Andrea Franchi ESRF Grenoble on behalf of the Beam Dynamics amp Diagnostics groups TWDULER 2018 DIAMOND 19 th 20 th April 2018 Andrea Franchi Optics Measurements ESRF 2 Outlines ID: 793456
Download The PPT/PDF document "Recent measurements of linear & nonl..." is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Slide1
Recent measurements of linear & nonlinear optics at the ESRF storage ring
Andrea Franchi (ESRF, Grenoble)on behalf of the Beam Dynamics & Diagnostics groups
TW-DULER 2018, DIAMOND, 19
th
-20
th
April 2018
Slide2Andrea Franchi Optics Measurements @ ESRF
2Outlines
Where we were in 2016
Fast measurement and analysis of the orbit response matrix (ORM)
Measuring ultra-low coupling via turn-by-turn (
TbT
) BPM data
Calibrating sextupole magnets via chromatic functions and off-momentum ORM
Accuracy studies
Extra: dealing
with “multiple beams”
Measuring momentum compaction: see Laura Torino’s talk
Slide3Andrea Franchi Optics Measurements @ ESRF
3Outlines
Where we were in 2016
Fast measurement and analysis of the orbit response matrix (ORM)
Measuring ultra-low coupling via turn-by-turn (
TbT
) BPM data
Calibrating sextupole magnets via chromatic functions and off-momentum ORM
Accuracy studies
Extra: dealing with “multiple beams”
Measuring momentum compaction: see Laura Torino’s talk
Slide4Andrea Franchi Optics Measurements @ ESRF
4
Where we were in 2016
Linear optics measured & corrected weekly via ORM (10’+15’ , no need of switch BPM in
TbT
mode, works for any sextupolar optics, i.e. filling mode) =>
rms
β
-beat ~4-5%
ultra-low coupling ε
y
/ε
x~1‰
32 correctors
64 correctors
PRSTAB 14,034002 (2011)
Slide5Linear optics measured & corrected weekly via ORM (10’+15’ , no need of switch BPM in TbT
mode, works for any sextupolar optics, i.e. filling mode) => rms β
-beat ~4-5% ultra-low coupling ε
y
/ε
x
~1
‰
Measuring ultra-low coupling with
TbT
BPM data with kicked beam unsuccessful because of the low signal/noise of the coupling line in the
TbT
spectrum
Andrea Franchi Optics Measurements @ ESRF
5
Where we were in 2016
Slide6Linear optics measured & corrected weekly via ORM (10’+15’ , no need of switch BPM in TbT
mode, works for any sextupolar optics, i.e. filling mode) => rms β
-beat ~4-5% ultra-low coupling ε
y
/ε
x
~1
‰
Measuring ultra-low coupling with
TbT
BPM data with kicked beam unsuccessful because of the low signal/noise of the coupling line in the
TbT
spectrum
Andrea Franchi Optics Measurements @ ESRF
6
Where we were in 2016
low kick
1mm@
βx=35m nonlinearities avoided coupling line ~ background noise
large kick
3mm
@
β
x
=35m
nonlinearities pollute lines
coupling line >> background noise
arxiv.org
: 1603.00281
Slide7Andrea Franchi Optics Measurements @ ESRF
7Where we were in 2016
Linear optics measured & corrected weekly via ORM (10’+15’ , no need of switch BPM in
TbT
mode, works for any sextupolar optics, i.e. filling mode) =>
rms
β
-beat ~4-5% ultra-low coupling ε
y
/ε
x
~1
‰
Measuring ultra-low coupling with TbT BPM data with kicked beam unsuccessful because of the low signal/noise of the coupling line in the TbT spectrum
nonlinear lattice model and sextupole calibration from harmonic analysis of TbT BPM data (~2’, but need BPM in TbT mode with MAF filter ~15’x2, works for a special sextupole optics only, tedious orbit control when calibrating sextupoles)
PRSTAB 17 074001 (2014)
Slide8Andrea Franchi Optics Measurements @ ESRF
8Where we were in 2016
Linear optics measured & corrected weekly via ORM (10’+15’ , no need of switch BPM in
TbT
mode, works for any sextupolar optics, i.e. filling mode) =>
rms
β
-beat ~4-5% ultra-low coupling ε
y
/ε
x
~1
‰
Measuring ultra-low coupling with TbT
BPM data with kicked beam unsuccessful because of the low signal/noise of the coupling line in the TbT spectrumnonlinear lattice model and sextupole calibration from harmonic analysis of TbT
BPM data (~2’, but need BPM in TbT mode with MAF filter ~15’x2, works for a special sextupole optics only, tedious orbit control when calibrating sextupoles)
PRSTAB 17 074001 (2014)
from norm.
