Evaluation of the acceptance

The acceptance required to capture an incoming particle by the stored beam is given by:

$${\mathcal A}_{z} = \beta_{z} \left( p^i_z - p^0_z \right)^2... ...ft( z^i - z^0 \right) + \gamma_{z} \left( z^i - z^0 \right)^2$$ (1)

where z stands for the plane where the acceptance is being evaluated, the superscript i for the injected particle and 0 for the stored.

In the case of an injected beam, the acceptance required to capture it is the one of the particle that requires the largest acceptance.

The acceptance required to capture the beam is shown, for the first 10 turns, in figure 24, for the four different scenarios. The dynamic acceptance of the lattice ($\approx$ 35 mm-mrad) is large enough to capture the injected beam. A nice feature of the evaluation of the acceptance by tracking is that we can appreciate the effects of the non-linearities, as can be seen by the change of the acceptance turn to turn.

  

Figure 24: Acceptance required to captured the injected beam.