Georg H. Hoffstaetter Future Light Source Workshop 2010. 04 March 2010
CLASSCLASSEE
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
Georg H. Hoffstaetter Future Light Source Workshop 2010. 04 March 2010
CLASSCLASSEE
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
Georg H. Hoffstaetter Future Light Source Workshop 2010. 04 March 2010
CLASSCLASSEE
Full magnetic lattice fromBMAD-optics code to Autocad
Georg H. Hoffstaetter Future Light Source Workshop 2010. 04 March 2010
CLASSCLASSEE
Two Turn Cornel x-ray ERL Lattice
Georg H. Hoffstaetter Future Light Source Workshop 2010. 04 March 2010
CLASSCLASSEE
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?
Georg H. Hoffstaetter Future Light Source Workshop 2010. 04 March 2010
CLASSCLASSEE
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.
Georg H. Hoffstaetter Future Light Source Workshop 2010. 04 March 2010
CLASSCLASSEE
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 Future Light Source Workshop 2010. 04 March 2010
CLASSCLASSEE
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 !
Georg H. Hoffstaetter Future Light Source Workshop 2010. 04 March 2010
CLASSCLASSEE
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 Future Light Source Workshop 2010. 04 March 2010
CLASSCLASSEE
ERL Layout at Cornell
4 degree bunch separation is sufficient to have only 2.5 times the HOM power.
Georg H. Hoffstaetter Future Light Source Workshop 2010. 04 March 2010
CLASSCLASSEE
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 Future Light Source Workshop 2010. 04 March 2010
CLASSCLASSEE
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
Georg H. Hoffstaetter Future Light Source Workshop 2010. 04 March 2010
CLASSCLASSEE
4-beam optics
Georg H. Hoffstaetter Future Light Source Workshop 2010. 04 March 2010
CLASSCLASSEE
BBU: Collective Instabilities
t
rxxce
x dttIttVttWTtV ')'()'()'()( 12
Higher Order Modes
Georg H. Hoffstaetter Future Light Source Workshop 2010. 04 March 2010
CLASSCLASSEE
HOM with BBU: Starting from Noise
Georg H. Hoffstaetter Future Light Source Workshop 2010. 04 March 2010
CLASSCLASSEE
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.
Georg H. Hoffstaetter Future Light Source Workshop 2010. 04 March 2010
CLASSCLASSEE
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 Future Light Source Workshop 2010. 04 March 2010
CLASSCLASSEE
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.
Georg H. Hoffstaetter Future Light Source Workshop 2010. 04 March 2010
CLASSCLASSEE
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
Georg H. Hoffstaetter Future Light Source Workshop 2010. 04 March 2010
CLASSCLASSEE
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 Future Light Source Workshop 2010. 04 March 2010
CLASSCLASSEE
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 Future Light Source Workshop 2010. 04 March 2010
CLASSCLASSEE
Perturbatio: Baseline Center Cell (minimize cryo-load) and optimized end cells (HOM damping)
+-1/16 mm perturbations, 400 cavities
Georg H. Hoffstaetter Future Light Source Workshop 2010. 04 March 2010
CLASSCLASSEE
Center Cell (optimized HOM passband widths), optimized end cells (HOM damping)
+-1/16 mm perturbations, 400 cavities
Georg H. Hoffstaetter Future Light Source Workshop 2010. 04 March 2010
CLASSCLASSEE
Center Cell (optimized HOM passband widths), optimized end cells (HOM damping)
+-1/8 mm perturbations, 400 cavities
Georg H. Hoffstaetter Future Light Source Workshop 2010. 04 March 2010
CLASSCLASSEE
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
Georg H. Hoffstaetter Future Light Source Workshop 2010. 04 March 2010
CLASSCLASSEE
+- 1/16 mm perturbations, no additional HOM frequency spread
One turn BBU Threshold current
Improved center cell with increased width passbands, and deformations
Georg H. Hoffstaetter Future Light Source Workshop 2010. 04 March 2010
CLASSCLASSEE
1 MHz only!
Detuning from deformations
+- 1/16 mm perturbations, no additional HOM frequency spread
Georg H. Hoffstaetter Future Light Source Workshop 2010. 04 March 2010
CLASSCLASSEE
Will lower frequency help?
Lower frequencies can help for BBU, but is expensive because of larger heat load and construction cost.
Georg H. Hoffstaetter Future Light Source Workshop 2010. 04 March 2010
CLASSCLASSEE
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
Georg H. Hoffstaetter Future Light Source Workshop 2010. 04 March 2010
CLASSCLASSEE
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.
Top Related