ILC Main Linac Beam Dynamics
Review
2013.05.28
K. Kubo
Low Emittance Preservation in ILC ML
Wakefields of cavities : Not very significant because of the
large aperture of the cavities. And we can reply on
• Mechanical alignment (~300 mm) and
• For multi-bunch effect, (natural) frequency spread of
resonant modes (~0.1%).
Dispersive effect, caused by Quad offset and Cavity tilt will
need more careful cures.
• Static effect
• Dynamic effect
Alignment and Beam Orbit in Curved Linac,
Following earth curvature
0
y (m)
-0.0005
Alignment line
Design Orbit
-0.001
-0.0015
-0.002
0
50
100
s (m)
150
Design orbit w.r.t. the reference line
and dispersion
0
0.0025
Not zero
0.002
-2 10
-5
0.0015
-3 10
-5
0.001
-4 10
-5
y
y (m)
-5
 (m)
-1 10
 (m)
y (m)
-5 10
0.0005
y
-5
0
0
50
100
150
s(m)
200
250
300
Injection orbit and dispersion are non-zero, and should be matched
to the optics.
Single bunch WakeField
• Requiring cavity misalignment < 300 um, single bunch
transverse wakefield effect is not significant.
• BBU: BNS Damping/Auto-phasing is not necessary.
– RF phase vs. beam chosen for minimizing energy spread.
– This choice makes the Dispersive Effect minimum.
3.145 10 7
2 105
3.14 10 7
1.5 105
3.135 10 7
1 105
wakefield
3.13 10 7
3.125 10 7
-0.001
-0.0005
0
z (m)
0.0005
5 104
0
0.001
wakefield (V/m)
Accelerating field (V/m)
RF field
Total acceleration
Multi-bunch Wakefield – Rely on random detuning
2
100
10
W
envelope
No detuning
(V/pC/m )
Wakefunction envelope from HOMs (from TESLA-TDR)
with/without random detuning (50 cavities) and damping
s =0, no damp
f
s =0, damp
1
f
0
1 10
3
2 10
3
3 10
3
4 10
3
5 10
3
6 10
3
fs =0.1%, no damp
f
s =0.1%, damp
100
f
10
W
envelope
2
Random detuning
sf/f=0.1%
(V/pC/m )
time (ns)
1
0
1 10
3
2 10
3
3 10
3
time (ns)
4 10
3
5 10
3
6 10
3
ILC ML static errors and cures
• Agreed “standard” errors: Next page
– Random Gaussian distributions are used for most studies
• DMS (Dispersion Matching Steering) correction as standard
correction method
– For dispersion measurement, change beam energy 10% ~
20%
– BPM scale error is important  non-zero design dispersion
– Simulation studies using many different codes and by different persons.
• Other methods (Kick minimum, Ballistic, wake bumps, etc.) as
additional or alternative corrections.
• No serious problem expected.
– An example shown: next-next page
Simulation code bench marking
• We rely on simulations and many codes have been developed.
• Most of them were compared and checked to be consistent.