sext
. lines to sextupole calibration
Slide9Andrea Franchi Optics Measurements @ ESRF
9Where we were in 2016
Linear optics measured & corrected weekly via ORM (10’+15’ , no need of switch BPM in
TbT
mode, works for any sextupolar optics, i.e. filling mode) =>
rms
β
-beat ~4-5% ultra-low coupling ε
y
/ε
x
~1
‰
Measuring ultra-low coupling with TbT
BPM data with kicked beam unsuccessful because of the low signal/noise of the coupling line in the TbT spectrumnonlinear lattice model and sextupole calibration from harmonic analysis of TbT
BPM data (~2’, but need BPM in TbT mode with MAF filter ~15’x2, works for a special sextupole optics only, tedious orbit control when calibrating sextupoles)
PRSTAB 17 074001 (2014)
from norm.
sext
. lines to sextupole calibration
Slide10Andrea Franchi Optics Measurements @ ESRF
10Where we were in 2016
Linear optics measured & corrected weekly via ORM (10’+15’ , no need of switch BPM in
TbT
mode, works for any sextupolar optics, i.e. filling mode) =>
rms
β
-beat ~4-5% ultra-low coupling ε
y
/ε
x
~1
‰
Measuring ultra-low coupling with TbT
BPM data with kicked beam unsuccessful because of the low signal/noise of the coupling line in the TbT spectrumnonlinear lattice model and sextupole calibration from harmonic analysis of TbT
BPM data (~2’, but need BPM in TbT mode with MAF filter ~15’x2, works for a special sextupole optics only, tedious orbit control when calibrating sextupoles)
PRSTAB 17 074001 (2014)
from norm.
sext
. lines to sextupole gradient error model
Slide11Andrea Franchi Optics Measurements @ ESRF
11Where we were in 2016
Linear optics measured & corrected weekly via ORM (10’+15’ , no need of switch BPM in
TbT
mode, works for any sextupolar optics, i.e. filling mode) =>
rms
β
-beat ~4-5% ultra-low coupling ε
y
/ε
x
~1
‰
Measuring ultra-low coupling with TbT
BPM data with kicked beam unsuccessful because of the low signal/noise of the coupling line in the TbT spectrumnonlinear lattice model and sextupole calibration from harmonic analysis of TbT
BPM data (~2’, but need BPM in TbT mode with MAF filter ~15’x2, works for a special sextupole optics only, tedious orbit control when calibrating sextupoles)
PRSTAB 17 074001 (2014)
from skew
sext
. lines to sextupole tilt model
Slide12Andrea Franchi Optics Measurements @ ESRF
12Where we were in 2016
Linear optics measured & corrected weekly via ORM (10’+15’ , no need of switch BPM in
TbT
mode, works for any sextupolar optics, i.e. filling mode) =>
rms
β
-beat ~4-5% ultra-low coupling ε
y
/ε
x
~1
‰
Measuring ultra-low coupling with TbT
BPM data with kicked beam unsuccessful because of the low signal/noise of the coupling line in the TbT spectrumnonlinear lattice model and sextupole calibration from harmonic analysis of TbT
BPM data (~2’, but need BPM in TbT mode with MAF filter ~15’x2, works for a special sextupole optics only, tedious orbit control when calibrating sextupoles)
PRSTAB 17 074001 (2014)
from norm.
oct
. lines to
octupole
field model (in quads)
Slide13Andrea Franchi Optics Measurements @ ESRF
13Where we were in 2016
Linear optics measured & corrected weekly via ORM
(
10’+15’
, no need of switch BPM in
TbT
mode, works for any sextupolar optics, i.e. filling mode) =>
rms
β
-beat ~4-5% ultra-low coupling ε
y
/εx~1‰Measuring ultra-low coupling with TbT BPM data with kicked beam
unsuccessful because of the low signal/noise of the coupling line in the TbT spectrumnonlinear lattice model and sextupole calibration
from harmonic analysis of TbT BPM data (~2’, but need BPM in TbT mode with MAF filter ~15’x2, works for a special sextupole optics
only, tedious orbit control when calibrating sextupoles)
we want a quicker (daily) analysis!
we’d like to do it!
we want an easier & more flexible analysis!
