1. Code parameters optimization & DTL Tank 1 error studies Maud Baylac, Emmanuel Froidefond Presented by JM De Conto LPSC-Grenoble HIPPI yearly meeting, Oxford, September, 2005

2. Overview Goal, recall TW inputs Optimization of code parameters Nb runs Nb calculations per βλ Nb particles Space charge routine: 2d vs 3d Mesh size Error study Individual sensitivity: longitudinal & transverse Effect of input distribution Global errors, loss Set of tolerances

3. Goal For us: learn how to use TraceWin Study sensitivity of DTL to quadrupole and field errors Determine set of tolerances for tank 1 for quadrupole alignment quadrupole gradient klystron field amplitude and phase gap field amplitude

4. TraceWin inputs Several inputs: evolutive DTL design Input distribution: mainly type -32 (Gaussian) file Worse case scenario & Same for all studies 2 types of simulations: Sensitivity: one type of error at a time (e.g.: δ x ) Global error effect: all types of errors at once Each error generated randomly & uniformly in [–max; +max] For all cases, transport to the end of the DTL

5. Number of runs Study convergence with nb of runs 1000 runs DTL 2004

6. Nb space charge calculations per βλ Inactive on DTL cells Default for DTL cells: was 1 space charge calc. per cell (ie: 20 calc. per betatron oscil.) modified to up to 3 calc. per cell (depending on cell length)

7. Number of particles Most simulations use 50 kparticles (1000 runs) –Fast calculation –Minimal loss: 20 ppm A few global error runs use 10 6 particles (5000 runs) –250 to 400 CPU hours –Minimal loss: 1 ppm

8. Space charge routines

9. Space charge routines comparison 2d vs 3d disagreement can be very large Not understood Example: 1 run with 1.5 mm x displacement of the 1 st quad with PICNIR & PICNIC PICNIR (2d) PICNIC (3d) DTL 2004

10. large for large emittance growth if X ≠ Y (our case) increases with beam current much more pronounced for FFDD vs FODO for transverse phenomenon Agreement for longitudinal errors (unexplained) Space charge routines disagreement  Use 3d PICNIC with optimized mesh size

11. Optimization of mesh size Gausup 3d (PICNIC) 2d (PICNIR) Mismatch beam (40% in x/y/z) at DTL input to generate large emittance growth

12. 7x7 mesh size through DTL Gausup 3d (PICNIC) 2d (PICNIR) Matched beam through DTL: validation of mesh size

13. DTL with all errors 7x7 mesh statistically compatible with high resolution mesh & keeps calculation time reasonable

14. Sensitivities to longitudinal errors Gaussian distribution, 50 kpart, 1000 runs Error type Max error amplitude (mm or deg) ± rms (%) ± rms (%) ± rms (%) Longitudinal errors  E klys /E klys = ± 1%  φ klys = ±1deg  E gap /E gap = ± 1% 0.0 ± 0.50.0 ± 0.60.5 ± 0.7 Very little effect for all 3 longitudinal errors combined DTL 2005

15. Sensitivities to transverse errors Gaussian distribution, 50 kpart, 1000 runs Error type Max error amplitude (mm or deg) ± rms (%) proba (%) ± rms (%) proba (%) ± rms (%) proba (%) Displ x±0.1 mm 1.0 ± 0.8 <1% : 60 <5% : 100 0.1 ± 0.1 <1% : 100 <5% : 100 0.7 ± 0.5 <1% : 76 <5% : 100 Rota x (pitch) ±0.5 deg 0.01 ± 0.01 <1% : 100 <5% : 100 1E-3±3E-3 <1% : 100 <5% : 100 0.01 ± 0.01 <1% : 100 <5% : 100 Rota z (roll) ±0.2 deg 0.8 ± 0.6 <1% : 76 <5% : 100 0.7 ± 0.6 <1% : 77 <5% : 100 0.02 ± 0.02 <1% : 100 <5% : 100  G/G ±0.5% 0.1 ± 0.2 <1% : 100 <5% : 100 0.1 ± 0.3 <1% : 100 <5% : 100 0.02 ± 0.07 <1% : 100 <5% : 100 Some emittance growth No loss Energy jitter: a few 10-4 Phase jitter: a few 10 -4 DTL 2005

