Ideal case

This case corresponds to an injected reference particle with the ideal input coordinates an ideal beam ellipse, being injected in the machine, without any kind of errors, neither in the lattice or the incoming beam.

The figure 3 shows the trajectory in the horizontal plane of the incoming beam for the injection turn, the following three turns (while the injection kickers are active), and the first turn with the kickers turned off. As can be seen, the particle stays comfortably inside the limits of the vacuum pipe ($\pm 32.5$ mm)

The figure 4 plots the behavior of the injected beam, the reference particle and the stored beam in the horizontal phase space for the first ten turns after injection, at the end of the septum. As can be seen from the plot, the small emittance of the injected beam (10 nm-rad) makes it relatively easy to inject the beam without touching the septum wall, providing for a large injection efficiency. The figure 5 shows the phase space plot for the reference injected particle, at the start of the lattice (not at the end of the septum) for a 15000 revolutions. The damping of the particle is clear, as can be seen from the reduction of the oscillation amplitude.

  

Figure 3: Orbit of the injected beam for the injection turn a nd the following 4 turns.

  

Figure 4: Evolution of the injected beam ellipse at the exit of the septum.

  

Figure 5: Evolution of the injected beam in phase space for a damping time.