|At the interaction point of a storage
ring each beam is subject to perturbations due to the electromagnetic field
of the counter-rotating beam. These perturbations lead to a limit of the
achievable luminosity in the storage ring. We investigate this limit in
the framework of the strong-strong picture. Motion is considered only in
the vertical direction and the beams are presumed to be one-dimensional.
Based on this model we try to find stability criteria for the beam in an
electron-position storage ring taking into account the damping of the betatron
oscillations by synchrotron radiation but neglecting the discrete nature
of the radiation process and presuming a Gaussian distribution. We analyze
the instabilities by solving a linearized "Fokker-Planck equation"
without the quantum excitation term.