Time-Reversed Particle Simulations In GPT (or “There And Back Again”)

1. Time-Reversed Particle Simulations In GPT(or “There And Back Again”) Simon Jolly Imperial College FETS Meeting, 12/10/05

2. Time-reversed Simulations • GPT only has capacity to run time forwards in simulations. • To make comparisons with “downstream” emittance measurements, need to find a way of running time backwards. • Create “reverse” simulation by making divergence negative ie. all angles are inverted: • Is this a realistic assumption to make? • Does it produce realistic results?

3. Backwards Simulations • “Time-reversed” (backwards) technique tested in the following way: • Create beam and track forwards 300mm; • Invert transverse velocity (angle) of each particle and reverse longitudinal profile: equivalent to a reflection in X-Y plane; • Re-insert “reversed” beam into GPT and track forward another 300mm. • “Reverse” beam a second time and compare to original model at t=0.

4. Simulation Parameters • 2 different beam models used: • “Parallel” beam - circular, uniform beam; xrms = yrms = 5mm, x’ = y’ = 0, z = 0, 35keV, 60mA, 100% SC, E = 0, 10,000 particles. • Gaussian beam - xrms = yrms = 1.6mm, x’rms = y’rms = 1.7mrad, x,rms = y,rms = 8.3x10-3 mm mrad, z = 0, 35keV, 60mA, 100% SC, E = 0, 10,000 particles. • 2 different space charge models used: 2Dline and tree2D (“reverse” simulation tests SC model accuracy).

5. Parallel/Gaussian X-Y Profiles Parallel beam Gaussian beam

6. Parallel Beam Trajectories (1) Forward trajectories: Z-X, tree2D model

7. Parallel Beam Trajectories (2) Reverse trajectories: Z-X, tree2D model

8. Parallel Beam: tree2D X-Y (1) Difference between transverse positions at 0mm of forward and reverse beams: X-Y, tree2D model

9. Parallel Beam: tree2D X-Y (2) Difference between transverse positions at 0mm of forward and reverse beams: X-Y, tree2D model

10. Parallel Beam: tree2D X’-Y’ Difference between transverse angles at 0mm of forward and reverse beams: X’-Y’, tree2D model

11. Parallel Beam Trajectories (3) Forward trajectories: Z-X, 2Dline model

12. Parallel Beam: 2Dline X-Y Difference between transverse positions at 0mm of forward and reverse beams: X-Y, 2Dline model

13. Parallel Beam: 2Dline X’-Y’ Difference between transverse angles at 0mm of forward and reverse beams: X’-Y’, 2Dline model

14. Parallel Beam SC Models (1) Difference between forward trajectories (Z-X) for tree2D and 2Dline space charge models

15. Parallel Beam SC Models (2) Difference between transverse positions at 0mm (X-Y) for tree2D and 2Dline space charge models

16. Gaussian Beam: Forward (1) Forward trajectories: Z-X, tree2D model

17. Gaussian Beam: Forward (2) Forward trajectories: Z-X, 2Dline model

18. Gaussian Beam: Reverse Reverse trajectories: Z-X, 2Dline model

19. Gaussian Beam: tree2D X-Y Difference between transverse positions at 0mm of forward and reverse beams: X-Y, tree2D model

20. Gaussian Beam: 2Dline X-Y Difference between transverse positions at 0mm of forward and reverse beams: X-Y, 2Dline model

21. Gaussian Beam: tree2D X’-Y’ Difference between transverse angles at 0mm of forward and reverse beams: X’-Y’, tree2D model

22. Gaussian Beam: 2Dline X’-Y’ Difference between transverse angles at 0mm of forward and reverse beams: X’-Y’, 2Dline model

23. Gaussian Beam: Z-X (1) Longitudinal particle position at 0mm for reverse beam: Z-X, 2Dline model

24. Gaussian Beam: Z-X (2) Longitudinal particle position at 0mm for reverse beam (enhanced): Z-X, 2Dline model

25. Gaussian Trajectory Diff (1) Difference between forward trajectories (Z-X) for tree2D and 2Dline space charge models

26. Gaussian Trajectory Diff (2) Difference between forward trajectories (Z-X) for tree2D and 2Dline space charge models (enhanced)

27. Gaussian Angle Diff (1) Difference between forward angles (Z-X’) for tree2D and 2Dline space charge models

28. Gaussian Angle Diff (2) Difference between forward angles (Z-X’) for tree2D and 2Dline space charge models (enhanced)

29. Gaussian Beam: 600mm (1) Trajectories for reverse Gaussian beam tracked for 600mm: Z-X, 2Dline model

30. Gaussian Beam: 600mm (2) Angle trajectories for reverse Gaussian beam tracked for 600mm: Z-X’, 2Dline model

31. Gaussian 2Dline Results • Using Gaussian beam distribution gives larger variations between forward and reverse beams (2Dline model, 0 mm): • Emittance: +0.1% x,rms (0.00833 to 0.00834  mm mrad), +0.3% y,rms (0.00833 to 0.00836  mm mrad). • Size: +1 nm xrms (1.62326 to 1.62327 mm), +1 nm yrms (1.62346 to 1.62347 mm). • Divergence: +280 nrad x’rms (1.72808 to 1.72836 mrad), +760 nrad x’rms (1.72881 to 1.72957 mrad).

32. Gaussian tree2D Results • Similar results for SCtree2D model (0 mm): • Emittance: +0.1% x,rms (0.00833 to 0.00834  mm mrad), +0.3% y,rms (0.00833 to 0.00836  mm mrad). • Size: +2 nm xrms (1.62326 to 1.62328 mm), -2 nm yrms (1.62346 to 1.62344 mm). • Divergence: +270 nrad x’rms (1.72808 to 1.72835 mrad), +760 nrad x’rms (1.72881 to 1.72957 mrad).

33. Conclusions • Space charge models are accurate enough to run “reverse” simulations in GPT. • Space charge models get worse with increasing angle: • From Pulsar: “We have no solid mathematical proof, but it seems to us that as long as the typical angle with respect to the z-axis times the 'thickness (in z)' of the bunch is less than the radius, all is fine.” • Inaccuracies clear from simulation results, but not large enough to affect RMS beam parameters.