1. Field and Phase Error Studies in Normal Conducting Structures LLRF and Beam Dynamics in Hadron Linacs – EuCARD2 Workshop Ciprian Plostinar 01.06.2015

2. Overview Context Projects Structures Errors Studies Conclusions Acknowledgements

4. Context HIPPI – High Intensity Pulsed Proton Injectors –European R&D collaboration aimed at developing a common European technology base for the construction of high intensity hadron linacs –Completed in 2008 –Linac4, FAIR Proton Injector, ISIS Upgrade Linac. –Several WP, including beam dynamics and cavity development. –Comparative assessment of several structures Work extended to include SNS and J-PARC

5. Projects – Linac4 Ion Species H-H- Output Energy 160MeV Frequency 352.21MHz Pulse Length 0.4ms Peak Current40mA Protons per Pulse1.0 x 10 14 Repetition Rate2Hz Duty Cycle0.08% Average Beam Power5.1kW Accelerating StructuresRFQ, DTL, CCDTL, PIMS (*CCL) Accelerator Length~80m

6. Projects – ISIS Linac Ion SpeciesH-H- Output Energy180MeV Frequency324/648MHz Pulse Length0.1 – 1ms Peak Current60mA Repetition Rate50Hz Duty Cycle0.5 – 5% Average Beam Power54 - 540kW Accelerating StructuresRFQ, DTL, CCL Accelerator Length~99m

7. Projects – FAIR Proton Injector Ion Species Protons Output Energy 70MeV Frequency 325.244MHz Pulse Length 36μsμs Peak Current35mA Protons per Pulse7.88 x 10 12 Repetition Rate4Hz Duty Cycle0.0144% Average Beam Power3.53kW Accelerating StructuresRFQ, CH-DTL Accelerator Length~31m

8. Projects – J-PARC Ion Species H-H- Output Energy 400MeV Frequency 324/972MHz Pulse Length 0.5ms Peak Current30/50mA Protons per Pulse9.4 x 10 13 / 1.5 x 10 14 Repetition Rate25Hz Duty Cycle1.25% Average Beam Power80/133kW Accelerating StructuresRFQ, DTL, SDTL, ACS Accelerator Length~244m

9. Projects – SNS Ion Species H-H- Output Energy 1GeV Frequency 402.5/805MHz Pulse Length 1.0ms Peak Current38mA Protons per Pulse1.5 x 10 14 Repetition Rate60Hz Duty Cycle6% Average Beam Power1.4MW Accelerating StructuresRFQ, DTL, CCL, SCL Accelerator Length~257m

10. Structures – DTL

11. Structures – SDTL

12. Structures – CH-DTL

13. Structures – CCDTL

14. Structures – PIMS

15. Structures – CCL

16. Structures – ACS

17. Field and Phase Error Studies - Method - RF errors at the klystron level translate directly into accelerating voltage errors Impact on the beam quality Precise tuning of RF amplitude and phase is indispensable to reduce uncontrolled beam loss and beam quality deterioration. Tuning goals at the klystron level can be different for different structure types

18. Field and Phase Error Studies - Method - Tracking a Gaussian distribution containing 100000 macro-particles over 1000 - 2000 runs, with random errors uniformly distributed Transmission, beam phase jitter, energy jitter and RMS emittance at the end of the structure analysed. Two different types of dynamic errors (“Klystron errors”) have been applied: –an error in RF phase –an error in amplitude Errors appear at the RF power source and are applied coherently to all RF gaps powered by the same source Cannot be “cured”

19. Field and Phase Error Studies - Linac4 DTL - Errors: E klystron [%], φ klystron [deg] Phase Jitter [deg] 1 sigma Energy Jitter [keV] 1 sigma RMS emittance [deg.MeV] Nominal--0.167 ± 0.5% - 0.5 ±deg0.8130.169±0.003 ± 0.5% - ±1deg0.9180.171±0.004 ± 0.5% - ± 2deg1.1310.175±0.009 ± 1% - ± 0.5deg1.6230.1707±0.005 ± 1% - ± 1deg1.6280.1719±0.006 ± 1% - ± 2deg1.8360.1772±0.011 ± 2% - ± 0.5deg5.1430.179±0.014 ± 2% - ± 1deg5.7460.180±0.017 ± 2% - ± 2deg8.6490.187±0.024

20. Field and Phase Error Studies - Linac4 DTL - Amplitude errors have more impact than the phase errors For small errors, the phase jitter is dominated by amplitude errors, while energy deviation by phase errors. A variation of ±2% in amplitude causes an emittance growth and an energy jitter above what is tolerable A control of the amplitude and phase within ±0.5% and ±0.5 degrees would be ideal But, ±1% and ±1 degree is also acceptable The same procedure was repeated for the SNS, J-PARC and RAL DTLs with similar conclusions

21. Field and Phase Error Studies - Linac4 CCDTL - Just like for the DTL, the results confirm the Klystron’s amplitude and phase should be controlled ideally to ±0.5 % and ±0.5 deg to control energy and phase jitter at the CCDTL output However, values of ±1% and ±1 deg are still acceptable Errors: E klystron [%], φ klystron [deg] Phase Jitter [deg] 1 sigma Energy Jitter [keV] 1 sigma RMS emittance [deg.MeV] Nominal--0.196 ± 0.5% - ± 0.5deg0.5390.196±0.003 ± 1% - ± 1deg1630.196±0.005 ± 2% - ± 2deg21150.198±0.009 ± 5% - ± 2deg42370.200±0.015

