1. Physics design on the main linac
IHEP
Physics design on the main linac
Yan Fang, Li Zhihui
C-ADS accelerator Physics Group
Institute of High Energy Physics
September 19, 2011

2. Outline Design philosophy The main linac lattice design:
IHEP
Outline
Design philosophy
The main linac lattice design:
The acceptance of each section
Simulation results
Summary
Outlook

3. IHEP C-ADS configuration（325/650 MHz)
—RFQ + Spoke*+Spoke021+ Spoke040+ Ellip063+ Ellip082
10MeV
Injector I
spoke021
spoke040
ellip063
ellip082
Injector II
Main linac

4. The design philosophy IHEP Equipartitioning design;
The zero current phase advance in all three planes
remains below 90 to avoid envelope resonance ;
Smaller longitudinal emittance than transverse
emittance to get more accelerating efficiency of the cavity;
Long drift at both end of the period to avoid
cryomodule separation causing emittance growth;
Derated cavity nominal gradient for compensation in
case any one cavity is lost;
Using triplets instead of doublets in the elliptical section;
For intersection matching we keep the phase advance per meter smooth.

5. Equipartitioning design
IHEP
Equipartitioning design
Theoretical tune depression of each section
tune depression
10mA
20mA
Transverse
Longitudinal
Entra.
exit
Spoke021
0.76
0.77
0.79
0.8
0.64
0.65
0.67
0.69
Spoke040
0.80
0.83
0.73
Ellip063
0.74
0.81
0.86
0.62
0.70
Ellip082
0.84
0.95
0.92
Tune depression bigger than 0.71:
Emittance dominated!
Tune depression smaller than 0.71:
Space charge dominated!

6. For the equipartitioning design:
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For the equipartitioning design:
From the chart in the previous slide the theoretically tune depression is very close in our design:
Then we keep zero current phase advance ratio constant to satisfy equipartitioning design approximately:

7. Emittance ratio choices
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Emittance ratio choices
We investigated three emittance ratio cases:
Case 1:
Small emittance growth;
Case 2:
Better accelerating efficiency than case 1;
Case 3:
Emittance growth is small too, but hard to achieve such a small longitudinal emittance ;
* Noted: Keep transverse emittance constant:

8. Main linac design on the basis of emittance ratio of 1.3 (case 1)
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Main linac design on the basis of emittance ratio of 1.3 (case 1)

9. Main linac design on the basis of emittance ratio of 1.3 (case 1)
IHEP
Main linac design on the basis of emittance ratio of 1.3 (case 1)
Norm. RMS emittance growth are: 2% / 4% / 3.5% ( x/y/z) respectively.

10. Main linac design on the basis of emittance ratio of 0.7 (case 3)
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Main linac design on the basis of emittance ratio of 0.7 (case 3)

11. Main linac design on the basis of emittance ratio of 0.7 (case 3)
IHEP
Main linac design on the basis of emittance ratio of 0.7 (case 3)
Norm. RMS emittance growth are: 4.9% / 3.7% / 3.9% ( x/y/z) respectively.

12. Main linac design on the basis of emittance ratio of 0.85
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Main linac design on the basis of emittance ratio of 0.85

13. Main linac design on the basis of emittance ratio of 0.85
IHEP
Main linac design on the basis of emittance ratio of 0.85
Normalized RMS emittance growth(x/y/z): 2.16% / 1.77% / 7.45%

14. IHEP
0.85 in our design
We adopted kz/kx=1.33 (1/0.75: the red line) instead of 1.18 (1/0.85)

15. IHEP
Main linac design on the basis of emittance ratio of 0.85, but keep kx/kz=0.75

16. IHEP
Main linac design on the basis of emittance ratio of 0.85, but keep kx/kz=0.75
Normalized RMS emittance growth(x/y/z): 2.5% / 4.2% / 2.1%

17. Outline Design philosophy The main linac lattice design:
IHEP
Outline
Design philosophy
The main linac lattice design:
The acceptance of each section
Simulation results
Summary
Outlook

18. IHEP
Lattice design
Which is determined mainly under the condition that the zero phase advance per period is less than 90 degree both transversely and longitudinally.

