Self-consistent dipole coherent oscillations of a coasting ion beam with strong space charge

For non-resonant collective interactions we discuss effects of the space charge fields of an intense coasting ion beam on Landau damping of its dipole coherent oscillations and fluctuations. Within the framework of a special simplifying model we use self-consistent expressions for the space charge fields of the ion beam to calculate the stability diagrams for coherent oscillations and the spectra of the transverse Schottky noise of the ion beam. We trace the deviations of the predictions of this model from that assuming the rigid beam approximation for the space charge fields. Since the dipole oscillations of the beam can be measured directly such a comparison enables to figure out more reliable predictions for such measurements