Contribution of Magnetic Anisotropic Accretion of Diamagnetic Iced Particles of the Saturn’s Protoplanetary Cloud to the Rings Formation and Stability

Cassini found 93% of the ice in the rings of particles. Ice can be diamagnetic. We study magnetic anisotropic accretion of protoplanetary cloud particles through the dynamics of uniformly magnetized sphere in the spherically-symmetric gravitational & axially-symmetric magnetic fields of Saturn. The problem of the interaction with external magnetic field of a single magnetized sphere as well as a spherical particle among identical particles scattered in a disk-like structure of uniformly distributed identical diamagnetic spheres simulating the dense rings of Saturn is solved. Differential equations of particle motion are obtained. The singular solution explains the stability of Saturn’s rings on the planet’s equator. Collisions in the movement of a huge number of protoplanetary cloud particles compensate for their azimuthal-orbital movements & all their orbits converge in the plane of the magnetic equator & create a strongly flattened disk of rings. Inside the disk of rings all particles are located in Kepler’s orbits where there is a balance of gravity force, centrifugal force & diamagnetic expulsion force. Particles cannot move along the meridian since they have minimal magnetic energy at the equator plane. Here their position is more stable than just due to the gravitational force. The magnetic force acting on a diamagnetic sphere in a disk with many magnetized spheres is stronger than the force acting on a single sphere. The stability of the disk of rings is stronger the more diamagnetic particles it contains, and the magnetic well is deeper here. The magnetic field in the plane of the disk of rings is inhomogeneous. Magnetic field lines will strive to go through the region with the highest magnetic permeability. All diamagnetic particles are collected in areas with a low magnetic field density. Density gradient flow of magnetic field is repels particles of each other. It also clears the gaps inside the ring system & forming a rigid thin structure of separated rings. The electromagnetism of the spokes in the ring B has received now an additional approval due to the diamagnetism of the ice particles that we proposed. In the anomalies of the magnetic field of Saturn the particles change their position & then return back due to the action of diamagnetic force of expulsion. For smaller particles the role of diamagnetism increases relative to gravity. It looks like ice of XIh type with orthorhombic lattice & ordered arrangement of protons is suitable for the rings particles due to stability of its parameters in the Saturn’s rings environment.