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12.4 Phase space plots

12.4.1 Transversal phase space, with and without space charge

Figure 12.9: Transversal phase space for the compressor without space charge forces. From left to right : before the compressor, at the middle of the four dipoles, and after the compressor

Figure 12.10: Transversal phase space for the compressor with space charge forces. From left to right : before the compressor, at the middle of the four dipoles, and after the compressor

12.4.2 Longitudinal phase space, with and without space charge

Figure 12.11: Longitudinal phase space for the compressor without space charge forces. From left to right : before the compressor, at the middle of the four dipoles, and after the compressor

Figure 12.12: Transversal phase space for the compressor with space charge forces. From left to right : before the compressor, at the middle of the four dipoles, and after the compressor

12.4.3 Projected densities for the phase space with space charge forces at the end of the compressor

Figure 12.13: Phase space at the end of the compressor with densities on each axis. (a) Traversal phase space - (b) Longitudinal phase space

(a) (b)

12.4.4 Introducing correlation with a cavity

The correlation between the $z'$ and $z$ can be introduced by a cavity. Thus placing a cavity before the compressor, and changing the phase will introduce diverent correlation between energy and $z$. In section 14.1.2 we indeed saw that the following relation exists for the relative momentum at the output of the cavity :

$$\delta_{out} = \delta_{in} + \alpha z$$ (12.1)

Nevertheless, few simulations have been done with the case of a cavity and a compressor. The results were the same than the one presented in the previous section.

Emmanuel Branlard
http://emmanuel.branlard.free.fr/