Recovering phase density distribution from line density

An algorithm to recover the longitudinal density distribution of the particles in a stationary bunch from experimentally obtained line density is presented. This algorithm can be used as an alternative to the analytical theory. It is shown that after all the particles have been deposited in the bunch according to the algorithm, the author uses the newly created bunch to reconstruct the line density. This gives an indication of the accuracy of the algorithm. The local density distribution rho was computed by direct counting of the particles near the phi -axis. For stability studies, this rho -distribution needs smoothing treatment.<>