The Saturnian 'gas-doughnut' hypothesis

It is hypothesized that constituents escaping the atmosphere of Titan are unlikely to have sufficient velocity to escape from Saturn. Thus most of the material will enter into elliptical orbits which, at some point, cross Titan's orbit at a small angle. In total, this matter will form a 'doughnut' shaped feature, roughly centered on Titan's orbit and having dimensions of about 20 Saturn radii in the Saturnian-equatorial plane and 10 Saturn radii normal to this plane. It is assumed that the material is lost from the doughnut when it is ionized or is recaptured by Titan's atmosphere. The upper limit on the density of hydrogen in the ring is estimated to be about 1,000 particles per cu cm, with up to 99% of the particles in the doughnut being recaptured by Titan.