Slide14Andrea Franchi Optics Measurements @ ESRF
14Outlines
Where we were in 2016
Fast measurement and analysis of the orbit response matrix (ORM)
Measuring ultra-low coupling via turn-by-turn (
TbT
) BPM data
Calibrating sextupole magnets via chromatic functions and off-momentum ORM
Accuracy studies
Extra: dealing with “multiple beams”
Measuring momentum compaction: see Laura Torino’s talk
Slide15Andrea Franchi Optics Measurements @ ESRF
15Fast ORM measurement and analysis
ORM analysis (dip. & quad. errors & tilts) needs to evaluate responses
N
&
S
Slide16Andrea Franchi Optics Measurements @ ESRF
16Fast ORM measurement and analysis
ORM analysis (dip. & quad. errors & tilts) needs to evaluate responses
N
&
S
today: done numerically (compute ORM for each magnet error & tilt) :
num@ESRF’17
~2’
x
2
(iterations), 64+256 magnets (existing storage ring)
num@ESRF’19
~4’
x
2
(iterations), 128+514 magnets ( new storage ring)
Slide17Andrea Franchi Optics Measurements @ ESRF
17Fast ORM measurement and analysis
arxiv.org
: 1711.06589
ORM analysis (dip. & quad. errors & tilts) needs to evaluate responses
N
&
S
today: done numerically (compute ORM for each magnet error & tilt) :
num@ESRF’17
~2’
x
2
(iterations), 64+256 magnets (existing storage ring)
num@ESRF’19
~4’
x
2
(iterations), 128+514 magnets ( new storage ring)
Analytic formulas for
N
&
S
were derived speeding up their computation
analyt@ESRF’17
~2”
x
2
(iterations)
analyt@ESRF’19
~4”
x
2
(iterations)
collaboration with Z.
Martí
of ALBA
Slide18Error:
~1-2% rmsNo measur
. difference in fit & correction of real data
Andrea Franchi Optics Measurements @ ESRF
18
Fast ORM measurement and
analysis
arxiv.org
: 1711.06589
ORM analysis (dip. & quad. errors & tilts) needs to evaluate responses
N
&
S
today: done numerically (compute ORM for each magnet error & tilt) :
num@ESRF’17 ~2’ x 2 (iterations), 64+256 magnets (existing storage ring)
num@ESRF’19 ~4’ x 2 (iterations), 128+514 magnets ( new storage ring)
Analytic formulas for
N
&
S
were derived speeding up their computation
analyt@ESRF’17
~2”
x
2
(iterations)
analyt@ESRF’19
~4”
x
2
(iterations)
ORM diagonal block line (
foc
. err.)
ORM off-diagonal block line (
coupl
.)
collaboration with Z.
Martí
of ALBA
Slide19Andrea Franchi Optics Measurements @ ESRF
19Fast ORM measurement and analysis
Today’s ORM measurement: vary
one by one
the DC component of 16x2 steerers, store de corresponding orbit and infer the ORM => ~10’ (The complete ORM with all 96x2 steerers requires ~50’) ~300
μm
rms
orbit
distor
.
Slide20Andrea Franchi Optics Measurements @ ESRF
20Fast ORM measurement and analysis
Today’s ORM measurement: vary
one by one
the DC component of 16x2 steerers, store de corresponding orbit and infer the ORM => ~10’ (The complete ORM with all 96x2 steerers requires ~50’) ~300
μm
rms
orbit
distor
.
As of 2010 @ Diamond Light Source (*) the fast orbit feedback electronics is used to drive
simultaneously
the AC steerers with a programmable amplitude and frequency and to retrieve the ORM via harmonic analysis => ~43’’ for 172x2 steerers (15’ in DC mode) & ~17
μm
rms orbit distortion (~170 μm in DC mode)
(*) G. Rehm et al
.,MOCNB01@BIW10, p.44, TUPRI083@IPAC14, …
Slide21Andrea Franchi Optics Measurements @ ESRF
21Fast ORM measurement and analysis
Today’s ORM measurement: vary
one by one
the DC component of 16x2 steerers, store de corresponding orbit and infer the ORM => ~10’ (The complete ORM with all 96x2 steerers requires ~50’) ~300
μm
rms
orbit
distor
.
As of 2010 @ Diamond Light Source (*) the fast orbit feedback electronics is used to drive
simultaneously
the AC steerers with a programmable amplitude and frequency and to retrieve the ORM via harmonic analysis => ~43’’ for 172x2 steerers (15’ in DC mode) & ~17
μm
rms orbit distortion (~170 μm in DC mode) Since then, AC ORM measurements implemented in other labs (^ non-exhaustive list)
(^) X. Yang et al. PRAB
20 054001 (2017), Z. Martí et al. MOPAB102@IPAC17, …
Slide22Andrea Franchi Optics Measurements @ ESRF
22Fast ORM measurement and analysis
Today’s ORM measurement: vary
one by one
the DC component of 16x2 steerers, store de corresponding orbit and infer the ORM => ~10’ (The complete ORM with all 96x2 steerers requires ~50’) ~300
μm
rms
orbit
distor
.
