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magnet is dependent on the energy of the particle being bent, particles of different energies will be bent along different trajectories through the magnet, even if their initial position and angle are the same. The effect of this dispersion on the beam emittance is given by:

:

where is the dispersion at location s, is the ideal particle momentum, and is the root mean square of the momentum difference of the particles in the beam from the ideal momentum. (This definition assumes F=0.15)

Longitudinal emittance

The

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