1. DTL: Basic Considerations M. Comunian & F. Grespan Thanks to J. Stovall, for the help!

2. OutLine Design parameters Design Method Design of PMQ, Field Law, Lattice RF optimization Beam dynamics optimization Example of a FODO DTL Conclusion

3. DTL Parameters Particles is proton. Input energy of 3 MeV. (β=0.0798) Output energy of 50 MeV. (β=0.314) Frequency is 352.2 MHz. Current of 70 mA. Duty cycle 4%. Total peak power (SF*1.2+Beam) < 6 MW. Total DTL length <20 m (inter tanks space?).

4. Beam Dynamics parameters Input Transverse RMS emittance Norm. of 0.22 mmmrad. (output of RFQ+10% in the MEBT) Input Longitudinal RMS emittance Norm. of 0.32 mmmrad (output of RFQ). Input distribution Gaussian (5 sigma on size, i.e. a very large total emittance). Simulation Code: TraceWin with 10^6 particles (max of 0.14 W for particle). Used calculated matched input beam conditions. Used TTF; TTF’; TTF’’ as calculated cell by cell by SuperFish. Constant PMQ gradient or Constant phase advance or Equipartitioning? PMQ size as Linac 4 PMQ tender?.

5. Design method Maximum of 1.4 Ekp? -> limited By Moretti Criteria. Maximum of 2 MW power for Tanks. -> From Klystron limit. Maximum Tank length of 7-8 m? -> From RF tuning. Maximum PMQ field of 50-70 T/m? -> From manufacturing. Maximum output emittance? -> From SC Linac Acceptance. Maximum losses allowed? (1 W/m?) -> From radioprotection. Maximize effective shunt impedance? -> From Cell design. Equipartitioned BD design? -> SNS design rule. Field E0 ramping? -> SNS yes, CERN no. Lattice? FFDD(CERN)? FODO? FFODDO(SNS)? O=space for steering/BPM. Intertank distance? 3β (CERN)? or 1 β (SNS)? Maximum Mechanical module length? ->2 m from manufacturing.

6. PMQ CERN Linac4 ID=22 mm L=45 mm Gmax=54 T/m Difficult to housing the Quad on the first DTL cell. The least expensive type has rectangular PM pieces. The most performing is the Bullet shape. Field clamp? Bore aperture ID? PMQ tolerance!!! First DTL Cell

7. Moretti Criteria is more demanding respect to the Kilpatrick “Brave” factor sparking in the region of collinear B & E fields. Clamp effects Sparking effects (@1.7kp) on Linac4 DTL prototype

8. Flat or Ramped Field E0? The idea is to model the longitudinal behavior of the field distribution with the goal of determining the dimensions of perturbations applied to the tank end walls that will pre-set the longitudinal field distribution to approximately that of the design. Shapes of the individual drift tubes are the same as the design except for the face angles. The ramped solution is better in term of performance.

9. Optimization of the effective shunt impedance 1.Increase the Transit Time Factor T → decrease the gap length adjusting the Face Angle - main limitation: in the initial cells for PMQ accommodation adjusting the Tank Diameter - main limitation: Post Coupler stabilization 2.Increase the ratio V 0 /I wall → decrease the gap capacitance, i.e. the Drift Tube Diameter adjusting the Tank Diameter - main limitation: Post Coupler stabilization

10. An initial small face angle is necessary to accommodate the PMQ. A large flat nose can induce multipacting. Ok for PMQ With optimized Gap Length for TTF, a smaller Drift Tube Diameter reduces power losses.

11. FODO lattice solution with asymmetric cell unit: PMQ every second drift tube periodic structure on  Post Coupler every second drift tube ZTT=39.397 MOhm/mZTT=47.331 MOhm/m Post Coupler stabilization requires -a number of Post Coupler per unit-length (n) -a certain capacitive coupling between Post and Tubes (C p ) → under study the stabilization of a DTL tank design with asymmetric cells.

