1. DTL
M. Comunian
M. Eshraqi

2. Outline
DTL Design.
Beam Dynamics.
Errors Study.

3. DTL Design Input energy of 3 MeV.
Maximum integrated field of 3.8T for PMQ.
Currents: 50 mA.
FODO PMQ Lattice.
PMQ law almost equipartitioned.
Input RMS emittance Tr. / Long. 0.22/0.28 mmmrad

4. Summary of boundary parameters for nominal DTL design (1)
Points defined at LNL meeting 9-10/7/2012
Parameter
Value or Range
Notes
Final energy
75MeV to 85 MeV
Maximum RF power/tank
2.15 MW
Including 1.25 margins.
PMQ law
Equipartitioned
Surface E field limit
At 3MeV:1.39 kp
Absolute max: of 1.6 kp
“Moretti” limit for 70 T/m PMQ
Tank Length
<8m
Mechanical modules of max 2 meters. E0
2.8 to 5.0 MV/m
Linearly ramped
Synch. phase
-35° to -20°
Keep large longitudinal acceptance
N° of Tank
4 or 5
Bore radius
Tank1 and 2=10 mm; Tank3=1.1 mm;
From Tank4= 1.2 mm
Intertank space
1 βλ

5. Summary of boundary parameters for nominal DTL design (2)
Points defined at LNL meeting 9-10/7/2012
Parameter
Value or Range
Notes
Losses
<1 W/m
Avoid radiation damages of PMQs
Longitudinal phase advance
Continuous along the DTL
Tune depression
> 0.4 for all planes
Sensitivity to mismatch
RMS emittance increasing
Long: < 40% Transv: < 20%
99% emittance over RMS emittance
< 10
Limit on Halo
Final longitudinal phase advance
18°/m ± 1°/m
Matching with SC linac
Final transverse phase advance
21°/m ± 1°/m
Phase change for intertank longitudinal matching.
< 5°
RF design
E0 error
± 2%
Phase error
± 4°

6. DTL Layout Tank Length [m] Cells Total Power [kW] Max Kp
Final Energy [MeV]
E0 [MV/m]
R bore
[mm]
Flat length
Phase
[deg] 1
7.953 66
2061
1.42
21.5
2.8 ÷ 3.2 10
0.7
-35 ÷ -24 2
7.628 36
2117
1.43
41.1
3.16
0.5
-24 3
7.762 29
2099
1.40
60.0 11 4
7.724 25
2076
1.36
77.7 12
0.4

7. Design Law on E0 phase and surface field

8. GEN DTL solution on design constrain

9. Ratio Bore/RMS from 9 to 6
Max size Gaussian 6σ

10. Beam Density with Input distribution Gaussian 6σ

11. Intertank space: 1 bl Each tank begins with a current monitor.
Matching by using 2 PMQ at tank end and 2 PMQ at tank begin and changing the phases with max of +/- 5°.
SNS Tank1-Tank2: 1 bl

12. bl bl bl Intertank space: 1 bl F O D O F O
From first to second tank= mm

13. Equipartitioning all along the DTL
Gradient High
Gradient Low
High order resonances

14. Phase advance at zero current
Input:
k0T=290 °/m
k0L=240 °/m
Output:
k0T=22 °/m
k0L=19 °/m

15. RMS Emittance along the DTL
Uniform:
ET/E0T=1.05
EL/E0L=1.09
99% Emittance along the DTL
Gaussian:
ET/E0T=1.14
EL/E0L=1.18

16. Acc/RMS Ratio: Transverse=53 Longitudinal=91
Max transverse acceptance=11.6 mmmrad norm.
Max Longitudinal acceptance=10 degMeV
Acc/RMS Ratio:
Transverse=53
Longitudinal=91

17. Error study on the DTL
All errors apply together with a Uniform input beam distribution
with added a “halo” distribution with 3times the emittance
and 3σ as gaussian size distribution, 0.625% of the beam as halo,
i.e. 1kW.
100 random DTL generated.
1.6*10^5 particles i.e. 1 W for particle at 50 mA, 80 MeV.
Separate X,Y Steerer used with max force of 1.6 mT*m.

18. Gaussian 6σ Uniform+Halo
With Uniform+Halo is increased the number of particles at large amplitude

19. Steerers on FODO Lattice
Using the empty space on the lattice it has been put steerers X or Y
4 Steerers and 2 BPM for each tank.
Max steerer strength of 1.6 mT*m.
Diagnostics BPM with 0.05 mm accuracy.
SNS Steerer,
max 1.9 mT*m

20. DTL BI layout Tank 1 Tank 2 Tank 3 Tank 4 Number of units Name
BLM
Beam
BLM FC FC WS WS
Tank 3
Tank 4
BLM WS FC FC
Number of units
Name
Number of units
Symbol
Name
Symbol
DTL Tank
BPM / Phase detector in DT 4 8
Current Monitor (Toroid) 4
Wire Scanner 3
Beam Loss Monitor 6
Faraday cup (Beam stop) 4
BLM FC
Energy degrader 3
Benjamin Cheymol

21. Steerers Position Element # Sx Sy BPM Tank1 7 10 23 26 62 67 Tank2 8083 92 95
106
111
Tank3
120
123
132
135
142
147
Tank4
155
158
167
169
178
183

22. Errors results on E0 without correction Steerers
Step 1  Maximum E0 shake cell by cell of ±5%

23. E0 Errors of +/- 2% cell by cell.
Total=0.7 Watts
E0 Errors of +/- 5% cell by cell.
Total=1.77 Watts

24. Errors results on ϕs without correction Steerers
Step 1  Maximum ϕs shake cell by cell of ±5°

25. ϕs Errors of +/- 2° cell by cell.
Total=1.9 Watts
ϕs Errors of +/- 5° cell by cell.
Total=2.45 Watts

26. Errors results on quad without correction Steerers
Step 1  Maximum Quad shake of X,Y ±0.2 mm; ±1°; ±1%
Quad shake of X,Y ±0.1 mm; ±0.5°; ±0.5%
Total loss=42 Watts
Max emittance growth=40%

27. Errors results on quad with correction Steerers
Step 1  Maximum Quad shake of X,Y ±0.2 mm; ±1°; ±1%
Quad shake of X,Y ±0.1 mm; ±0.5°; ±0.5%
Total loss=2 Watts
Max emittance growth=20%

28. Conclusion Complete definition of DTL parameters.
Solution with 4 Tanks.
With the steerers the losses are reduced by a factor 10 and the emittance growth by a factor 2.
Max error on E0 shape +/- 2%.
Max error on Phase +/- 2°.
Max quad error X,Y ±0.2 mm; ±1°; ±1%.
The quad error are reduces due to the steerers: doubled the CERN specifications.
Beam Dynamics with SuperFish full fields map and/or other simulation code.
Design with the real quadrupoles family.
Still possible further DTL optimizations?