22. Field and Phase Error Studies - J-PARC SDTL - SDTL results comparable with DTL ±1% error in amplitude and ±1 deg error in phase are acceptable Errors: E klystron [%], φ klystron [deg] Phase Jitter [deg] 1 sigma Energy Jitter [keV] 1 sigma RMS emittance [deg.MeV] Nominal--0.126 ± 0.5% - ± 0.5deg0.8420.126±0.004 ± 1% - ± 1deg1.5750.128±0.005 ± 2% - ± 2deg3.11250.130±0.008

23. Field and Phase Error Studies - Linac4 CCL - Again, for the CCL, the ±1% - ±1 deg case is acceptable, but it also depends on requirements for energy painting at injection into PSB. SNS and RAL CCL study also indicates a similar error budget. Errors: E klystron [%], φ klystron [deg] Phase Jitter [deg] 1 sigma Energy Jitter [keV] 1 sigma RMS emittance [deg.MeV] Nominal--0.18 ± 0.3% - ± 0.3deg0.6730.1827±0.0036 ± 0.6% - ± 0.6deg1.121440.1926±0.036 ± 1% - ± 1deg1.922390.2106±0.0324

24. Field and Phase Error Studies - J-PARC ACS - J-PARC ACS comparable with CCL (Pi/2 structures) ±1% error in amplitude and a ±1 deg error in phase acceptable from a beam dynamics point of view. Errors: E klystron [%], φ klystron [deg] Phase Jitter [deg] 1 sigma Energy Jitter [keV] 1 sigma RMS emittance [deg.MeV] Nominal--0.140 ± 0.5% - ± 0.5deg0.81020.141±0.003 ± 1% - ± 1deg1.22170.145±0.005 ± 2% - ± 2deg2.53150.148±0.009

25. Field and Phase Error Studies - Linac4 PIMS - For the PIMS structure, klystron phase and amplitude should ideally be controlled to ±0.5% and ±0.5 deg to limit energy and phase jitter Values of ±1% and ±1 deg are still acceptable. However, this is a hard limit as for successful energy painting at injection into the PSB, the maximum energy jitter acceptable is 125 keV. Errors: E klystron [%], φ klystron [deg] Phase Jitter [deg] 1 sigma Energy Jitter [keV] 1 sigma RMS emittance [deg.MeV] Nominal--0.180 ± 0.3% - ± 0.3deg0.3650.181±0.00088 ± 0.5% - ± 0.5deg0.4780.181±0.00094 ± 1% - ± 1deg0.661260.181±0.0012 ± 2% - ± 1deg0.852200.181±0.0013

26. Field and Phase Error Studies - FAIR Linac CH-DTL - The probability that the degradation of the emittance due to errors is within 1% or 5% is presented. ±1deg error in phase is tolerable However, due to the distinctive characteristics of the KONUS focusing scheme, a reduction in voltage is not desirable, that is why the design aims for a ±0.2% error in voltage at the klystron level. Errors: E klystron [%], φ klystron [deg] |Δε x /ε x | Probability |Δε y /ε y | Probability |Δε z /ε z | Probability ± 1% <5% 80.3 <10% 96.9 <5% 82.3 <10% 97.8 <5% 60.5 <10% 80.6 ± 1deg<5% 100<5% 97.4 <10% 100 <5% 67.1 <10% 87.6

27. DTLSDTLCH-DTLCCDTLPIMSCCLACS Ideal±0.5% ±0.5 deg --±0.5% ±0.5 deg ±0.5% ±0.5 deg ±0.5% ±0.5 deg - Acceptable±1% ±1 deg ±1% ±1 deg ±0.2% ±1.0 deg ±1% ±1 deg ±1% ±1 deg ±1% ±1 deg ±1% ±1 deg Conclusions

28. For most structures a ±1% error in amplitude and ±1 deg error in phase is tolerable. The control should ideally be to within ±0.5% in amplitude and ±0.5 deg in phase CH-DTL has tighter requirements for amplitude control Some limitations might come from downstream machines (i.e. injection). Sensitivity to input jitter from upstream structures could also alter the “error budget”

29. Acknowledgements Linac4 error studies done as part of HIPPI by A. Lombardi, M. Baylac, G. Bellodi, M. Eshraqi, J ‑ B Lallement, E. Sargsyan and others at CERN, LPSC. M. Baylac et al., “Statistical Simulations of Machine Errors for Linac4“, “Proceedings of HB'06", Tsukuba, Japan (2006). G. Bellodi et al., “Effects of RF Errors on the Linac4 Performance“, “HIPPI 2008 Annual Meeting", Geneva, Switzerland (2008). FAIR Proton Linac error studies done by G. Clemente and others at GSI and Frankfurt University. G. Clemente et al., “Beam Dynamics Layout and Loss Studies for the Fair P-Injector”, Proc. of EPAC’08, Genoa, Italy (2008).