NASA NTRS1982
Viscous shear stress of a ring of particles in orbit about a planet due to the radial gradient of orbital velocity is discussed. This stress tends to spread the ring with time. At low optical depth (t) and at high t, the shear stress is an increasing function of t. In the intermediate range stress may decrease with increasing t, leading to a diffusive instability which tends to break an initially uniform ring into ringlets of high and low optical depths. According to the shepherd satellite model of narrow ring confinement, the viscous shear stress is opposed by tidal torques from neighboring shepherds, so that radial spreading does not occur. By requiring that the gradient of the viscous shear stress (i.e., angular momentum deposited) be equal to the shepherd satellite torque density at all radii in the rings, equilibrium radial density profiles of a confined ring were constructed. The most noteworthy feature of these profiles is a narrow, high density ringlet surrounded by a low optical density halo of greater width.