In accelerator physics, the mapping matrix M(s+L|s) is utilized to analyze the motion of particles. The discussion reveals that after one turn, the values of (x, x') change, indicating that the particle's position and angle are not constant, leading to non-closed trajectories. This phenomenon occurs due to inherent imperfections in components, causing unaccounted deviations that accumulate over time. Consequently, maintaining closed trajectories is impractical, as they result in rapid loss of particles.
PREREQUISITESPhysicists, engineers, and researchers in accelerator physics, particularly those focused on particle motion analysis and trajectory optimization.
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.Ruihu Zhu said:This shows the trajectory of this particle is not closed.I can't understand why this happens.