16. Longitudinal rotation (roll) Emittance growth similar in x & y (coupling) Emittance growth quadratic with roll angle Confirmed by theoretical calculations No longitudinal emittance growth DTL 2005

17. Effect of input distribution Design & Distribution ± rms (%) proba (%) ± rms (%) proba (%) ± rms (%) proba (%) RMS x (mm) & RMS x’ (mrad) RMS y (mm) & RMS y’ (mrad) Losses 2005 Gaussian 2.0 ± 1.0 <1% : 13 <5% : 99 1.9 ± 1.0 <1% : 15 <5% : 99 1.5 ± 0.8 <1% : 28 <5% : 100 0.9 & 1.0 1.1 & 0.8 Loss < 2E-5 2005 KV 1.5 ± 1.0 <1% : 35 <5% : 100 1.5 ± 1.0 <1% : 37 <5% : 100 1.1 ± 0.7 <1% : 57 <5% : 100 0.9 & 1.1 1.1 & 0.9 Loss < 2E-5 Gaussian distribution, 50 kpart, 1000 runs Simple shift (30-50%), no broadening DTL 2005

18. Effect of input distribution: transverse errors DTL 2005

19. Global effect with high statistics: transverse & longitudinal errors and  φ/φ=±1 deg  E/E klystron =±1%  E/E gap =±1% Design & errors ± rms (%) proba (%) ± rms (%) proba (%) ± rms (%) proba (%)  E ± rms (keV)  φ ± rms (deg) Losses 2005 Trans. 2.0 ± 1.0 <1% : 13.8 <5% : 98.7 2.0 ± 1.0 <1% : 14.2 <5% : 98.6 1.5 ± 0.8 <1% : 26.5 <5% : 99.9 56.6 ± 0.4 3.11 ± 0.01Loss < 1E-6 2005 Trans.+ longi. 2.0 ± 1.2 <1% : 20.4 <5% : 98.5 2.0 ± 1.2 <1% : 20.3 <5% : 98.1 1.9 ± 1.1 <1% : 20.1 <5% : 99.1 56.5 ± 2.6 3.13 ± 0.15Loss < 1E-6 10 6 particles, 4291 runs, Gaussian input, 250 to 400 CPU hours for each run δ x/y = ±0.1 mm Φ x/y = ± 0.5 deg Φ z = ± 0.2 deg  G/G = ±0.5% Some broadening in longitudinal direction

20. Main trends of quadrupole alignment Transverse displacement (symmetric x/y ) transverse & longitudinal emit. growth 2005 design: ~ 1% for ±0.1 mm Transverse rotation (pitch & yaw): no effect Longitudinal rotation (roll): transverse emit. growth 2005 design: ~ 0.8% for ±0.2 deg Emittance growth with 2005 design vs 2004 design: slightly worse with errors on all tanks Individual sensitivities roughly add up

21. DTL tank 1 tolerances Tolerances agreed upon by DTL task force: quadrupoles: longitudinal displacements: δ x,y = ±0.1 mm longitudinal rotations: Φ x,y = ±0.5 deg transverse rotations: Φ z = ±0.2 deg gradient:  G/G = ±0.5% accelerating field: klystron field amplitude:  E klys /E klys = ±1% klystron field phase:  φ klys = ±1deg gap field amplitude:  E gap /E gap = ±1%

22. Conclusions Sensitive parameters: transverse displacement & roll Little effect due to longitudinal errors (longitudinal shift cannot be tested with TW) With present tolerance budget, beam quality sees little degradation through DTL: Emittance growth x, y and z < 5% in 98% of runs Loss < 10 -6 RMS width in x and y < 1.2 mm RMS width in x’ and y’ < 1.1 mrad Multipolar component contribution: waiting for TW debug Code benchmarking to validate results

23. Acknowledgements Didier URIOT (CEA/DSM) for discussions and multiple debugs Nicolas PICHOFF (CEA/DAM) for discussions regarding space charge calculations Edgar Sargsyan, Alessandra Lombardi and Frank Gerigk (CERN) for inputs and discussions