As of 2010 @ Diamond Light Source (*) the fast orbit feedback electronics is used to drive
simultaneously
the AC steerers with a programmable amplitude and frequency and to retrieve the ORM via harmonic analysis => ~43’’ for 172x2 steerers (15’ in DC mode) & ~17
μm
rms orbit distortion (~170 μm in DC mode) Since then, AC ORM measurements implemented in other labs (^ non-exhaustive list)
After first tests in 2012, AC ORM measurements have been resumed in 2017: measurement: 34’’ for 96x2 steerers (7’’x2+20’’ DS overhead) orbit distortion: 250
μm rms (H), 25 μm rms (V), to be optimized
8 steerers in parallel at steps of 2 Hz within 114Hz & 130 Hz, 0.5’’ to be repeated 14 times data analysis duration: 12’ ( 3’x4 ORM blocks, to be optimized)
Slide23Andrea Franchi Optics Measurements @ ESRF
23Fast ORM measurement and analysis
Today’s ORM measurement: vary
one by one
the DC component of 16x2 steerers, store de corresponding orbit and infer the ORM => ~10’ (The complete ORM with all 96x2 steerers requires ~50’) ~300
μm
rms
orbit
distor
.
As of 2010 @ Diamond Light Source (*) the fast orbit feedback electronics is used to drive
simultaneously
the AC steerers with a programmable amplitude and frequency and to retrieve the ORM via harmonic analysis => ~43’’ for 172x2 steerers (15’ in DC mode) & ~17
μm
rms orbit distortion (~170 μm in DC mode) Since then, AC ORM measurements implemented in other labs (^ non-exhaustive list)
After first tests in 2012, AC ORM measurements have been resumed in 2017: measurement: 34’’ for 96x2 steerers (7’’x2+20’’ DS overhead) orbit distortion: 250
μm rms (H), 25 μm rms (V), to be optimized
8 steerers in parallel at steps of 2 Hz within 114Hz & 130 Hz, 0.5’’ to be repeated 14 times data analysis duration: 12’ ( 3’x4 ORM blocks, to be optimized)
implementation plan
perform it daily after special
bunch cleaning (
long
top-up
sequence @9am): prefer
short duration and accept
large orbit distortion while IDs do not move
Slide24Today’s ORM measurement: vary one by one the DC component of 16x2 steerers, store de corresponding orbit and infer the ORM => ~10’ (The complete ORM with all 96x2 steerers requires ~50’) ~300
μm rms orbit distor.
As of 2010 @ Diamond Light Source (*) the fast orbit feedback electronics is used to drive
simultaneously
the AC steerers with a programmable amplitude and frequency and to retrieve the ORM via harmonic analysis => ~43’’ for 172x2 steerers (15’ in DC mode) & ~17
μm
rms
orbit distortion (~170
μm
in DC mode)
Since then, AC ORM measurements implemented in other labs (^ non-exhaustive list)
After first tests in 2012, AC ORM measurements have been resumed in 2017:
measurement: 34’’ for 96x2 steerers (7’’x2+20’’ DS overhead)
orbit distortion: 250
μm rms (H), 25 μm rms
(V), to be optimized8 steerers in parallel at steps of 2 Hz within 114Hz & 130 Hz, 0.5’’ to be repeated 14 times data analysis duration: 12’ ( 3’x4 ORM blocks, to be optimized)
Andrea Franchi Optics Measurements @ ESRF
24Fast ORM
measurement
and analysis
ORM diagonal block line AC Vs DC
ORM off-diagonal block line AC Vs DC
Slide25Andrea Franchi Optics Measurements @ ESRF
25Outlines
Where we were in 2016
Fast measurement and analysis of the orbit response matrix (ORM)
Measuring ultra-low coupling via turn-by-turn (
TbT
) BPM data
Calibrating sextupole magnets via chromatic functions and off-momentum ORM
Accuracy studies
Extra: dealing with “multiple beams”
Measuring momentum compaction: see Laura Torino’s talk
Slide26Andrea Franchi Optics Measurements @ ESRF
26ultra-low coupling via (TbT) BPM data
Idea: replace pulsed excitation with continuous AC excitation close to the betatron tune,
d
=Q-Q
AC
(RHIC 1998 [*],
Tevatron
/RHIC 2008- [^], LHC 2009-[
&
], ….)
thousands of
TbT
with no
decoherence efficient data cleaning
but some precautions & corrections to interpret data (theory not completed yet)
[*] S. Peggs, C. Tang, RHIC/AP/159, 1998; M. Bai
et al. , PRL 80, 4673 (1998)[^] R. Miyamoto, PhD thesis, Univ. of Texas, Austin 2008; BNL C-A/AP/#410, 2010;
PRSTAB
11
084002 (2008), X.
Shen
et al.
, PRSTAB
16
111001 (2013), …
[
&
] R.
Tomás et al.
