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A study of the transverse dynamics of coasting ion beams with moderate space charge is presented. An analytic model based on the dispersion relation with a linear space-charge force is used to describe the impact of space charge on transverse beam transfer functions (BTFs) and the stability limits of a beam. The dielectric function obtained in this way is employed to describe the transverse Schottky spectrum with linear space charge as well. The difference between space charge and impedancedoi:10.1103/physrevstab.13.022802 fatcat:vkbnhkkhqren5ljswrxiud2lmq