Analysis of Multi-Turn ERLs for X-ray Sources

Georg H. Hoffstaetter Future Light Source Workshop 2010. 04 March 2010

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Analysis of Multi-Turn ERLs for X-ray Sources

Georg HoffstaetterCornell 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


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ERL Layout at Cornell

Cornell Electron

Storage Ring Tunnel

1: injector2: acceleration to 2.8GeV3: turn around with 2.8GeV4: acceleration to 5GeV

5: to x-ray beamlines6: return through CESR7: further x-ray beamlines

2: deceleration to 2.2GeV3: turn around with 2.2GeV8: dump at 10MeV


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Full magnetic lattice fromBMAD-optics code to Autocad


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Two Turn Cornel x-ray ERL Lattice


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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 thata) eRHIC has been contemplating a 5-turn ERLb) MEeIC has been contemplating a 3-turn ERLc) LeHC has been contemplating a multi turn ERLd) KEK compact ELR plans for 2 turns, 5GeV ERL plans for 2 turne) NPGS is plans a 2 turn ERLf) bERLinPro would like to include a 2 turn ERLg) 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?


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Concerns

1. Space charge forces for superimposed beams and emittance growth.

2. Intra beam scattering between superimposed beams and halo/background creation.

3. Increasing Higher Order Mode (HOM) power for separated bunches.

4. More sophisticated Beam spectrum and RF control.

5. Tighter orbit and return time tolerances.

6. Limits of orbit corrections for 4 simultaneous beams.

7. Linac optics for 4 simultaneous beams.

8. Reduced Beam-Breakup (BBU) tolerances.

9. Reduced effectiveness of polarized cavities and coupled optics for fighting the BBU instability.

10. Impedance budget and increased energy spread.


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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


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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

Bunches have to be separated in RF phase !


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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.


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ERL Layout at Cornell

4 degree bunch separation is sufficient to have only 2.5 times the HOM power.


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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 !


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RF power requirenments

RF needs are given by return time errors and microphonic detuning.

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 !

Detuning: 0Hz 10Hz 20Hz


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4-beam optics


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BBU: Collective Instabilities

t

rxxce

x dttIttVttWTtV ')'()'()'()( 12

Higher Order Modes


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HOM with BBU: Starting from Noise


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Single cavity BBU

BMAD-BBU: Uses the BMAD latticeand readily computes BBU

Single cavity BBU compares superbly with estimates from the 2005 Hoffstaetter – Bazarov PRST-AB BBU paper.


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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.


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X-ray ERL BBU 1 vs 2 turn

Full optics calculation:

With TTF like HOM characteristics andNo frequency spread 10mHz frequency spreadOne turn: 12mA Two turn: 6mA One turn: 235mA Two turn: 53mAWith optimized 7-cell cavitiesOne 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 improvementHOM 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.


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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! Red: Optimized cavity;

blue: perturbed cavities

Higher-Order-modes


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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.


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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.


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Perturbatio: Baseline Center Cell (minimize cryo-load) and optimized end cells (HOM damping)

+-1/16 mm perturbations, 400 cavities


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Center Cell (optimized HOM passband widths), optimized end cells (HOM damping)



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Center Cell (optimized HOM passband widths), optimized end cells (HOM damping)



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Improved center cell with increased width passbands

1000 simulations

One turn BBU Threshold current

Preliminary optimized end-cells, no perturbations, 10 MHz HOM frequency spread


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+- 1/16 mm perturbations, no additional HOM frequency spread

One turn BBU Threshold current

Improved center cell with increased width passbands, and deformations


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1 MHz only!

Detuning from deformations

+- 1/16 mm perturbations, no additional HOM frequency spread


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Will lower frequency help?

Lower frequencies can help for BBU, but is expensive because of larger heat load and construction cost.


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Cornell Electron

Storage Ring Tunnel

2-turn ERL operation

1: injector2: acceleration to 2.5GeV3: return to the East4: 2.5GeV turnaround to the linac5: acceleration to 5GeV

6: to x-ray beamlines7: return through CESR8: 5GeV beam separation9: 5GeV turnaround to the linac10: deceleration to 2.5GeV

11: return to East12: 2.5GeV turnaround to linac13: deceleration to 2.5GeV14: dump at 10MeV


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Conclusion

1. Space charge forces for superimposed beams and emittance growth.

2. Intra beam scattering between superimposed beams and halo/background creation.

3. Increasing Higher Order Mode (HOM) power for separated bunches.

4. More sophisticated Beam spectrum and RF control.

5. Tighter orbit and return time tolerances.

6. Limits of orbit corrections for 4 simultaneous beams.

7. Linac optics for 4 simultaneous beams.

8. Reduced Beam-Breakup (BBU) tolerances, esp. with cavity errors.

9. Reduced effectiveness of polarized cavities and coupled optics for fighting the BBU instability.

10. Impedance budget and increased energy spread.

Documents

Analysis of Multi-Turn ERLs for X-ray Sources