1. Analysis of Multi-Turn ERLs for X-ray Sources
Georg Hoffstaetter Cornell Physics Dept. / CLASSE Progress report on a paper with I. Bazarov, S. Belomestnyk, J. Crittenden, M. Ehrlichman, M. Liepe, C. Mayes, S. Peck, M. Tigner
Georg H. Hoffstaetter, October 5, 2004

2. Cornell Electron Storage Ring Tunnel
ERL Layout at Cornell
Cornell Electron Storage Ring Tunnel
1: injector
2: acceleration to 2.8GeV
3: turn around with 2.8GeV
4: acceleration to 5GeV
5: to x-ray beamlines
6: return through CESR
7: further x-ray beamlines
2: deceleration to 2.2GeV
3: turn around with 2.2GeV
8: dump at 10MeV
Georg H. Hoffstaetter, October 5, 2004

3. Full magnetic lattice from BMAD-optics code to Autocad
Georg H. Hoffstaetter, October 5, 2004

4. Two Turn Cornel x-ray ERL Lattice
Georg H. Hoffstaetter, October 5, 2004

5. Advantages Less linac length and less tunnel length
Less capital investment
Less static heat load
Less dynamic heat load
These seem so tempting and obvious that
eRHIC has been contemplating a 5-turn ERL
MEeIC has been contemplating a 3-turn ERL
LeHC has been contemplating a multi turn ERL
KEK compact ELR plans for 2 turns, 5GeV ERL plans for 2 turn
NPGS is plans a 2 turn ERL
bERLinPro would like to include a 2 turn ERL
JLAB-ligh source goes to 2 turn (initially without ERL, possibly later with ERL)
The pandemic is spreading, but is it analyzed sufficiently to bear promise?

6. Concerns
Space charge forces for superimposed beams and emittance growth.
Intra beam scattering between superimposed beams and halo/background creation.
Increasing Higher Order Mode (HOM) power for separated bunches.
More sophisticated Beam spectrum and RF control.
Tighter orbit and return time tolerances.
Limits of orbit corrections for 4 simultaneous beams.
Linac optics for 4 simultaneous beams.
Reduced Beam-Breakup (BBU) tolerances.
Reduced effectiveness of polarized cavities and coupled optics for fighting the BBU instability.
Impedance budget and increased energy spread.
Georg H. Hoffstaetter, October 5, 2004

7. Space charge forces for superimposed beams in one bucket
The high energy beam with adiabatically damped emittance is inside the wider low energy beam and produces strong space charge forces.
Analytic estimate: 1.9micron/meter for a 0.3micron initial emittance
Georg H. Hoffstaetter, October 5, 2004

8. Space charge forces for superimposed beams in one bucket
Bunches have to be separated in RF phase !
The high energy beam with adiabatically damped emittance is inside the wider low energy beam and produces strong space charge forces.
Analytic estimate: 1.9micron/meter for a 0.3micron initial emittance
Georg H. Hoffstaetter, October 5, 2004

9. HOM heating due to more bunch charge
With twice the bunch charge there is the potential for 4 times the HOM heating. But if bunches are well separated, one expect only 2 times the HOM heating.
The wake diminishes quickly after the bunch, giving the potential for close to only 2 times the HOM heating for slightly separated bunches.
Georg H. Hoffstaetter, October 5, 2004

10. ERL Layout at Cornell
4 degree bunch separation is sufficient to have only 2.5 times the HOM power.
Georg H. Hoffstaetter, October 5, 2004

11. More complex bunch spectrum
Even for separated bunches, the basic frequency remains 2.6GHz and the bunch spectrum thus has the same lines, only with different weights, up to 2 times as large.
Should be no problem !
Georg H. Hoffstaetter, October 5, 2004

12. RF power requirenments
RF needs are given by return time errors and microphonic detuning.
Detuning: 0Hz Hz Hz
In a two turn ERL there are three return loops instead of one.
Simple estimate: Three times the RF need for the same return time tolerances.
Additional RF installation is expensive !
Georg H. Hoffstaetter, October 5, 2004

13. 4-beam optics
Georg H. Hoffstaetter, October 5, 2004

14. BBU: Collective Instabilities
Higher Order Modes
Georg H. Hoffstaetter, October 5, 2004

15. HOM with BBU: Starting from Noise
Georg H. Hoffstaetter, October 5, 2004

16. Single cavity BBU BMAD-BBU: Uses the BMAD lattice
and readily computes BBU
Single cavity BBU compares superbly with estimates from the 2005 Hoffstaetter – Bazarov PRST-AB BBU paper.
Georg H. Hoffstaetter, October 5, 2004

