1. PyHEADTAIL-PyECLOUD Simulations for LHC and HL- LHC Aaron Axford 27/05/20151

2. Contents ● LHC simulation parameters compared to SPS simulations ● Low energy instability scans for LHC ● High energy instability scans for LHC ● Overview of instability threshold change over energy values ● Summary and next steps 27/05/20152

3. LHC simulation parameters ParameterSPS 26 GeVLHC 450 GeV Circumference6911m26658m X and Y aperture Varying Depending on device. Eg. Quadrupole: X=7.6e-2 Y=1.9e-2 Constant X=2.3e-2 Y=1.8e-2 Dh_Sc0.4e-30.2e-3 Number of segments≈30≈80 Sigma_Z0.230.10 27/05/20153

4. LHC Injection Simulations Injection Dipole 27/05/20154

5. LHC Injection Simulations Injection Dipole 27/05/20155 Decoherence shown with slight narrowing of horizontal motion, with the horizontal emittance slightly increasing

6. LHC Injection Simulations Injection Dipole 27/05/20156 The instability threshold is, here, defined as the lowest electron density where the emittance increases by 5% The Threshold here is at 7e11 edens

7. Instability against Intensity Dipole at injection 27/05/20157 For this range of beam densities, there is no noticeable correlation between Intensity and Instability Threshold.

8. LHC Injection Simulations Injection Quadrupole 27/05/20158

9. LHC Injection Simulations Injection Quadrupole 27/05/20159 The instability threshold is, here, defined as the lowest electron density where the emittance increases by 5% The Threshold here is at 5e11 edens

10. Instability against Intensity Quadrupole at injection 27/05/201510 For this range of beam densities, there is no noticeable correlation between Intensity and Instability Threshold.

11. High Energy LHC simulations 27/05/201511 ParameterLHC 450GeVLHC 7TeV Gamma4797460 N_kicks≈80≈30 Dh_sc (meters)0.2e-30.07e-3 Dt_ref (seconds)10e-125e-12 Sigma_Z (meters)0.100.075

12. High Energy LHC simulations 27/05/201512 At low ecloud density and high energy, all results completely stable

13. High Energy LHC simulations (Unstable results) Quadrupole 27/05/201513

14. High Energy LHC simulations (Unstable results) Quadrupole, Instability threshold vs Intensity 27/05/201514 For this range of beam densities, a link between beam intensity and Instability threshold is unobservable with random particle generation at the beginning causing a large error

15. High Energy LHC simulations (Unstable results) Dipole 27/05/201515

16. High Energy LHC simulations (Unstable results) Dipole, Instability threshold vs Intensity 27/05/201516

17. Instability change of a range of Energy values 27/05/201517 ● Energy from 0.45TeV to 7TeV ● Constant bunch length used throughout ● Constant RF voltage used throughout ● Bunch matched to the bucket ● Magnetic fields changing with energy ● Number of kicks inversely proportional to Energy ● Grid size inversely proportional to Energy ● Intensity of 2.3e11 ppb ● Electron cloud density from 1e11 to 70e11

18. Instability change of a range of Energy values Dipole 27/05/201518 450 GeV2TeV5TeV

19. Instability change of a range of Energy values Dipole 27/05/201519 The Error bars for the instability thresholds refer to the size step of the simulations (±1.75e11)

20. Instability change of a range of Energy values Quadrupole 27/05/201520 450 GeV2TeV5TeV

21. Instability change of a range of Energy values Quadrupole 27/05/201521 Large impact from random generation however still a very strong correlation between instability and energy

22. Conclusion and next steps 27/05/201522 The beam intensity (when between 1.3e11 and 2.3e11 ppb) appears to have very little impact on the instability threshold for the LHC arc dipoles and quadrupoles Instability threshold increases with energy as expected from the increased beam rigidity Investigate the importance of number of kicks, slices and grid size for flat top LHC simulations