, PRSTAB
5
054001 (2002),
8
024401 (2005) …
15
, 091001 (2012), 16 -81003 (2013) …
19
, 054001 (2016), …
high spectral resolution
Slide27Andrea Franchi Optics Measurements @ ESRF
27Idea: replace pulsed excitation with continuous AC excitation close to the betatron tune, d
=Q-Q
AC
(RHIC 1998 [*],
Tevatron
/RHIC 2008- [^], LHC 2009-[
&
], ….)
thousands of
TbT
with no
decoherence
efficient data cleaning
but some precautions & corrections to interpret data (theory not completed yet) Very successful on hadron machines (beating, coupling, nonlinearities). Can it work in lepton rings with radiation damping & diffusion (and high chroma
@ ESRF)?
[*] S. Peggs, C. Tang, RHIC/AP/159, 1998; M. Bai
et al. , PRL 80, 4673 (1998)[^] R. Miyamoto, PhD thesis, Univ. of Texas, Austin 2008; BNL C-A/AP/#410, 2010;
PRSTAB
11
084002 (2008), X.
Shen
et al.
, PRSTAB
16
111001 (2013), …
[
&
] R.
Tomás et al. , PRSTAB
5
054001 (2002),
8
024401 (2005) …
15
, 091001 (2012), 16 -81003 (2013) …
19
, 054001 (2016), …
high spectral resolution
ultra-low coupling via (TbT) BPM data
Slide28Andrea Franchi Optics Measurements @ ESRF
28
ultra-low coupling via (TbT) BPM data
Betatron coupling described by two
CRDTs
F
xy
&
F
yx
(*)
Measurement with
low
chroma
& detuning sextupole optics
compare
(
ε
y
/ε
x
~1‰)
ORM model with
TbT
harmonic analysis
(*) PRSTAB
17
074001 (2014)
AMPLITUDE
PHASE
Slide29Andrea Franchi Optics Measurements @ ESRF
29
ultra-low coupling via (TbT) BPM data
Betatron coupling described by two
CRDTs
F
xy
&
F
yx
(*)
Measurement with
low
chroma
& detuning sextupole optics
compare
(ε
y
/ε
x
~1‰)
ORM model with
TbT
harmonic analysis
(*) PRSTAB
17
074001 (2014)
AMPLITUDE
PHASE
Slide30Andrea Franchi Optics Measurements @ ESRF
30
ultra-low coupling via (TbT) BPM data
Betatron coupling described by two
CRDTs
F
xy
&
F
yx
(*)
Measurement with
large
chroma
operational sextupole optics
compare
(
ε
y
/ε
x
~1‰)
ORM model with
TbT
harmonic analysis
(*) PRSTAB
17
074001 (2014)
AMPLITUDE
PHASE
Slide31Andrea Franchi Optics Measurements @ ESRF
31
ultra-low coupling via (TbT) BPM data
Betatron coupling described by two
CRDTs
F
xy
&
F
yx
(*)
Measurement with
large
chroma
operational sextupole optics
compare
(
ε
y
/ε
x
~1‰)
ORM model with
TbT
harmonic analysis
(*) PRSTAB
17
074001 (2014)
AMPLITUDE
PHASE
synchrotron
radiation+diffusion
& high
chroma
=> a dilemma:
small distance
d
=Q-Q
AC
for coupling
large distance
d
=Q-Q
AC
for
β
-beating (extra slides)
in both case accuracy is limited, until new theory including them is developed
AC dipole & data cleaning OK for low-
chroma
lepton rings
Slide32Andrea Franchi Optics Measurements @ ESRF
32Outlines
Where we were in 2016
Fast measurement and analysis of the orbit response matrix (ORM)
Measuring ultra-low coupling via turn-by-turn (
TbT
) BPM data
Calibrating sextupole magnets via chromatic functions and off-momentum ORM
Accuracy studies
Extra: dealing with “multiple beams”
Measuring momentum compaction: see Laura Torino’s talk
Slide33Andrea Franchi Optics Measurements @ ESRF
33sextupoles Vs chromatic functions & ORM
Motivation
Until
TbT
BPM data are quickly available and harmonic analysis is proved effective on any sextupole setting (high
chroma
&
detuning, …) and bunch filling pattern, we seek a way to extend the linear analysis via ORM to obtain
&
correct sextupole models
Slide34Andrea Franchi Optics Measurements @ ESRF
34sextupoles Vs chromatic functions & ORM
Motivation
Until
TbT
BPM data are quickly available and harmonic analysis is proved effective on any sextupole setting (high
chroma
&
detuning, …) and bunch filling pattern, we seek a way to extend the linear analysis via ORM to obtain
&
correct sextupole models
Measurement
&
correction of sextupoles
RDTs @ Touschek-dominated ESRF did not result in improved beam lifetime (unlike @ Diamond[^] ). Simulations indicate RDTs <-> DA, injection efficiency
Chromatic functions <-> momentum acceptance, Touschek lifetime
[^] R.
