2 Beam Dynamics
37
Fig. 2.17 How the conserved phase space appears at different points in a FODO cell
Fig. 2.18 The parameters of a phase-space ellipse containing an emittance ε at a certain point in
the lattice. The shape and orientation of the ellipse are determined by the Twiss parameters at the
given location
divergence will be large, while in an F quadrupole (d) where the betatron function
is maximum, its divergence will be small. The beam is also seen at a broad waist or
maximum in the beta function and a place where the beam is diverging.
In Fig. 2.18 we see how the various features of the ellipse are related to the
Twiss parameters. The equation of the ellipse, often called the Courant and Snyder
37
Fig. 2.17 How the conserved phase space appears at different points in a FODO cell
Fig. 2.18 The parameters of a phase-space ellipse containing an emittance ε at a certain point in
the lattice. The shape and orientation of the ellipse are determined by the Twiss parameters at the
given location
divergence will be large, while in an F quadrupole (d) where the betatron function
is maximum, its divergence will be small. The beam is also seen at a broad waist or
maximum in the beta function and a place where the beam is diverging.
In Fig. 2.18 we see how the various features of the ellipse are related to the
Twiss parameters. The equation of the ellipse, often called the Courant and Snyder