  We use the Fokker-Planck equation and model the dispersive dynamics of solid
particles in annular protoplanetary disks whose gas component is more massive
than the particle phase. We model particle--gas interactions as hard sphere
collisions, determine the functional form of diffusion coefficients, and show
the existence of two global unstable modes in the particle phase. These modes
have spiral patterns with the azimuthal wavenumber $m=1$ and rotate slowly. We
show that in ring-shaped disks, the phase space density of solid particles
increases linearly in time towards an accumulation point near the location of
pressure maximum, while instabilities grow exponentially. Therefore,
planetesimals and planetary cores can be efficiently produced near the peaks of
unstable density waves. In this mechanism, particles migrating towards the
accumulation point will not participate in the formation of planets, and should
eventually form a debris ring like the main asteroid belt or classical Kuiper
belt objects. We present the implications of global instabilities to the
formation of ice giants and terrestrial planets in the solar system.
