time-reversed particle simulations in gpt (or “there and back again”)
DESCRIPTION
Time-Reversed Particle Simulations In GPT (or “There And Back Again”). Simon Jolly Imperial College FETS Meeting, 12/10/05. Time-reversed Simulations. GPT only has capacity to run time forwards in simulations. - PowerPoint PPT PresentationTRANSCRIPT
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Time-Reversed Particle Simulations In GPT
(or “There And Back Again”)
Simon JollyImperial College
FETS Meeting, 12/10/05
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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?
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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.
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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).
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Parallel/Gaussian X-Y Profiles
Gaussian beamParallel beam
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Parallel Beam Trajectories (1)
Forward trajectories: Z-X, tree2D model
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Parallel Beam Trajectories (2)
Reverse trajectories: Z-X, tree2D model
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Parallel Beam: tree2D X-Y (1)
Difference between transverse positions at 0mm of forward and reverse beams: X-Y, tree2D model
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Parallel Beam: tree2D X-Y (2)
Difference between transverse positions at 0mm of forward and reverse beams: X-Y, tree2D model
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Parallel Beam: tree2D X’-Y’
Difference between transverse angles at 0mm of forward and reverse beams: X’-Y’, tree2D model
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Parallel Beam Trajectories (3)
Forward trajectories: Z-X, 2Dline model
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Parallel Beam: 2Dline X-Y
Difference between transverse positions at 0mm of forward and reverse beams: X-Y, 2Dline model
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Parallel Beam: 2Dline X’-Y’
Difference between transverse angles at 0mm of forward and reverse beams: X’-Y’, 2Dline model
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Parallel Beam SC Models (1)
Difference between forward trajectories (Z-X) for tree2D and 2Dline space charge models
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Parallel Beam SC Models (2)
Difference between transverse positions at 0mm (X-Y) for tree2D and 2Dline space charge models
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Gaussian Beam: Forward (1)
Forward trajectories: Z-X, tree2D model
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Gaussian Beam: Forward (2)
Forward trajectories: Z-X, 2Dline model
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Gaussian Beam: Reverse
Reverse trajectories: Z-X, 2Dline model
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Gaussian Beam: tree2D X-Y
Difference between transverse positions at 0mm of forward and reverse beams: X-Y, tree2D model
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Gaussian Beam: 2Dline X-Y
Difference between transverse positions at 0mm of forward and reverse beams: X-Y, 2Dline model
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Gaussian Beam: tree2D X’-Y’
Difference between transverse angles at 0mm of forward and reverse beams: X’-Y’, tree2D model
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Gaussian Beam: 2Dline X’-Y’
Difference between transverse angles at 0mm of forward and reverse beams: X’-Y’, 2Dline model
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Gaussian Beam: Z-X (1)
Longitudinal particle position at 0mm for reverse beam: Z-X, 2Dline model
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Gaussian Beam: Z-X (2)
Longitudinal particle position at 0mm for reverse beam (enhanced): Z-X, 2Dline model
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Gaussian Trajectory Diff (1)
Difference between forward trajectories (Z-X) for tree2D and 2Dline space charge models
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Gaussian Trajectory Diff (2)
Difference between forward trajectories (Z-X) for tree2D and 2Dline space charge models (enhanced)
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Gaussian Angle Diff (1)
Difference between forward angles (Z-X’) for tree2D and 2Dline space charge models
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Gaussian Angle Diff (2)
Difference between forward angles (Z-X’) for tree2D and 2Dline space charge models (enhanced)
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Gaussian Beam: 600mm (1)
Trajectories for reverse Gaussian beam tracked for 600mm: Z-X, 2Dline model
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Gaussian Beam: 600mm (2)
Angle trajectories for reverse Gaussian beam tracked for 600mm: Z-X’, 2Dline model
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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).
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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).
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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.