Code parameters optimization & DTL Tank 1 error studies

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.: δx ) 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 DTL 2004 1000 runs

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 106 particles (5000 runs) • 250 to 400 CPU hours • Minimal loss: 1 ppm

8. Space charge routines

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

10. Space charge routines disagreement • 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) • Use 3d PICNIC with optimized mesh size

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

12. Gausup 3d (PICNIC) 2d (PICNIR) 7x7 mesh size through DTL 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 DTL 2005 Gaussian distribution, 50 kpart, 1000 runs Very little effect for all 3 longitudinal errors combined

15. Sensitivities to transverse errors DTL 2005 Some emittance growth No loss Energy jitter: a few 10-4 Phase jitter: a few 10-4 Gaussian distribution, 50 kpart, 1000 runs

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

17. Effect of input distribution DTL 2005 Gaussian distribution, 50 kpart, 1000 runs Simple shift (30-50%), no broadening

18. Effect of input distribution:transverse errors DTL 2005 DTL 2005

19. Global effect with high statistics: transverse & longitudinal errors 106 particles, 4291 runs, Gaussian input, 250 to 400 CPU hours for each run δx/y= ±0.1 mm Φx/y = ± 0.5 deg Φz = ± 0.2 deg G/G = ±0.5% and φ/φ=±1 deg E/Eklystron=±1% E/Egap=±1% 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: δx,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: Eklys/Eklys = ±1% klystron field phase: φklys = ±1deg gap field amplitude: Egap/Egap = ±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