A hydrodynamic approximation is used to study the behavior of dipole modes of the transverse oscillations of an ion beam in a storage ring with an electron cooling section. It is shown that in addition to the finite interaction time of the beams, instability may be caused by a specific interaction effect between the ion and electron beams in the magnetic field which leads to redistribution of energy between the various modes of the ion beam oscillations. In this case, the condition that the determinant of the transfer matrix for the cooling section does not exceed unity no longer guarantees the stability of the transverse coherent oscillations of the ion beam and all the eigenvalues of the complete matrix of the ion motion including the storage ring must be analyzed. Calculations of the stability of ion beam dipole oscillations are presented for the parameters of CELSIUS.
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