12. FODOFFODDO FFDDFFDDO FDO FD Particles density plot for different focusing scheme along the DTL LATTICE DESIGN

13. LatticeFODOFFODDOFFDDFFDDOFDOFD # PMQ628312410083124 G PMQ [T/m]5431 - 2752 - 4540 - 3554 Emit(x,y) increase [%]1827131836 Emit(z) increase [%]384638314661 Power Loss [W]0.0331220.017500 The best lattice appear to be the FODO and the FFDD, with less PMQ, low emittance growth and almost no losses.

14. Emittance evolution on the DTL UNIFORM Distribution GAUSSIAN Distribution The emittance increase depend from the input beam distribution

15. Beam Losses by power density probability Shaking of PMQ by +/- 0.1 mm, for an Example of FFDD lattice: The RED line show 1 W power level

16. Equipartitioning Design Gaussian input distribution Envelope Calculation The error study show little difference for the DTL, but what about the following linac?

17. Example of a FODO DTL Space inside DTL for steering and BPM. Optimizations of Shunt impedance by asymmetric cell. Reduce number of PMQ. High gradient of PMQ, from 54 T/m to 66 T/m.

18. DTL with a FODO Lattice SF runs from 3 to 50 MeV Data collect and analysis on Excel Power by SF*1.2 Design Summary TankNo ofLengthWfinalPower CellsmMevMW 1647.3019.271.989 2295.7534.962.010 3245.9450.342.034 Total11718.996.03

19. FODO Lattice with G=54 T/m

20. Resonance Chart High order

21. RMS beam size Total beam size with gaussian input distribution

22. Emittance and halo with Gaussian beam Transversal Emit increase=14% Longitudinal Emit increase=25% Transversal Halo increase=60% Longitudinal Halo increase=30%

23. Emittance and halo with Uniform beam Transversal Emit increase=0% Longitudinal Emit increase=12% Transversal Halo increase=20% Longitudinal Halo increase=217%

24. Final Phase Space Gaussian Uniform

25. Magnets “shake” Magnetic center respect the geometrical center shake of +/- 0.1 mm Yaw/pitch/Roll of +/-1°=17mrad Gradient error of +/-1% All errors apply together with a Gaussian input beam distribution

26. Emittance and Halo with error Transversal Emit increase=36% Longitudinal Emit increase=41% Transversal Halo increase=50% Longitudinal Halo increase=30%

27. Final Phase Space with Magnets “shake”

28. Statistics on 200 runs with magnets “shake” Max power lost on 200 runs about 42W, Average 0.6W, minimum=0 Power density probability red line=1W

29. Emittances growth on 200 DTLs with errors on PMQ Transv. Emittance increase=43% Long. Emittance increase=36% (Gaussian Distribution) Increase respect to the input value

30. Longitudinal and transversal DTL acceptance Acceptance Long. about 10 MeVdeg, i.e. for a 5σ gaussian beam dist. The max RMS emittance is 0.4 MeVdeg Acceptance Trans. about 6.5 mmmrad, i.e. for a 5σ gaussian beam dist. The max RMS emittance is 0.26 mmmrad norm.

31. Conclusion on FODO example A possible solution with PMQ G=54 T/m -> as Linac4 DTL tender. Space for steering and BPM -> low tolerance on PMQ; reduced intertank distance. No problem by losses -> low tolerance on PMQ. Which input beam emittance and distribution? Which impact on the following Linac?

32. DTL Status and Future Work Almost defined the design parameters. Started the Lattice configuration analysis. Started the RF design -> ZT^2 optimization. Carry out the still missing design parameters. Beam dynamics design. RF design. Integrate iteration on BD and RF design.

33. Warm Linac Layout Integration Defined the common language: TraceWin. Defined the lattice database schema. Not yet defined: – Repository files site for projects, field maps, particles. – Version Release Numbers. – Global BD design with errors study impacts.