weight [43]. The experimental set up of how high temperature superconductivity is working on the best way B. Almog presented in Chicago at the ASTC Conference in 2011. It is based on theoretical discovery of A. Abrikosov of the vortex structure as a quantum nature of the superconductor [44]. Then U. Essmann, H. Träuble [45] and A. Tonomura [46] for the first time demonstrated experimentally and visualized it that the magnetic field may quantized inside the superconductor.
An interaction of superconductor of the second group with external magnetic field is a quantum physical phenomenon. The magnetic field inside superconductor behaves like a quantum particle, like a quantum object. And as a fact magnetic field is magnetized inside superconductor and strands of lines of the magnetic field remain inside superconductor, they gets locked inside superconductor (please, see Figure 2). Some of the flux line becomes to be pin, and they never could take move. The reason for that is that superconductor doesn't like magnetic fields lines moving around. What it actually does, it locks them in place. By doing that it blocks itself. Phenomenon of "Abrikosov vortex" is known as the partial penetration of the magnetic field in the superconductor of the second group, which does not lead to the complete destruction of superconductivity. The volume of material is pierced by the single quanta of magnetic flux, each of which is shielded from the rest of the sample circular superconducting currents. Why it happens? Under the low temperature some of magnetic lines will be expelled outside of the sample of superconductor of the second group. Because it is not a classical Meissner phenomenon, it's a quantum phenomenon. At the same time some of lines will remain inside the sample and superconductor locks this magnetic field flux lines inside itself (please, see Figure 2(b) and Figure 2(c)).
The action of locking prevents superconducting particles from moving within the disc. It is quantum trapping, quantum locking and quantum levitation. Also the action of trapping prevents the disc itself from moving in space. It is interesting notes that almost all new superconducting compound, open from the early sixties up to the present time, are superconductors of the second group [47]. The list includes organic superconductors, fullerenes (composed of atoms of carbon) and high temperature superconductors, and others.
Flux pinning is the phenomenon where a superconductor is pinned in space above a magnet. The superconductor must be a type-II superconductor  . Analysis of low-field isotropic vortex glass containing vortex groups in YBa 2 Cu 3 O 7−x thin films visualized by scanning SQUID microscopy. Scientific Reports, 5, 8677. https://www.nature.com/articles/srep08677); (c) Natural superconducting iced particle of the rings which is located along the horizontal equator plane is interacting with vertical Saturn's magnetic field lines. We can see that some of magnetic lines will be expelled outside of the sample of superconductor of the second group. And at the same time some of them will remain inside the sample and superconductor locks this magnetic field flux lines inside itself (https://en.wikipedia.org/wiki/Flux_pinning). In case of Saturn rings we do have situation which looks similar to the case shown above in [43]. The rings particles contain 93% of ice and only 7% of carbon. It means that even if ice of the rings particles is not completely superconducting, still phenomenon of superconductivity will be responsible for the rings disk formation due to contains 7% of carbon. But superconductivity of ice is demonstrated in [39] and [40] and for carbon C36 in [41]. Consequently superconducting iced particles will be locked within the rings disc of the magnetic equator plane by the Saturn magnetic field due to phenomena of quantum locking, quantum trapping and quantum levitation. The rings disk itself will be suppressed by the magnetic pressure from both sides along the z axis, because along a meridian the magnetic energy becomes to be bigger on the distance from the minimum value at the magnetic equator. Finally we have a magnetic well of the rings disc which is sufficiently disturbing picture of Saturn magnetic field lines in the area of magnetic equator, Figure 3. As a result each particle of the rings disk of Saturn is locked strong enough within three-dimensional magnetic well. Thus it means we have a stable enough structure of the rings disk which is stabilized by the magnetic force on the vertical direction due to the gradient of magnetic flux and on the horizontal direction by the quantum locking and quantum pinning of the Abrikosov vortex structure for each particle. Following our superconducting model for the rings origin we are coming to new understanding of the "spokes" formation in the B ring. Just as any wheel spokes, the spokes of the rings are aligned almost radially. The size of the spokes is about 10 4 km along the radius and about 10 3 km along the orbit of the rings. The matter of the spokes consists of micron and submicron size particles. There were many attempts to explain the nature of these spokes. Generally, all the models are based on the action of the force of gravity. A different idea was put forward that the nature of rotating spokes is related to electromagnetic force of the diamagnetic expulsion due to Meissner effect. Analysis of the spectral radiation power of spokes provides a specific periodicity about 640.6 ± 3.5 min which almost coincides with the period of rotation of the magnetic field of Saturn (639.4 min). Moreover a strong correlation of maxima and minima of activity of spokes with the spectral magnetic longitudes is connected to presence or absence of the radiation of Saturn's Kilometric Radiation (SKR). It enhances the assumption of dependence of the spokes dynamics on the magnetic field of Saturn and it testifies to the presence of large-scale anomalies in the magnetic field of Saturn. As a result we have the next explanation.