Bartolini et al. PRAB 11 104002 (2008)
Slide35Andrea Franchi Optics Measurements @ ESRF
35sextupoles Vs chromatic functions & ORM
Motivation
Until
TbT
BPM data are quickly available and harmonic analysis is proved effective on any sextupole setting (high
chroma
&
detuning, …) and bunch filling pattern, we seek a way to extend the linear analysis via ORM to obtain
&
correct sextupole models
Measurement
&
correction of sextupoles
RDTs @ Touschek-dominated ESRF did not result in improved beam lifetime (unlike @ Diamond[^] ). Simulations indicate RDTs <-> DA, injection efficiency
Chromatic functions <-> momentum acceptance, Touschek lifetime
The idea is to measure & fit the off-energy ORM & 2nd-order dispersion
Chromatic functions ineffective for harmonic sextupoles, but new ESRF ring will have chromatic sextupoles only => OK
[^] R.
Bartolini
et al.
PRAB
11
104002 (2008)
Slide36Andrea Franchi Optics Measurements @ ESRF
36sextupoles Vs chromatic functions & ORM
Chromatic functions
arxiv.org
: 1711.06589
D’
y
is a bit more complicated expression
from meas. & fit of standard on-energy ORM
from meas. & fit
of 1 or 2 off
-energy
ORM
the dispersive off-axis orbit across sextupoles introduces additional focusing (
d
β/
d
δ
) and dispersion (
D’
).
Slide37Andrea Franchi Optics Measurements @ ESRF
37sextupoles Vs chromatic functions & ORM
Chromatic functions from off-energy
ORM
example
ORM at +- 100Hz (delta=0.16%)
agreement meas. Vs AT model better in V than H (not understood)
Slide38Andrea Franchi Optics Measurements @ ESRF
38sextupoles Vs chromatic functions & ORM
Chromatic functions from off-energy
ORM
Varying a sextupole (corrector) strength
(i.e. current [-2,+2] A) and measuring variation of chromatic beating
w.r.t
. sextupole OFF
good response
???
Slide39Andrea Franchi Optics Measurements @ ESRF
39sextupoles Vs chromatic functions & ORM
Chromatic functions from off-energy
orbit
horizontal closed orbit at all
BPMs
for different RF frequencies from [-400, 400] Hz in 10 Hz steps & fit a third-order polynomial
Varying a sextupole (corrector) strength (i.e. current [-2,+2] A)
BPM @ large lin. dispersion
BPM @ low lin. dispersion
Slide40Andrea Franchi Optics Measurements @ ESRF
40sextupoles Vs chromatic functions & ORM
Sextupole Calibration
from
Chromatic functions
The calibration factor from magnetic measurements is 0.1569 m
-2
A
-1
removing horizontal chromatic beating
Slide4141
Andrea Franchi
Resonance Driving Terms
ORM
analysis
TbT
analysis
observables: chromatic terms
better for lifetime (
tbc
experimentally)
linear
system to be solved
requires at least
3
measurements at
δ
=0
&
δ
=±
ε
works with
BPMs
in normal orbit mode
resolution independent upon sextupole setting
for
octupoles
& higher-order multipoles you need several measurements at large
δ
observables: resonant
driving terms
better for calibration of nonlinear magnets & DA
(
tbc
experimentally)
linear system to be solved
requires 1 measurement at
δ
=0
requires
BPMs
switch
to
TbT
(MAF) mode
resolution dependent upon sextupole setting (high
chroma
=> low accuracy)
you may characterize
octupoles
& higher-order multipoles with a single measurement
nonlinear magnetic model from …
Slide42Andrea Franchi Optics Measurements @ ESRF
42Outlines
Where we were in 2016
Fast measurement and analysis of the orbit response matrix (ORM)
Measuring ultra-low coupling via turn-by-turn (
TbT
) BPM data
Calibrating sextupole magnets via chromatic functions and off-momentum ORM
Accuracy studies
Extra: dealing with “multiple beams”
Measuring momentum compaction: see Laura Torino’s talk
Slide4343
Andrea Franchi
Resonance Driving Terms
Accuracy studies: ORM Vs
TbT
analysis
from L.
Malina’s
talk, LER workshop 2018 @ CERN
systematic
errors
statistical
errors
Slide4444
Andrea Franchi
Resonance Driving Terms
Accuracy studies: ORM Vs
TbT
analysis
from L.
Malina’s
talk, LER workshop 2018 @ CERN
artificial
β
-beating
from
TbT
data
Slide4545
Andrea Franchi
Resonance Driving Terms
Accuracy studies: ORM Vs
TbT
analysis
from L.
