Question about accelerator physics

[Ruihu Zhu]

In accelerator physics, mapping matrix is often used to describe particle's motion.For a given one turn mapping matrix,namely M(s+L|s) ,and initial (x,x').After matrix multiplication, I find the value of (x,x') changes which means particle's position and angle changes at the same s after one turn mapping.This shows the trajectory of this particle is not closed.I can't understand why this happens.

 

[mfb]

I moved the thread to classical physics.

This shows the trajectory of this particle is not closed.I can't understand why this happens.

That's how it has to be. A closed trajectory might work in mathematics but not in reality. Components are never perfect, so particles will get some unaccounted deviation. With a closed trajectory after one turn they will always get the same deviation which accumulates, and they will get lost quickly. Even a closed trajectory after 2-5 turns should be avoided.