Longitudinally space charge dominated beams in a synchrotron

For a given RF cavity voltage amplitude, V_RF, there is a maximum attainable peak current in an ion storage ring. This occurs when the electric field from the beam space charge balances the RF cavity field. In this limit, the linear charge density distribution, λ(s), is parabolic and incoherent synchrotron motion is suppressed. The beam energy spread cannot be determined from the bunch time spread, T_FWHM, which depends only upon the beam current, I, and V_RF. This paper summarizes this work, discusses planned measurements, and conjectures about possible results