An advantage of a proton Super‐Conducting Linac (SCL) is that RF cavities can be operated independently, allowing easier beam transport and acceleration. But cavities are to be separated by drifts long enough to avoid they couple to each other. Moreover, cavities are placed in cryostats that include inactive insertions for cold‐warm transitions; and interspersed are warm insertions for magnets and other devices. The SCL is then an alternating sequence of accelerating elements and drifts. No periodicity is present, and the longitudinal motion is not adiabatic. This has the consequence that the beam bunch ellipse will tumble, dilute and create a halo in the momentum plane because of inherent nonlinearities. When this is coupled to longitudinal space‐charge forces, it may cause beam loss with latent activation of the accelerator components. © 2003 American Institute of Physics