Space Charge Study Group

1. Space Charge Study Group • Mandate • Webpage • Kick-off Meetings concerning PTCORBIT • First impressions about PTCORBIT (PS, SPS)

2. Mandate • Revisiting the space charge limits for PSB, PS & SPS in the context of the LHC Injection Upgrade (LIU) which is part of the High Luminosity project of the LHC (HL-LHC). • This mandate might be reformulated as: "Finding the limits of the machine performance of the 3 machines due to space charge in presence of a full nonlinear model of these machines.“ ==> PTCORBIT? • This task will require reviewing the theory with the help of space charge experts around the world. • Equally relevant will be to compare the theoretical predictions with machine experiments.

3. Webpage • Web address: cern.ch/frs/Source/space_charge • Mandate • Core Team and collaborators • Literature • Meetings • In fact we have had a kick off meeting on 13th of May when Etienne & Sasha have been discussing their plans for the advancement of PTCORBIT. Christian and Elias have introduced the PSB and PS/SPS respectively in terms of space charge issues. • And on the 30th of May Sasha gave a presentation about what has been achieved during this period.

4. Do we need PTCORBIT for our space charge Studies? My personal View… I have asked the following questions to the PSB, PS & SPS collaborators: A) Do you consider PTCORBIT relevant for the analysis of your machine? B) I know that for the PSB the demands on the features of PTCORBIT are most relevant and it seems that there is still a need for more development that we should ask Etienne for, if we decide to go for PTCORBIT. Personally, I think we should continue this development even if it is not easy to communicate with Etienne nor with Sasha. Etienne is properly the one to fix the remaining problems with PTCORBIT. C) My general feeling has been that one might need a closer look at the optics models of all 3 machines. Please excuse me, since I am coming from the LHC and we had the luxury to measure everything and have very sophisticated models. This will be difficult to do for these reliable but old machines nevertheless we should make our best effort to come up with the best we can know about those machines. Of course, we need sufficient manpower to do so! Do you agree with this analysis? D) Most exciting is the fact that apparently Hannes has found issues with the results of his space charge calculations in ORBIT itself. It would be great if Hannes could elaborate on this a little bit. After all, the PTC part is only single particle part to serve ORBIT.

5. PTC-ORBIT @ PS (Simone) • Needs: • Simulate eventual emittance blow-up of high-intensity LHC beams (for PS upgrade or not…) • Help in determining the maximum acceptable Laslett tune spread, i.e., maximum intensity per bunch and/or minimum emittance • Identify, if possible, an eventual cure (resonance compensation, change of working point?) • Understand continuous losses observed during the injection process of the high intensity non-LHC beams

6. Code status for PS • PTC-Orbit running for single particle case • able to reproduce the collapsing of the injection bump with time-varying fields • Tune and chromaticity correct as in the standard PTC standalone simulation • Space charge simulation • Only one run done so far • Technically the code works but the physical parameters have to be optimized • Missing: • Lattice optimization to speed-up the simulation

7. Space charge simulations for SPS (Hannes) • Motivation • High intensity single bunches are produced since 2010 and injected into SPS • A series of parallel MD sessions were dedicated to finding intensity limitations first with the nominal LHC optics and later with the new low γt optics (which should provide higher beam stability) • Space charge tune spread of ΔQ~0.05 for nominal LHC beams (1.3e11 p/b, εn,xy=2.5 μm) • Recent studies with up to 3.3e11 p/b and injected emittances of εn,xy~1.2-1.5 μm ==> significantly increased space charge tune spread (ΔQ~0.15 and higher) • MD sessions are currently devoted to studies of emittance preservation for high intensity and working point optimization • Working point optimization should/could be accompanied by space charge simulations with PTC-ORBIT • Benefit/relevance of PTC-ORBIT for SPS space charge simulations • Ultimate goal is to develop an “effective” machine model including the nonlinear (multipole) components of the machine (presently ongoing) and use this model for optimizing the working point in the presence of space charge tune shift • For this purpose, PTC-ORBIT seems to be a suitable tool …

8. Present status of PTC-ORBIT simulations for SPS • Ideal lattice used for beginning • Nominal and low γt optics – ideal lattice without field errors or misalignment • Static magnetic fields and RF-voltage ==> very simple case, no acceleration • Actual configuration of travelling wave RF-cavities is modeled (thanks to a modification in PTC) • “2.5D” space charge model is used • Around 2500 transverse space charge nodes around the lattice • 1 longitudinal space charge kick • 2.5D simulation is good approximation for “long bunches”: longitudinal size much bigger than transverse size (should be satisfied in SPS for LHC beams, full bunch length around 1.1m and transverse beam sizes on the order of a few cm) • For now, beam pipe is not included in simulations • Beam size much smaller than vacuum chamber ==> only small contribution to tune spread expected from wall effects • Taking wall effects into account requires huge grid size compared to beam size and therefore long computation time • Full 3D simulation would require vacuum chamber definition • Again the problem of the small beam size compared to chamber size • Unpractical due to the different kind of vacuum chambers in the SPS

9. First simulations - Observations • Simulated one set of parameters for both optics cases to gain confidence in code • Intensity 2e11 p/b, emittances εn,xy~2.5 μm • Phase space distributions matched to the corresponding optics functions and bucket sizes of the respective optics: • Transverse: Gaussian cut at 3σ • Longitudinal: parabolic with a cut around 2.2σ • Nominal working points for the 2 optics (ξx,y=0.1) • Low γt: (Qx, Qy)=(20.13, 20.18) • Nominal optics: (Qx, Qy)=(26.13, 26.18) • Simulation of 3000 turns (~60ms) • Low γt opics: • Minimal emittance blow-up (<1%) in both planes • Nominal optics: • Significant emittance growth in horizontal plane: initially exponential growth by a factor of 1.5 and beam halo formation!?? Minimal emittance blow-up (<1%) in vertical plane!! • The exponential emittance growth disappears for increased RF-voltages (twice the RF-voltage, but still matched bucket by increasing longitudinal emittance) or by switching off longitudinal space charge calculations!!