0. PTC-pyOrbit code development
H. Bartosik
Acknowledgements: G. Rumolo, R. Wasef
Space charge meeting June 5th 2014

1. Introduction Status of SC simulations at CERN
PSB
PTC-ORBIT with “2.5D” module  excellent agreement with measurements (see presentations of Vincenzo and Elena)
According to Elena, could be of interest to use the Orbit Teapot tracker, but need double RF (presently being developed by Sabrina Appel at GSI) PS
PTC-ORBIT simulations with “2.5D” module is very time consuming
MADX frozen SC  excellent agreement with measurements (see presentations of Raymond)
IMPACT as alternative for self consistent simulations (but not on CERN cluster)
SPS
PTC-ORBIT and PTC-pyOrbit simulations with “2.5D” module gives unphysical results for certain simulation parameters  under investigation; it seems that a 2D slice-by-slice space charge solver could help
Looked into frozen space charge simulations with MAD  need to include dispersion for initialization (presently being implemented by Valery Kapin)
Ideas for code development in PTC-pyOrbit
Frozen space charge
2D slice-by-slice space charge PIC solver
SC meeting June 5th 2014

2. Implementing frozen SC in PTC-pyOrbit - motivations
Frozen SC with PTC
Machine model and lattice description
Double RF
Direct comparison with self consistent (PIC) simulations
Using the same PTC lattice
Using the same simulation scripts and analysis tools
Full parallelization
efficient use of our 48 core machines on SC cluster
All the tools of pyOrbit can be used
Eventually could allow for closed orbit errors
Correct placement frozen SC kicks around closed orbit feasible
Updating the SC parameters (emittance, bunch length, intensity) on the Python level  very flexible
SC meeting June 5th 2014

3. Implementing frozen SC in PTC-pyOrbit - status
First version implemented (C++ & Python) in private version of PTC-pyOrbit
Based on Bassetti Erskine formula for electric field calculation
Installation of SC nodes like for the PIC solvers
Uses lattice functions provided by PTC
Takes into account the dispersion for beam size calculation
Space charge kick is weighted by longitudinal density with options:
Coasting beam
Gaussian longitudinal profile
Benchmarking and testing presently ongoing
Speed comparison for the case of the PS lattice
MADX frozen SC (4 cores): 50k turns / day (Raymond)
PTC-PyOrbit (48 nodes on SC cluster): 270k turns / day (with PTC!)
Great speed in PTC-pyOrbit given that the CPUs on our SC cluster are rather slow …
SC meeting June 5th 2014

4. Tune spread comparison frozen SC vs. PIC
Tune spread from the new frozen SC module consistent with PTC-pyOrbit PIC simulations (“2.5D”)
Example for the SPS including Gaussian line density profile
SC meeting June 5th 2014

5. Tune spread comparison frozen SC vs. PIC
Tune spread from the new frozen SC module consistent with PTC-pyOrbit PIC simulations (“2.5D”)
Example for the PS including Gaussian line density profile in frozen SC
Many thanks to Raymond for providing the PS lattice and particle distribution files!
Small difference comes from the fact that actual longitudinal line density of particle distribution is parabolic …
SC meeting June 5th 2014

6. Implementing frozen SC in PTC-pyOrbit - outlook
Implement also
Possibility to update bunch parameters
Longitudinal parabolic distribution
Arbitrary line density profile (using interpolation)
Field calculation around non-zero closed orbit (requires PTC modifications)
Possibility to use with Teapot lattice of pyOrbit
Benchmark with results from MADX frozen SC in the PS for evolution of transverse profiles  ongoing (together with Raymond)
Benchmarking test of Giuliano
Simulations for the SPS
Integration into official pyOrbit version once we are confident about the results
SC meeting June 5th 2014

7. Implementing slice-by-slice 2D SC in PTC-pyOrbit
Motivation
Correct modeling of SC in case of intra-bunch motion and/or beam size variation along the bunch (e.g. due to momentum spread variation along the bunch)
Hope to suppress unphysical coherent dipole oscillations obtained for some machine parameters of the SPS (it seems that the intra-bunch motion due to the head-tail phase shift for non-zero chromaticity is the origin of the problem when using the Orbit “2.5D” model)
Status
First version implemented (C++)
Using the 2D FFT solver of pyOrbit for individual longitudinal slices along a 3D grid  also boundary conditions can be used
Tests with SPS lattice are presently ongoing
SC meeting June 5th 2014

8. Tune spread comparison 2.5D vs. 2D slice-by-sclice
Tune spread from the new 2D slice-by-slice SC module consistent with PTC-pyOrbit 2.5D simulations for SPS
Slightly smaller tune spread in slice-by-slice as beam size variation along the bunch properly taken into account
SC meeting June 5th 2014

9. Other ideas Indirect space charge
Can be treated by including boundary conditions in the PIC solver
Limited to simple geometries
Computationally heavy if beam size is small compared to vacuum chamber (like LHC beams in PS and SPS)
Could also be treated like wake field (like in HEADTAIL)
Single kick in the machine
Also the full impedance model could be included
Wake field implementation in pyOrbit should not be too difficult
Use the Teapot tracker of Orbit for faster simulations
Symplectic thin lens integrator, faster than PTC
Needs to be fully tested with CERN machines (first trials with SPS lattice look promising: tunes exactly identical to MADX, chromaticity not too far off, …)
Misalignments and magnet errors?
SC meeting June 5th 2014

10. Summary Development of frozen space charge in PTC-PyOrbit
Interesting to use FSC with PTC (PS, SPS, also PSB?) with affordable computation time on our SC cluster
First implementation done  tune spread agrees with PIC simulation
Further benchmarking in the pipeline
Extension to longitudinal profiles other than constant or Gaussian soon
Advantage of different SC simulation approaches (frozen and PIC) with the same tool!
Development of 2D slice-by-slice PIC solver in PTC-PyOrbit
Needed for the SPS (also to properly take into account the wall effects in other machines)
First implementation is done – benchmarking and tests with SPS lattice ongoing
Tune spread for SPS case as expected
Other ideas
Implementing the indirect space charge through wake fields looks feasible
Maybe using the Teapot tracker could be interesting in some cases
Anything else ?
SC meeting June 5th 2014