Who needs phi_s ?

Example 1: Depending on the phase of the RF wave, the stable point is at different points in time, but if we use dE = q V sin(phi_s), we can calculate a common stable phase, that can be also converted to a time coordinate. This is easy.

Example 2: things get more complicated, there are several stable phases, and is has to be agreed on what phi_s means and how it relates to the RF waveform parameters. Not an impossible task, but I assume that there are conflicting definitions depending on the institution/accelerator.

Adding wakefields, multi-rf, etc. will introduce further perturbations, at which time the stable point might be.

Overall, its always easy/obvious to yield t_stable, but how to convert it to a phase relies on additional conversion rules, that might need to be implemented.

So here is my questions: Who needs phi_s, what is it used for, and could it be replaced by t_stable? Thus we could eliminate error-prone conversions to phi_s and deal with more universal internal data.