Effect of alignment errors on Touschek lifetime, dynamic
apertures and injection efficiency
S.M. Liuzzo, (Post-Doc, ESRF),
10-13 march 2015, CAoPAC Workshop, GSI, Darmstadt
OUTLINE
The influence of errors on the ESRF upgrade lattice will be presented:
- Uncorrected errors
- BPM and correctors locations in the ESRF cell
- Corrections scheme
- Strategies for error tolerance definitions: comparable tables and
tolerable errors list
- Random alignment errors
- Multipole errors
- Long range and survey errors
- Effects on beamlines
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l CAoPAC Workshop l GSI, Darmstadt 10-13 March 2015 l S.M.Liuzzo
MISALIGNMENTS
Real accelerators are not perfectly aligned. Unwanted fields are
present in the lattice:
Quadrupole
Sextupole
Sextupole
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Misaligned
Quadrupole
Quadrupole
Dipole
Vertically Misaligned
Sextupole
Sextupole
Skew Quadrupole
Dipole
Horizontally Misaligned
Sextupole
Sextupole
Quadrupole
Dipole
l CAoPAC Workshop l GSI, Darmstadt 10-13 March 2015 l S.M.Liuzzo
NUMBER OF TURNS VS ERROR AMPLITUDE WITHOUT CORRECTION
On axis
Increasing the vertical displacement
of quadrupoles introduces vertical
orbit and coupling.
Off axis
For an uncorrected lattice a beam
injected on axis can perform 100
turns with 50 um vertical
quadrupole offsets
A beam injected off axis, can
perform only 10 turns for the same
error rms.
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NEEDS AND CHALLENGES FOR OPTICS CORRECTION: CORRECTORS AND BPM
Correctors in all sextupoles plus 3 separated correctors
All magnets have independent power supplies
10 BPM
9 correctors, horizontal,
vertical and skew
quadrupole in all
sextupoles and 3 dedicated
correctors
16 quadrupoles
DL
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DL
DQ
DQ
EXAMPLE OF CORRECTION OF RANDOM ERRORS
Simulation of the whole correction
sequence, from transfer line to ORM* fit.
-
Find a closed orbit correcting open
trajectories
-
Correct orbit
-
Create lattice error model fitting
‘measured’ RM (partial, 14/288 cor.)
ORMerr = [ ORM/K ] * Kfit
-
Compute Resonance Driving Terms and
correct simultaneously normal and
skew quadrupole RDT and dispersion
After
tuning
Current
ESRF
X [mm]
160(675)
116
61
Y [mm]
111(250)
58
70
Dx-Dx0 [m]
0.017
0.001
0.028
Dy [m]
0.002
0.0002
0.002
b-beating x [%]
26.2
0.7
4.9
b-beating y [%]
26.5
0.8
3.3
Tune x [.21]
0.208
0.21
0.44
Tune y [.34]
0.336
0.34
0.39
Q’x [6]
6.328
6.00
3.89
Q’y [4]
3.971
4.00
6.92
-
Fix tune and chromaticity
ex [134.7 pmrad]
250.4
134.7
4099
-
Iterate a few times
ey [ 0.04 pmrad]
2.2
0.18
3.123
*Orbit Response Matrix
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Closed
orbit only
l CAoPAC Workshop l GSI, Darmstadt 10-13 March 2015 l S.M.Liuzzo
Corrector strengths [rad/L]
INITIAL OPEN TRAJECTORY CORRECTION
Orbit corrector #
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DISPERSION AND BETA BEATING CORRECTION (NORMAL AND SKEW QUAD.)
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DEFINITION OF TOLERABLE ERRORS
To define tolerable errors, we need a deterministic procedure, applicable to any
lattice, and comparable.
1. Compute relevant parameters vs interesting error sources
2. Define accepted threshold for each parameter
3. Chose tolerable error has the minimum value that exceeded a threshold
4. Consider combinations of errors
For the ESRF upgrade lattice some additional care in the error definitions is also required:
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•
for magnets modeled in more parts: longitudinal gradient dipoles, combined function
magnets, sextupoles.
•
distinguish between errors and correction in quadrupoles.
•
Dipole errors do not change the reference trajectory.
l CAoPAC Workshop l GSI, Darmstadt 10-13 March 2015 l S.M.Liuzzo
LIFTIME AND DYNAMIC APERTURES VS ERROR SOURCES
17h
DA=-10mm
Lifetime = 10h
10h
A CLUSTER is crucial for this analysis. Each error set to analyze requires 1CPUx4h
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COMPARABLE TOLERANCE TABLE
•
•
•
•
•
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DQ (combined function dipoles) behave as quadrupoles concerning errors. Evident the impact on vertical
dispersion compared to the other quadrupoles (defocussing quadrupoles).