Movements of the Superconducting Iced Particles to the Magnetic Equator Plane
Here b is the value for the uniform magnetic field inside the particle: We place the origin of the coordinates at the center of a planet, and the z axis directly along the magnetic moment of a planet (orthogonal to equator). Then the magnetic energy will become as: Here θ-the angle between the vector r and the z axis. It can be seen from this expression, that the magnetic energy of the superconducting particle has a minimum value when the radius-vector r is in a plane of the magnetic equator plane, ( ) cos 0 θ = . It means that eventually a particle during an interaction with magnetic field of planet tries to get position within magnetic equator plane and then it continues move around Saturn within the rings disk in accordance with Kepler's low [24]- [36].
Now going to spherical coordinates we get The Newton equation of motion is then In order to do calculations we take the following values for parameters: at

Notes about Time of the Rings Disc Formation
We made modeling for one particle. In reality time for particles to come to magnetic equator plane will be much larger due to collisions and the influence of Also there is a probability of contribution to the matter of the rings disc from the debris of the asteroids, moon and satellites migrated inward towards Saturn and coming superconducting meteorites. Another situation may happen when particles of the frozen water coming from the geyser of the geologically active satellite go to the rings disc due to magnetic coupling between Saturn and its satellite ( Figure 4).
An important discovery was made in 2005. The Cassini spacecraft started multiple close flybys of Enceladus, revealing its surface and environment in greater detail. In particular, Cassini discovered water-rich plumes venting from the south polar region [50]. Cryovolcanoes near the south pole shoot geyser-like jets of water vapor up to 500 km, molecular hydrogen, other volatiles, and solid material, including sodium chloride crystals and ice particles, into space, totaling about 200 kg per second [51]. Over 100 geysers have been identified [52]. Some of the water vapor falls back as "snow"; the rest escapes, and supplies most of the material making up Saturn's E ring [53] [54] (Figure 4 and Figure 5). The intensity of the geysers of Enceladus depends on how close or far the satellite is from Saturn [55].
Certainly process of supplying particles to the rings disc from the geyser of the satellite of Saturn could not continue forever. It works only during the time of

Conclusions
Recently we coined the hypotheses that the ice matter of the Saturn rings particles or part of it may be superconducting. The above consideration has demon- the rings disc become to be locked by the quantum locking in the horizontal direction and suppressed by external magnetic field along a meridian. As a result, each particle of the rings disk of Saturn is locked strong enough within three-dimensional magnetic well.
Magnetic well of the rings disc is a sufficiently disturbing picture of Saturn magnetic field in the area of equator. If some other superconducting particle is flying nearby the rings disc, then the magnetic well will eventually attract the particle within the disc and get locked it inside.
Thus it means we have blocked enough structure of the rings disk which is stabilized by the magnetic force of Meissner effect on the vertical direction due to the gradient of magnetic flux in the both directions from the magnetic equator and it is stabilized on the horizontal direction by the quantum pinning of the Abrikosov vortex structure for each particle.
When particles of the B ring come to anomaly area of the Saturn magnetic field, they receive additional azimuth-radial movements by electromagnetic force due to Meissner effect and they start to move. In optical range it is registered as a spokes. During collision of the particles, their dot contact may generate registered wideband pulse radiation due to non-stationary Josephson phenomenon.
It is an interesting feature that the suggested mechanism of the rings formation due to electromagnetic interaction works even in case when only small fraction of the iced particles may have superconductivity. This conclusion is based on results of laboratory experiment when the small scale frozen superconductor located on the big enough size of substrate is trapped in external magnetic field and it is able to hold much more times its weight. Magnetic field is magnetized inside the superconductor. Some of the flux line becomes to be pin, they don't move. And superconductor blocks itself within magnetic field. It happened because superconductivity has quantum nature. So, the time of initial formation of the rings disc system with thickness of a ten meters due to electromagnetic interaction of superconducting iced particles of the protoplanetary cloud with magnetic field of Saturn may be estimated as from a few thousand years up to few tens of thousands years. And this is the time of the origin, dynamics and formation of the initial state of the system of Saturn rings after appearance of the magnetic field of Saturn. During this time the chaotic orbits of the superconducting iced particles of the protoplanetary cloud which are moving around Saturn will collapse into the disc of rings.
At the same time due to a long time existence of the Saturn rings the other processes also need to be considered which could contribute to the dynamics and evolution of the rings disk. It is necessary to underline that some other sudden event like satellite coming to the Saturn and becomes to be destroyed to the debris, and coming superconducting meteorites or water eruption by the geyser of the satellite of Saturn, all of them could contribute to the dynamic and evolution of the existing structure of the rings disc matter. For example, some of the water vapor of the geyser of Enceladus falls back as "snow"; the rest escapes, and V. V. Tchernyi (Cherny), A. Yu. Pospelov International Journal of Astronomy and Astrophysics supplies most of the material making up Saturn's E ring. We can imagine the same situation could happen some moment of time earlier with another satellite and B ring.
In fact orbital resonances between Saturn, satellites, moons and rings particles play an important role in forming a specific structure of the rings system gaps and enhancing the influence of the satellites as well as the gravitational, mechanical, magnetohydrodynamic, dusty plasma and gas-plasma interactions.
It is a pleasing surprise, how many features of the Saturn rings our model of the superconductivity of the Saturn rings particles can explain. If applied to other systems, it has the potential to enrich our understanding of the space natural laboratory in general.