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

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

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

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

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

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

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

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

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

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

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