19. IHEP
IHEP
Spoke021 period
The lattice including 2 cavities and one solenoid:
A 117mm is remained in each side of the cavity
for tuner and bellows;
The effective length of the solenoid is 150mm
and 75mm in each side is remained for the
flange and necessary shielding;
An 100mm space in between solenoid and
cavity is remained for the cold BPM.
400mm at both side of the period to accommodate possible cryomodule separation.
40mm
250mm

20. Spoke040 period IHEP IHEP The lattice including 4 cavities and
one solenoid:
An additional 100mm in between the
cavities is allotted for the bellows and tuner
of the two cavities.
60mm
380mm

21. Schematic figure of ellip063 cavity
IHEP
Schematic figure of ellip063 cavity

22. IHEP
Ellip063 period
The inter cavity distance, 500mm is allotted here to
accommodate both the main power coupler and HOM
coupler in case is needed.
This number is determined according to ESS design:
the inter cavity distance for ESS design is 400mm.*
* Quoted from: M.Eshraqi et al, Proceedings of HB2010, Morschach, Switzerland.

23. IHEP
Ellip082 period

24. Phase advance evolution along each section
IHEP
Phase advance evolution along each section

25. Phase advance per meter along main linac
IHEP
Phase advance per meter along main linac

26. How do we determine the space needed in between the cavity & solenoid!
IHEP
How do we determine the space needed in between the cavity & solenoid!

27. Project-X SSR0 lattice IHEP A117mm is allotted in between
the cavity and solenoid.
Courtesy of FNAL Project-X:
T. Khabiboulline, S. Barbanotti,
I Gonin, N. Solyak, I. Terechkine and
V. Yakovlev et al, “CW RF system of
the project-X accelerator front end”,
proceedings of LINAC2010,
Tsukuba, Japan.
117mm

28. Project-X lattice period
IHEP
Project-X lattice period
Sol. Effective length:
Leff=100mm
Extension length:
Lext=95/2=47.5mm
Leff
Lext
Courtesy of FNAL Project-X:
T. Khabiboulline, S. Barbanotti, I Gonin, N. Solyak, I. Terechkine and V.
Yakovlev et al, “CW RF system of the project-X accelerator front end”,
Proceedings of LINAC2010, Tsukuba, Japan.

29. FRIB β=0.045 section lattice
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FRIB β=0.045 section lattice
Sol. Effective length:
Leff=200mm
Extension length:
Lext=( )/2
=76mm
Leff
Lext

30. Outline Design philosophy The main linac lattice design:
IHEP
Outline
Design philosophy
The main linac lattice design:
The acceptance of each section
Simulation results
Summary
Outlook

31. How do we determine the Synchronous phase?
IHEP
How do we determine the Synchronous phase?
Which is mainly decided under the condition that the acceptance emittance ratio bigger than 10.

32. Acceptance of spoke021( φ:-30°)
Longitudinal
transverse
Acceptance emittance ratio:9
Acceptance emittance ratio:6.6

33. Acceptance of spoke040 ( φ:-23°)
Longitudinal
transverse
Acceptance emittance ratio:>10
Acceptance emittance ratio:>10

34. Acceptance of ellip063 ( φ:-15°)
Longitudinal
Transverse
Acceptance emittance ratio:>10
Acceptance emittance ratio:>10

35. Acceptance of ellip082 ( φ:-12°)
Longitudinal
Transverse
Acceptance emittance ratio:>10
Acceptance emittance ratio:>10

36. Conditions & Conclusions
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Conditions & Conclusions
Beam is assumed to be lost if the energy spread is bigger than 10%; (Question: is it reasonable?)
Conclusions:
Longitudinally, try to keep the acceptance emittance
ratio bigger than 10 (Question: is it necessary?) ;
The longitudinal acceptance emittance ratio of spoke021 section is smaller than 9, but it’s a trade off between acceleration efficiency & big acceptance;
Transverse: the acceptance is 6.6 times of the emittance in the spoke02 section, but the beam tube radius is 8-10 times of the RMS beam size (Question: is it enough?).