Quadrupoles have large impact on orbit and horizontal dispersion, also in this case, lifetime and DA are
strongly affected. QF6 and QF8 are dominant.
Sextupoles have the largest impact on DA, they are also the strongest source of beta-beating and
emittance as expected.
Octupoles influence is limited compared to quadrupole and sextupoles, nevertheless they do have an
impact on DA. Their effect on lifetime is very small.
Rotations up to 100urad have impact on the various parameters but limited.
l CAoPAC Workshop l GSI, Darmstadt 10-13 March 2015 l S.M.Liuzzo
COMPARABLE TOLERANCE TABLE
• This table provides a deterministic way to compare error impact on
lattices.
• It is used also to asses the performances of correction schemes and
correction algorithms
• Further reduction of this data is needed to provide a tolerance table.
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DEFINITION OF A LIST OF TOLERABLE ERRORS
Compare magnet groups for the same error
beta beating = 1%
Compare error sources for the same magnet group
Hor. Disp. = 1mm
Tolerated errors
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TOLERABLE RANDOM ERRORS
Each error, on each magnet family, is studied individually looking at the
dependence of DA, lifetime, emittances and all relevant parameters vs error
amplitude.
Required: DX
DY
DS
DPSI
DK
mm
mm
mm
mrad
10^-4
>100
>100
1000
500
10
DQ, QF[68]
70
50
500
200
5
Q[DF][1-5]
100
85
500
500
5
SFD
70
50
500
1000
35
OF
100
100
500
1000
DL
Sextupoles and high gradient quadrupoles are the most relevant limitations,
nevertheless, this alignment specifications are currently achievable.
(DX=DY=60mm, 84 mm between two magnets).
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LIFETIME, DYNAMIC APERTURE AND INJECTION EFFICIENCY
With the dedicated injection section and an appropriate injected beam
the upgrade lattice has injection efficiency of 98+/-1% (average of 10 seeds),
With a lifetime of 21+/-1 h (average of 10 seeds), 43 h without errors.
septum
Injected beam
Kicked beam
This figure uses as
errors the table
above. It might be
used as the
standard candle for
the lattice
accompanied by
lifetime and
injection efficiency
Stored beam
averages.
Injection bump
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MULTIPOLE ERRORS
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LAMINATED MAGNET MULTIPOLE ERRORS: EFFECT ON DYNAMIC APERTURE
D.A.: 10.3+/-0.5 mm
L.T. : 21.3 +/- 1 h
I.E. : 98%
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D.A.: 10.7+/-0.6 mm
L.T. : 21.3 +/- 1 h
I.E. : 98%
CORRECTOR MULTIPOLES
Bx(x)/B0
G(x)/G0
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By(x)/B0
At every update of the
correctors values this
multipoles must be
recomputed.
CORRECTOR MULTIPOLES + STANDARD ERRORS
D.A.: 10.3+/-0.5 mm
L.T. : 21.3 +/- 1 h
I.E. (30nm,round) : 98%
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D.A.: 9.8+/-0.7 mm
L.T. : 21.4+/-1.2 h
I.E. (30nm,round) :97+/-2 %
LONG RANGE ERRORS
nominal
measured
storage ring survey data
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simulated 1st harmonic,
ERROR AMPLITUDE GIVING 30UM ORBIT AFTER CORRECTION VS WAVELENGTH
Amplitude is X, Y and rotation about s (rad) simultaneously
Simulations performed on the OAR asd cluster, about 8h-600cpu
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DYNAMIC APERTURE AND LIFETIME
Lifetime: 16.6h
range:[16.4 17.1]
nominal
measured
-10mm (-8.1mm @injection)
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CURRENT ESRF SURVEY
X-ray beam direction is strongly influenced by the position of the storage ring
and orbit distortion.
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X-RAY BEAM POSITION AT ID (60 METERS)
All ID are assumed to be at 60m from the source.
The position of the beam after 60m is very similar for
ESRF and S28A considering the current survey
measurement.
The position if the ring was aligned on the reference
circumference would be about (0,0) for al ID.
