Motion of particles in storage rings in the presence of a   counterpropagating laser beam I
  The dynamics of charged particle beams interacting with laser beams and material targets in storage rings is presented. Formulas for the radiative damping, quantum excitation and equilibrium parameters of ion and electron beams determined by the backward rayleigh and backward compton scattering are derived. General case is considered. It takes into account the possibility of the periodical displacement of the laser beam in the radial direction with varying velocity in the process of the interaction of the beams and includes the possibility of the description of dynamics of muon beams interacting with material targets in storage rings (enhanced ionization cooling). The example is considered and some applications of being cooled beams are discussed. 
E.G.Bessonov (P.N.Lebedev Physical Institute AS, Moscow, Russia)