1. Synchrotron Motion S.A. Bogacz, G.A. Krafft, S. DeSilva and R. Gamage
Jefferson Lab and Old Dominion University
USPAS, Fort Collins, CO, June 13-24, 2016

2. Transition Energy
USPAS, Fort Collins, CO, June 13-24, 2016

3. Transition Energy
USPAS, Fort Collins, CO, June 13-24, 2016

4. Transition Energy
USPAS, Fort Collins, CO, June 13-24, 2016

5. Phase staibility below transition
USPAS, Fort Collins, CO, June 13-24, 2016

6. Phase stability above transition
USPAS, Fort Collins, CO, June 13-24, 2016

7. Standing Waves
USPAS, Fort Collins, CO, June 13-24, 2016

8. Standing Waves
USPAS, Fort Collins, CO, June 13-24, 2016

9. Standing Waves
USPAS, Fort Collins, CO, June 13-24, 2016

10. Standing Waves
USPAS, Fort Collins, CO, June 13-24, 2016

11. Standing Waves
USPAS, Fort Collins, CO, June 13-24, 2016

12. Standing Waves
USPAS, Fort Collins, CO, June 13-24, 2016

13. Construct a Difference Equation
USPAS, Fort Collins, CO, June 13-24, 2016

14. Difference Equation
USPAS, Fort Collins, CO, June 13-24, 2016

15. Difference Equation
USPAS, Fort Collins, CO, June 13-24, 2016

16. Longitudinal oscillation equation
USPAS, Fort Collins, CO, June 13-24, 2016

17. Small Oscillations
USPAS, Fort Collins, CO, June 13-24, 2016

18. Example
USPAS, Fort Collins, CO, June 13-24, 2016

19. Large Amplitude Oscillations
USPAS, Fort Collins, CO, June 13-24, 2016

20. Large Amplitude Oscillations
USPAS, Fort Collins, CO, June 13-24, 2016

21. Large Amplitude Oscillations
USPAS, Fort Collins, CO, June 13-24, 2016

22. Large Amplitude Oscillations
USPAS, Fort Collins, CO, June 13-24, 2016

23. Separatrices and Buckets
USPAS, Fort Collins, CO, June 13-24, 2016

24. Separatrices and Buckets
USPAS, Fort Collins, CO, June 13-24, 2016

25. Wrong way to integrate
USPAS, Fort Collins, CO, June 13-24, 2016

26. Large Amplitude Oscillations
USPAS, Fort Collins, CO, June 13-24, 2016

27. Better way: Leapfrog integration
USPAS, Fort Collins, CO, June 13-24, 2016

28. Better way: Leapfrog integration
USPAS, Fort Collins, CO, June 13-24, 2016

29. Hamiltonian formalism
USPAS, Fort Collins, CO, June 13-24, 2016

30. Hamiltonian formalism
USPAS, Fort Collins, CO, June 13-24, 2016

31. Adiabatic invariant
USPAS, Fort Collins, CO, June 13-24, 2016

32. Invariant for small oscillations
USPAS, Fort Collins, CO, June 13-24, 2016

33. Stationary bucket
USPAS, Fort Collins, CO, June 13-24, 2016

34. Stationary bucket
USPAS, Fort Collins, CO, June 13-24, 2016

35. Stationary bucket
USPAS, Fort Collins, CO, June 13-24, 2016

36. Momentum spread gets big at transition
USPAS, Fort Collins, CO, June 13-24, 2016

37. Direction of phase space rotation
USPAS, Fort Collins, CO, June 13-24, 2016