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

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

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

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

6. 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

7. 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

8. 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

9. +-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

10. +-1/16 mm perturbations, 400 cavities
Center Cell (optimized HOM passband widths), optimized end cells (HOM damping)
+-1/16 mm perturbations, 400 cavities

11. +-1/8 mm perturbations, 400 cavities
Center Cell (optimized HOM passband widths), optimized end cells (HOM damping)
+-1/8 mm perturbations, 400 cavities

12. 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

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

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

15. Need for BBU investigation
Is an ERL test loop needed and why? For BBU studies?
Trapped modes above the beam pipe cutoff are hard to measure without a return loop. Are there beam based measurements without return loop? Excite by beam of 1MHz rep rate as function of x offset to get R/Q*Q. From the width of the resonances one can get Q.
Needs a linac cryomodule with beam, possibly a shortened model.
Important to measure Q of HOMs in vertical test as quality test.
Study is needed on keeping production tolerances.
Conclusion: BBU effects are well understood and mitigations have been well understood in experiments with existing return loops.
Georg H. Hoffstaetter, October 5, 2004