J. C. Smith, et.al., “Benchmarking / Crosschecking DFS in the ILC Main Linac”
FERMILAB-TM-2373-CD, SLAC-TN-06-035
Agreed “standard” errors
“standard” alignment errors
Error
RTML and ML Cold
with respect to
300 μm
cryo-module
300 μrad
design
300 μm
cryo-module
300 μrad
cryo-module
BPM Offset (initial)
300 μm
cryo-module
Cryomoduloe Offset
200 μm
design
Cryomodule Pitch
20 μrad
design
Quad Offset
Quad roll
RF Cavity Offset
RF Cavity tilt
BPM
BPM resolution (fraction of beam pulse)
BPM scale error
1 mm
5%
“Standard” static errors + BPM resolution 1um + DMS
3.4 10
-8
3.2 10
-8
3 10
-8
2.8 10
-8
2.6 10
-8
2.4 10
-8
2.2 10
-8
init
20%
Einit:
Change of initial
From 15 GeV Einit 20%
energy for dispersion
From 15 GeV E 10%
init
measurement
From 5 GeV E
y
Mean -corrected  (m)
From 5 GeV E
init
10%
Final Energy was changed
Keeping the total length of
linac
100
150
200
250
Final Energy (GeV)
K.Kubo LCWS 2011 Oregon
ILC ML major dynamic errors
(Affecting Transverse Motion)
ML 15 GeV to 250 GeV
Source
Assumption
(Tolerance)
Induced orbit
jitter
Induced emittance
growth
Quad vibration (offset change)
100 nm
1.5 sigma
0.2 nm
Quad+steering strength jitter
1E-4
1 sigma
0.1 nm
Cavity tilt change
3 urad
0.8 sigma
0.5 nm
Cavity to cavity strength
change, assuming 300 urad
fixed tilt
1%
0.8 sigma
0.5 nm
Pulse to pulse and in each pulse (flatness)
Hard to correct
The orbit jitter will be corrected in post-linac fast feedback
Emittance growth by Cavity tilt
Emittance growth along ML
Cavity tilt random change 15 urad,
equivalent to Fixed 300 urad + 5% gradient change
Emittance growth proportional to square of the change
-8
1.2 10
-8
1 10
5% gradient change
-9
y (m)
8 10
-9
6 10
-9
4 10
   ln( E / Einit ) 3
-9
2 10
0
0
50
100
150
200
250
E (GeV)
Gradient change 1%  emittance growth 1/25 of this figure.
Energy upgrade Ebeam 250 to 500 GeV
• ML starts from 15 GeV in both old and new linac.
• Special quad magnets for low energy part, 15 to 25 GeV.
• Keep most part of old linac (25 to 250 GeV) as downstream part of new
linac (275 to 500 GeV).
– Strength is limited. Strength at 250 GeV of old linac.
• Upstream part of new linac (15 to 250 GeV) identical to the old linac
(FODO).
• FOFODODO for E_beam > 250 GeV
– For keeping vertical dispersion small (following earth curvature).
15 GeV
15 GeV
25 GeV
25 GeV
275 GeV
250 GeV
500 GeV
FODO
Vertical dispersion
FOFODODO
Vertical dispersion
Simulation results of DFS with “standard” static
errors + BPM Scale error 5%
-8
5 10
FDFD, BPM scale error 5%
FFDD BPM scale error 5%
-8
<
y, -corrected
> (m)
4.5 10
-8
4 10
-8
3.5 10
-8
3 10
-8
2.5 10
-8
2 10
0
5000
4
1 10
4
1.5 10
4
2 10
s (m)
average of 40 seeds
Other considered issues, examples
• Coupler wake and RF transverse kicks
– No problem because of short bunch length (compare with in RTML)
• Emittance dilution in undulator for e+ production
– Dispersive effect will be small, with orbit correction.
– Wakefield in the narrow beam pipe can be significant.
• No problem with movers.
• Specification of magnet change speed
– For BBA, or startup after shutdown, etc.
– Required speed will be achievable without serious R&D.
• Quadrupole: 0.01 T/m*m/s (0.033%/s)
• Steering: 3E-4 Tm/s (0.6%/s)
Possible Further studies
(some studies already exist but not completed)
• Studies with realistic alignment model
– Alignment engineers and beam dynamics physicists
should agree.
• More realistic DMS procedure
– E.g. Simulations combined with upstream (RTML)
• Optics choice, for making less sensitive to BPM scale error.
– See next slide
• Simulations with failed components (BPM, Cavities, Magnets)
• , , , RTML-ML-BDS combined studies, , ,
None of these are expected to be critical.
Vertical Orbit and Dispersion
Base line optics (same as RDR) and new possible optics
0.0001
New Optics
RDR
y (m)
0
-0.0001
-0.0002
-0.0003
-0.0004
1.6 10
3
3
1.7 10
1.8 10
3
1.9 10
3
2 10
3
3
2 10
s (m)
New Optics
RDR
0.001
y
 (m)
0.0015
0.0005
0
1.6 10
3
1.7 10
3
1.8 10
3
1.9 10
3
s (m)
K.Kubo, ILC-CLIC-LET-Workshop, 2009 CERN