Obtaining the bunch shape in a linac from beam spectrum measurements

If we know the Green function wake of the linac, we can still obtain the bunch shape from beam spectrum measurements. In this report, we present two such methods. One requires one spectrum measurement and involves the solution of a Volterra integral equation. The other requires a knowledge of upstream beam and transport properties and involves a least squares minimization to simulated spectra. We then apply these methods to the SLC.