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TRAJECTORYBEAM ENVELOPE
2
2 0d Y K s Yds
2
2 31d K s
d
BEAM ENVELOPE
cosY s A s s 2 3ds
2s s
cosY s s s
Amplitude of betatron oscillations
• Single Particle Phase Space• Beam Envelope
angle
position• Real Accelerator• Non-linear
Shape of phase space changes along accelerator latticeArea constant -> Liouville