Analysis of Multi-Turn ERLs for X-ray Sources
CLASSE
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
Future Light Source Workshop 2010.
04 March 2010
ERL Layout at Cornell
CLASSE
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
Georg H. Hoffstaetter
2: deceleration to 2.2GeV
3: turn around with 2.2GeV
8: dump at 10MeV
Future Light Source Workshop 2010.
04 March 2010
Full magnetic lattice from
BMAD-optics code to Autocad
Georg H. Hoffstaetter
Future Light Source Workshop 2010.
CLASSE
04 March 2010
Two Turn Cornel x-ray ERL Lattice
Georg H. Hoffstaetter
Future Light Source Workshop 2010.
CLASSE
04 March 2010
Advantages
CLASSE
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
a) eRHIC has been contemplating a 5-turn ERL
b) MEeIC has been contemplating a 3-turn ERL
c) LeHC has been contemplating a multi turn ERL
d) KEK compact ELR plans for 2 turns, 5GeV ERL plans for 2 turn
e) NPGS is plans a 2 turn ERL
f) bERLinPro would like to include a 2 turn ERL
g) 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
Concerns
CLASSE
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
Space charge forces for superimposed
beams in one bucket
CLASSE
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
Space charge forces for superimposed
beams in one bucket
CLASSE
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
Future Light Source Workshop 2010.
04 March 2010
HOM heating due to more bunch charge
CLASSE
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
ERL Layout at Cornell
CLASSE
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
More complex bunch spectrum
CLASSE
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
RF power requirenments
CLASSE
RF needs are given by return time errors and microphonic detuning.
Detuning: 0Hz
10Hz
20Hz
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
Future Light Source Workshop 2010.
04 March 2010
4-beam optics
Georg H. Hoffstaetter
Future Light Source Workshop 2010.
CLASSE
04 March 2010
BBU: Collective Instabilities
CLASSE
Higher Order Modes
t
Vx (t )  T12 ce  Wx (t  t ' )Vx (t 't r ) I (t ' )dt '

Georg H. Hoffstaetter
Future Light Source Workshop 2010.
04 March 2010
HOM with BBU: Starting from Noise
CLASSE
Georg H. Hoffstaetter
Future Light Source Workshop 2010.
04 March 2010
Single cavity BBU
CLASSE
BMAD-BBU: Uses the BMAD lattice
and readily computes BBU
Single cavity BBU compares
superbly with estimates from the
2005 Hoffstaetter – Bazarov PRSTAB BBU paper.
Georg H. Hoffstaetter
Future Light Source Workshop 2010.
04 March 2010
Single cavity 2 turn BBU
CLASSE
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
X-ray ERL BBU 1 vs 2 turn
CLASSE
Full optics calculation:
With TTF like HOM characteristics and
No frequency spread
One turn: 12mA
Two turn: 6mA
With optimized 7-cell cavities
One turn: 30mA
Two turn 8mA
10mHz frequency spread
One turn: 235mA
Two turn: 53mA
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
Future Light Source Workshop 2010.
04 March 2010
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!
Georg H. Hoffstaetter
CLASSE
Higher
Ordermodes
Red: Optimized cavity;
blue: perturbed cavities
Future Light Source Workshop 2010.
04 March 2010
Cavities with misalignments
CLASSE
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
Reason for high sensitivity of HOMs
CLASSE
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
Perturbatio: Baseline Center Cell (minimize cryoload) and optimized end cells (HOM damping)
CLASSE
+-1/16 mm perturbations, 400 cavities
Georg H. Hoffstaetter
Future Light Source Workshop 2010.
04 March 2010
Center Cell (optimized HOM passband widths),
optimized end cells (HOM damping)
CLASSE
+-1/16 mm perturbations, 400 cavities
Georg H. Hoffstaetter
Future Light Source Workshop 2010.
04 March 2010
Center Cell (optimized HOM passband widths),
optimized end cells (HOM damping)
CLASSE
+-1/8 mm perturbations, 400 cavities
Georg H. Hoffstaetter
Future Light Source Workshop 2010.
04 March 2010
Improved center cell with increased width
passbands
CLASSE
Preliminary optimized end-cells, no perturbations, 10 MHz
HOM frequency spread
One turn BBU Threshold current
1000 simulations
Georg H. Hoffstaetter
Future Light Source Workshop 2010.
04 March 2010
Improved center cell with increased width
passbands, and deformations
CLASSE
+- 1/16 mm perturbations, no additional HOM frequency spread
One turn BBU Threshold current
Georg H. Hoffstaetter
Future Light Source Workshop 2010.
04 March 2010
Detuning from deformations
CLASSE
+- 1/16 mm perturbations, no additional HOM frequency spread
 1 MHz only!
Georg H. Hoffstaetter
Future Light Source Workshop 2010.
04 March 2010
Will lower frequency help?
CLASSE
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
2-turn ERL operation
CLASSE
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
Georg H. Hoffstaetter
11: return to East
12: 2.5GeV turnaround to linac
13: deceleration to 2.5GeV
14: dump at 10MeV
Future Light Source Workshop 2010.
04 March 2010
Conclusion
CLASSE
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.
Georg H. Hoffstaetter
Future Light Source Workshop 2010.
04 March 2010