Time-Reversed Particle Simulations In GPT

(or “There And Back Again”)

Simon JollyImperial College

FETS Meeting, 12/10/05

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?

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.

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).

Parallel/Gaussian X-Y Profiles

Gaussian beamParallel beam

Parallel Beam Trajectories (1)

Forward trajectories: Z-X, tree2D model

Parallel Beam Trajectories (2)

Reverse trajectories: Z-X, tree2D model

Parallel Beam: tree2D X-Y (1)

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

Parallel Beam: tree2D X-Y (2)

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

Parallel Beam: tree2D X’-Y’

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

Parallel Beam Trajectories (3)

Forward trajectories: Z-X, 2Dline model

Parallel Beam: 2Dline X-Y

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

Parallel Beam: 2Dline X’-Y’

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

Parallel Beam SC Models (1)

Difference between forward trajectories (Z-X) for tree2D and 2Dline space charge models

Parallel Beam SC Models (2)

Difference between transverse positions at 0mm (X-Y) for tree2D and 2Dline space charge models

Gaussian Beam: Forward (1)

Forward trajectories: Z-X, tree2D model

Gaussian Beam: Forward (2)

Forward trajectories: Z-X, 2Dline model

Gaussian Beam: Reverse

Reverse trajectories: Z-X, 2Dline model

Gaussian Beam: tree2D X-Y

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

Gaussian Beam: 2Dline X-Y

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

Gaussian Beam: tree2D X’-Y’

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

Gaussian Beam: 2Dline X’-Y’

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

Gaussian Beam: Z-X (1)

Longitudinal particle position at 0mm for reverse beam: Z-X, 2Dline model

Gaussian Beam: Z-X (2)

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

Gaussian Trajectory Diff (1)

Difference between forward trajectories (Z-X) for tree2D and 2Dline space charge models

Gaussian Trajectory Diff (2)

Difference between forward trajectories (Z-X) for tree2D and 2Dline space charge models (enhanced)

Gaussian Angle Diff (1)

Difference between forward angles (Z-X’) for tree2D and 2Dline space charge models

Gaussian Angle Diff (2)

Difference between forward angles (Z-X’) for tree2D and 2Dline space charge models (enhanced)

Gaussian Beam: 600mm (1)

Trajectories for reverse Gaussian beam tracked for 600mm: Z-X, 2Dline model

Gaussian Beam: 600mm (2)

Angle trajectories for reverse Gaussian beam tracked for 600mm: Z-X’, 2Dline model

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).

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).

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.