Dipole coherent oscillations and fluctuations 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 ion beam on Landau damping of its dipole coherent oscillations and fluctuations. The calculations of the stability diagrams for coherent oscillations show that effect of the space charge can be very strong and can substantially change the threshold currents of instabilities. The combination of the cubic nonlinearity of the lattice and of the space charge can result in the Landau antidamping of coherent oscillations. The variations of the stability diagrams and of the Schottky noise spectra enable direct measurements of the Laslett tune shifts of ion beams with strong space charge.