17. Single cavity 2 turn BBU
Rough estimate for multi turn form 2005 paper: approximately factor of n*(n+1), i.e. 6 less current in a 2 turn ELR.
Georg H. Hoffstaetter, October 5, 2004

18. X-ray ERL BBU 1 vs 2 turn Full optics calculation:
With TTF like HOM characteristics and
No frequency spread mHz frequency spread
One turn: 12mA Two turn: 6mA One turn: 235mA Two turn: 53mA
With optimized 7-cell cavities
One turn: 30mA Two turn 8mA One turn: 307mA Two turn: 87mA
30mA seems low, but (2006 Paper by Song & Hoffstaetter)
HOM frequency spread leads to a factor of 16 improvement
HOM polarization by 50MHz and a coupled optics leads to an additional factor of 5 improvement. (2007 Paper by Hoffstaetter, Bazarov, Song)
For Cornell’s 1turn x-ray ERL: potential for 2A BBU limit
However, polarization couples x to y in a 1 turn ERL, but back to x in a 2 turn ERL, an thus does not work as well.
Estimate: a 100mA threshhold may bearly be met with frequency spread in a 2 turn ERL.
Georg H. Hoffstaetter, October 5, 2004

19. Main Linac Cavity Optimization
Optimize shape of cavity (>70 parameter…) to minimize cryogenic losses and maximize limits to beam current
Understand sensitivity of optimized design to fabrication errors; find “sloppy” parameter!
Higher-Order-modes
Red: Optimized cavity;
blue: perturbed cavities

20. Cavities with misalignments
R/Q and Q in cavities with misalignments can be significantly worse then expected, but orders of magnitude. (Here for 1/16mm construction error)
A very good safety margin for BBU is therefore needed.
Georg H. Hoffstaetter, October 5, 2004

21. Reason for high sensitivity of HOMs
Trapped TTF HOMs:
Construction errors in cells change the individual cell’s HOM frequencies and hinder good coupling between cells, leading to trapped modes with much larger Q.
Georg H. Hoffstaetter, October 5, 2004

22. +-1/16 mm perturbations, 400 cavities
Perturbatio: Baseline Center Cell (minimize cryo-load) and optimized end cells (HOM damping)
+-1/16 mm perturbations, 400 cavities

23. +-1/16 mm perturbations, 400 cavities
Center Cell (optimized HOM passband widths), optimized end cells (HOM damping)
+-1/16 mm perturbations, 400 cavities

24. +-1/8 mm perturbations, 400 cavities
Center Cell (optimized HOM passband widths), optimized end cells (HOM damping)
+-1/8 mm perturbations, 400 cavities

25. One turn BBU Threshold current
Improved center cell with increased width passbands
Preliminary optimized end-cells, no perturbations, 10 MHz HOM frequency spread
One turn BBU Threshold current
1000 simulations

26. Improved center cell with increased width passbands, and deformations
+- 1/16 mm perturbations, no additional HOM frequency spread
One turn BBU Threshold current

27. Detuning from deformations
+- 1/16 mm perturbations, no additional HOM frequency spread
 1 MHz only!

28. Will lower frequency help?
Lower frequencies can help for BBU, but is expensive because of larger heat load and construction cost.
Georg H. Hoffstaetter, October 5, 2004

29. Cornell Electron Storage Ring Tunnel
2-turn ERL operation
Cornell Electron Storage Ring Tunnel
1: injector
2: acceleration to 2.5GeV
3: return to the East
4: 2.5GeV turnaround to the linac
5: acceleration to 5GeV
6: to x-ray beamlines
7: return through CESR
8: 5GeV beam separation
9: 5GeV turnaround to the linac
10: deceleration to 2.5GeV
11: return to East
12: 2.5GeV turnaround to linac
13: deceleration to 2.5GeV
14: dump at 10MeV

30. Conclusion
Space charge forces for superimposed beams and emittance growth.
Intra beam scattering between superimposed beams and halo/background creation.
Increasing Higher Order Mode (HOM) power for separated bunches.
More sophisticated Beam spectrum and RF control.
Tighter orbit and return time tolerances.
Limits of orbit corrections for 4 simultaneous beams.
Linac optics for 4 simultaneous beams.
Reduced Beam-Breakup (BBU) tolerances, esp. with cavity errors.
Reduced effectiveness of polarized cavities and coupled optics for fighting the BBU instability.
Impedance budget and increased energy spread.
Georg H. Hoffstaetter, October 5, 2004