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Page 1: Lecture05 - hep.physics.utoronto.ca · Microsoft PowerPoint - Lecture05 [Compatibility Mode] Author: Bob Created Date: 1/30/2012 5:25:28 PM
Page 2: Lecture05 - hep.physics.utoronto.ca · Microsoft PowerPoint - Lecture05 [Compatibility Mode] Author: Bob Created Date: 1/30/2012 5:25:28 PM
Page 3: Lecture05 - hep.physics.utoronto.ca · Microsoft PowerPoint - Lecture05 [Compatibility Mode] Author: Bob Created Date: 1/30/2012 5:25:28 PM
Page 4: Lecture05 - hep.physics.utoronto.ca · Microsoft PowerPoint - Lecture05 [Compatibility Mode] Author: Bob Created Date: 1/30/2012 5:25:28 PM
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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

Page 27: Lecture05 - hep.physics.utoronto.ca · Microsoft PowerPoint - Lecture05 [Compatibility Mode] Author: Bob Created Date: 1/30/2012 5:25:28 PM

• Single Particle Phase Space• Beam Envelope

angle

position• Real Accelerator• Non-linear

Shape of phase space changes along accelerator latticeArea constant -> Liouville

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