A word is in order about the definition of , which we've described as the total, equivalent distance traveled. First, by total distance we mean that is not measured relative to the bunch center or a fiducial particle. It is entirely a property of the individual particle and its path through the accelerator.
To explain what we mean by equivalent distance, note that the relationship between and arrival time at the observation point is, for each particle, , where is the instantaneous velocity of the particle. Whenever a particle's velocity changes, elegant recomputes to ensure that this relationship holds. is thus the ``equivalent'' distance the particle would have traveled at the present velocity to arrive at the observation point at the given time. This book-keeping is required because elegant was originally a matrix-only code using as the longitudinal coordinate.
Users should keep the meaning of in mind when viewing statistics for , for example, in the sigma or watch point output files. A quantity like Ss is literally the rms spread in . It is not defined as . A nonrelativistic beam with velocity spread will show no change in Ss in a drift space, because the distance traveled is the same for all particles.