Malina’s
talk, LER workshop 2018 @ CERN
artificial
β
-beating
from
TbT
data
~10
μm
/√Hz (
TbT
,
353
kHz)
Vs
~10 nm/√Hz (ORM, 10 Hz
aqn
)
Slide4646
Andrea Franchi
Resonance Driving Terms
Accuracy studies: ORM Vs
TbT
analysis
from L.
Malina’s
talk, LER workshop 2018 @ CERN
artificial
β
-beating
from
TbT
data
The measured BPM phase advance is no longer the betatron BPM phase advance
Slide4747
Andrea Franchi
Resonance Driving Terms
Accuracy studies: ORM Vs
TbT
analysis
from L.
Malina’s
talk, LER workshop 2018 @ CERN
artificial
β
-beating
from
TbT
data
~1/N
2
(
TbT
)
Vs
no dependence for ORM
Slide4848
Andrea Franchi
Resonance Driving Terms
Accuracy studies: ORM Vs
TbT
analysis
See L.
Malina
LER workshop 2018 @ CERN & PRAB 20, 082802 (2017)
Error contribution
to
rms
β
-beating (in
‰
)
Statistical
errors
(precision)
the most significant (machine vibrations,
orbit
drifts
[@ ESRF
15 μm rms
=>
5‰
], …)
Systematic (accuracy):
SVD on ORM:
3‰
(simulations over ten
sets,
w/wo
10 nm BPM noise)
Reproducibility (precision):
5‰
(H) & 2
‰
(V) over 5 consecutive ORM measurements (orbit corrected within 2μm
rms
)
Lattice non-
linearities
polluting
TbT
tune line (from simulations): 1-2
‰
accuracy @
lowest kick amplitude
BPM noise and harmonic analysis of
TbT
data: depends on methods
Mean
error
Method
β
x
-beating
precision [
‰
]
β
y
-beating
precision [
‰
]
TbT
@ ESRF
4
4
ORM @ ESRF
6
4
Slide49Andrea Franchi Optics Measurements @ ESRF
49Summary
Fast measurement and analysis of the orbit response matrix (ORM):
analysis OK, operational implementation ongoing
Measuring ultra-low coupling via turn-by-turn (
TbT
) BPM data:
OK for low-
chroma
rings,
not yet for high-
chroma
lepton machines
Calibrating sextupole magnets via chromatic functions and off-momentum ORM:
calibration OK, some open questions, sextupole model not yetLinear optics: @ ESRF accuracy of ORM Vs TbT ~same (with precautions)
Slide50Andrea Franchi Optics Measurements @ ESRF
50Outlines
Where we were in 2016
Fast measurement and analysis of the orbit response matrix (ORM)
Measuring ultra-low coupling via turn-by-turn (
TbT
) BPM data
Calibrating sextupole magnets via chromatic functions and off-momentum ORM
Accuracy studies
Extra: dealing with “multiple beams”
Measuring momentum compaction: see Laura Torino’s talk
Slide51Andrea Franchi Optics Measurements @ ESRF
51Dealing with “multiple beams”
from P
.
Goslawski
“
TRIBs
at BESSY II /
MLS”, 21/9 NOCE 2017
Slide52Andrea Franchi Optics Measurements @ ESRF
52Dealing with “multiple beams”
beamlets
into
islands
orbit
meas
. & correct.
One or few RF
buckets are filled with
only 1 beamlet
in 1
island
Slide53Andrea Franchi Optics Measurements @ ESRF
53Dealing with “multiple beams”
beamlets
into
islands
orbit
meas
. & correct.
One or few RF
buckets are filled with
only 1 beamlet
in 1
island
N
beamlets
in N
islands
(N=3
here
) ~ CASE
1.
Slide54Andrea Franchi Optics Measurements @ ESRF
54Dealing with “multiple beams”
beamlets
into
islands
orbit
meas
. & correct.
One or few RF
buckets are filled with
only 1 beamlet
in 1
island
N
beamlets
in N
islands
(N=3
here
)
~ CASE
1.
N
beamlets
in N
islands
+
beamlet
at
the centre
Slide55Andrea Franchi Optics Measurements @ ESRF
55Dealing with “multiple beams”
beamlets
into
islands
orbit
meas
. & correct.
One or few RF
buckets are filled withcentre of
gravity of 3 islands
is not x=0 (~300μm in this plot) and varies
along the ring
how to
distinguish
island’s
orbit
(in
some
RF
buckets
)
from
the one of the
beam
on axis (in
most
of the RF
buckets
)?
How to correct
those
two
orbits
separately
?
