  We discuss the optical stochastic cooling (OSC) method in applications to the
beams of charged particles, circulating in accelerators and storage rings. In
this publication we concentrated on various OSC schemes in a diluted beam
approximation, when the heating of selected particle by its neighboring ones
could be neglected. Even so, this approximation allows us to identify important
features in the beam cooling. In the forthcoming publication, on the basis of
approach developed here, we will include effects of heating in the dynamics of
cooling.