37. Outline Design philosophy The main linac lattice design:
IHEP
Outline
Design philosophy
The main linac lattice design:
The acceptance of each section
Simulation results
Summary
Outlook

38. Conditions & Specifications
IHEP
Conditions & Specifications
Input Energy : 10MeV
Average current: 10mA
The normalized RMS emittance:
εnt=0.252πmm.mad=0.21(1+20%) πmm.mad ,
εnl=0.2136πmm.mad=0.065x(1+20%) πdeg.MeV
εl/εt=0.848
* Note: the emittance growth is assumed to be 20% increase
from the exit of RFQ to the entrance of the main linac.
6D Gaussian distribution: (truncated at ±3σ)
particles used for the simulation.

39. Envelope evolution of the main linac
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Envelope evolution of the main linac

40. emittance evolution of the main linac
IHEP
emittance evolution of the main linac
Normalized RMS emittance growth(x/y/z): 2.5% / 4.2% / 2.1%

41. Sync. phase evolution of the main linac
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Sync. phase evolution of the main linac

42. Phase advance ratio & tune depression
IHEP
Phase advance ratio & tune depression
Transv. phase Adv over long. phase Adv

43. IHEP
Halo & phase

44. Energy gain (total: 210 cavities)
IHEP
Energy gain (total: 210 cavities)
No:16*5=80
MeV
Spoke cavity number: 102
No: 7*4=28
MeV
No:18*4=72
MeV
Ellipse cavity number: 108
No:15*2=30
MeV

45. Increased the current up to 20mA
IHEP
Increased the current up to 20mA

46. Increase the current up to 20mA
IHEP
Increase the current up to 20mA
Normalized RMS emittance growth(x/y/z): 8.5% / 11.6% / 11%

47. The general layout of main linac current design
Section
spoke021
spoke040
ellip063
ellip082
Input energy(MeV) 10
36.6
185
378
Output energy(MeV)
1498
Geometry Beta
0.21
0.40
0.63
0.82
Cavity type 2 5
Number of cavities 30 72 28 80
Focusing type
solenoid
triplet
Cavity per period 4
Synchronous phase (deg)
-30°
-23°to -30°
-15°
-12°
period length(m)
2.168
3.8
7.3756
9.62
Section length(m)
32.52
68.4
51.6
153.88
Eacc (MV/m)
≤6.87
≤ 5.26
7.9
9.75
Nominal Ep (MV/m) 25 35

48. Focusing devices of main linac
IHEP
Focusing devices of main linac
FOCUSING DEVICES
spoke021
spoke040
ellip063
ellip082
Focusing type
solenoid
triplet
Aperture (mm) 50 70
Field Range (T)
2.4 to 3.2
3.2 to 5.2
Gradient Range (T/m)
6.8 to 14.1
5.8 to 15.1

49. summary The emittance ratio after RFQ is ;
IHEP
summary
The emittance ratio after RFQ is ;
The zero current phase advance ratio is kept constant along the whole linac with ;
The acceptance emittance ratio is bigger than 10 except spoke021 section (a tradeoff between acceptance and acceleration efficiency);
The total cavity needed acceleration from 10MeV to 1.5GeV is 210 cavities;
The total length of the main linac is around 306 m;
The RMS normalized emittance growth are:
2.5% / 4.2% / 2.1% respectively.

50. IHEP
Outlook
When we match the intersection the absolute value of sync. phase are changed smaller than nominal setting,
in the next step we need to keep the sync. phase below the nominal setting;
Further optimization of cavity parameter optimization;
Different lattice design comparing;
Compensation study;
Error analysis;
HOM analysis;
………

51. That’s all! Thank you for your attention!
IHEP
That’s all! Thank you for your attention!