Slide56Andrea Franchi Optics Measurements @ ESRF
56EXTRA SLIDES
Slide57Andrea Franchi Optics Measurements @ ESRF
57large sextupole “tilts” & octupole fields in quads
PRSTAB
17
074001 (2014)
Slide58Andrea Franchi Optics Measurements @ ESRF
58sextupoles Vs chromatic functions & ORM
Sextupole Calibration
from
Chromatic functions
The calibration factor from magnetic measurements is 0.1569 m
-2
A
-1
removing horizontal chromatic beating
Slide59Andrea Franchi Optics Measurements @ ESRF
59sextupoles Vs chromatic functions & ORM
Sextupole Calibration
from
Chromatic functions
The calibration factor from magnetic measurements is 0.1569 m
-2
A
-1
with all 3 chromatic functions
Slide60Andrea Franchi Optics Measurements @ ESRF
60AC dipole @ ESRF: magnetic kicker (shaker) producing H & V magnetic field with 2 sets of 6 coils inside a ferrite enclosure and outside a ceramic vacuum chamber (internally coated with a thin metallic layer to lower HF impedance). The shaker is driven by a 700 W (H) & 100 W (V) amplifiers.
store 6000 turns and perform an SVD cleaning prior harmonic analysis
harmonic analysis over 1024 or 2048 only on real signals
x
&
y
, not the complex
x+ip
x
&
y+ip
y
!
betatron coupling described by two CRDTs F
xy & Fyx (*)
(*) PRSTAB 17
074001 (2014)
ultra-low coupling via (TbT) BPM data
Slide61Andrea Franchi Optics Measurements @ ESRF
61
ultra-low coupling via (TbT) BPM data
low Vs high
chroma
sextupole optics
Artificial
β
-beating from
multiparticle
&
leptonic
nature of the beam
Low
chroma
& detuning
Slide62Andrea Franchi Optics Measurements @ ESRF
62
ultra-low coupling via (TbT) BPM data
low Vs high
chroma
sextupole optics
Artificial
β
-beating from
multiparticle
&
leptonic
nature of the beam
High
chroma
& detuning
Slide63Andrea Franchi Optics Measurements @ ESRF
63
ultra-low coupling via (TbT) BPM data
low Vs high
chroma
sextupole optics
Artificial
β
-beating from
multiparticle
&
leptonic
nature of the beam
High
chroma
& detuning
Slide64Andrea Franchi Optics Measurements @ ESRF
64
ultra-low coupling via (TbT) BPM data
low Vs high
chroma
sextupole optics
Artificial
β
-beating from
multiparticle
&
leptonic
nature of the beam
High
chroma
& detuning
synchrotron radiation and diffusion & high
chroma
seem to limit the possibility of accurate measurement (& correction) of
β
-beating via AC dipole excitation …
until new theory including them is developed
Slide6565
nonlinear magnetic model from orbit BPM data
off energy additional focusing is provided by sextupoles
by measuring the ORM off energy information on sextupoles can be extracted
on momentum
δ
=0:
off momentum δ≠0 including linear error model, to be pseudo-inverted:
approach Nr. 1
Slide6666
nonlinear magnetic model from orbit BPM data
off energy additional focusing is provided by sextupoles
by measuring the ORM off energy information on sextupoles can be extracted
on momentum
δ
=0:
approach Nr. 2
Slide6767
nonlinear magnetic model from orbit BPM data
off energy additional focusing is provided by sextupoles
by measuring the ORM off energy information on sextupoles can be extracted
on momentum
δ
=0:
off momentum δ≠0 :
approach Nr. 2
Slide6868
nonlinear magnetic model from orbit BPM data
off energy additional focusing is provided by sextupoles
by measuring the ORM off energy information on sextupoles can be extracted
approach Nr. 2
on momentum
δ
=0:
off momentum δ≠0 :
being tested @ ESRF
chromatic terms
to be pseudo-inverted
Slide69Andrea Franchi Optics Measurements @ ESRF
69Measuring momentum compaction
A quicker technique consists in measuring the variation of the x-ray intensity onto a monitor Vs
D
f
RF
Variation of
δ
=> Variation of
synchr
. rad. intensity
DI
SR
/I
0≅T δ => δ≅(DISR/I0)/
T Infer δ from DISR after
DfRF
(~30mm Cu) Crotch absorber
(~6mm Al/Fe) Extraction window
(~6mm
CdW
)
Scintillator
Objective
CCD
bending mag.
a
c
value (10
-4
)
Ideal model
1.7795
Model with errors
1.827
±0.004 (*)
ID
20
1.76
±0.14
ID 21
1.87
± 0.11
hard
x-ray monitor
1.867
± 0.004
(^)
(*
) from 11 ORM models last 2017 run
(^) statistical error, systematic to be found
sources of systematic error:
absolute energy error 1% => 1.6%
dipole field uncertainty (not-measured unsaturated soft end Vs measured saturated main hard part) 1% => 0.8%