Current
(simulated)
position of the
X-ray at the
beamline
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l CAoPAC Workshop l GSI, Darmstadt 10-13 March 2015 l S.M.Liuzzo
position of the
X-ray at the
beamline for
S28A on the
same survey
CONCLUSIONS
ESRF lattice sensitivity to lattice errors has been shown
A complete correction scheme is used to deduce the lattice parameters
after correction
Random alignment errors are studied to determine a tolerable errors table
Long range errors and survey errors are also analyzed, and the impact of
the alignment on the beamlines positions is considered.
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l CAoPAC Workshop l GSI, Darmstadt 10-13 March 2015 l S.M.Liuzzo
THANK YOU FOR YOUR ATTENTION!
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l CAoPAC Workshop l GSI, Darmstadt 10-13 March 2015 l S.M.Liuzzo
ALIGNMENT ERRORS DEFINITION IN THE SIMULATIONS
Notice:
- longitudinal displacement for
dipoles is not trivial
- Everything respect to the nominal
beam trajectory.
DS
R
q
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l CAoPAC Workshop l GSI, Darmstadt 10-13 March 2015 l S.M.Liuzzo
ORBIT CORRECTOR STRENGTHS DISTRIBUTION
Vertical
Horizontal
The central vertical corrector is the strongest. Solutions are under study to
reduce its force. This may require a larger corrector, only H-V, or tighter error tolerances.
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H corrector
V corrector
Required
0.6 mrad
0.78 mrad (SH2 only!) 0.2 T
Magnet design
0.6 mrad
0.3 mrad
l CAoPAC Workshop l GSI, Darmstadt 10-13 March 2015 l S.M.Liuzzo
Skew quadrupole
0.43 T
DIPOLE FIELDS ERRORS (CONSTANT FIELD INTEGRAL)
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ONLY DIPOLE FIELD VARIATION
D.A.: 12.4 mm (no errors)
L.T. : 43.1 h (no errors)
I.E. (30nm,round) : 100%
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l CAoPAC Workshop l GSI, Darmstadt 10-13 March 2015 l S.M.Liuzzo
D.A.: 12.1 +/-0.1 mm
L.T. : 40.2 +/- 0.3 h
I.E. (30nm,round) : 100%
ESRF LATTICE CELL
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COIL CURRENTS IN SEXTUPOLE CORRECTION COILS, 10 ERROR SEEDS
PS1
1
PS4
6
PS3
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l CAoPAC Workshop l GSI, Darmstadt 10-13 March 2015 l S.M.Liuzzo
PS2
COIL CURRENTS IN SH DEDICATED CORRECTORS, 10 ERROR SEEDS
PS2
PS1
PS3
3
5
2
4
1
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l CAoPAC Workshop l GSI, Darmstadt 10-13 March 2015 l S.M.Liuzzo
PARAMETERS OF INTEREST VERSUS ERRORS IN SPECIFIC MAGNET FAMILIES
40 instead of
10 seeds, (no
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Horizontal dispersion variation
Horizontal emittance variation
DA computation)
l CAoPAC Workshop l GSI, Darmstadt 10-13 March 2015 l S.M.Liuzzo
Errors ranges
listed in legend
SUMMARY TABLE OF ERROR VALUES TO ACHIEVE A GIVEN DISTORTION
Example: 28 um of Quadrupole displacements to generate 50um of orbit rms
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THRESHOLD CROSSING ERROR VALUES. THRESHOLD @ 9.5 MM DA
Overall improvement compared to
previously used correction algorithm
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Less influence
on emittances
DETAIL FOR EACH FAMILY
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DETAIL ON X-Y DISPLACEMENT FOR EACH FAMILY, 10 ERROR SEEDS
DQ1, QF6 and
QF8 are the
most sensitive
to
x-y
misalignment.
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DETAIL ON DPSI FOR EACH FAMILY, 10 ERROR SEEDS
DQ1, QF6 and
QF8 are the
most sensitive
to
Rotations about
the s-axis.
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GIRDER ERRORS
Girder displacements and rotations
Girder displacements and rotations
+ random errors Quad. and Sext.
4 girders, BPMs are moved with the girder.
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GIRDER ERRORS
Hor. DA @ QFI, X0.81 to scale at S3,
8mm required at S3, 10mm accepted at QFI
17h
10h
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(g) Stands for
girder errors,
no (g), are
quadrupole and
sextupole
individual
misalignments
SUMMARY TABLE OF GIRDER ERRORS
(g) Stands for girder
errors, no g, are
quadrupole and
sextupole individual
misalignments
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SEXTUPOLAR RESONANT DRIVING TERMS AFTER CORRECTION
Sextupolar RDT no errors
Sextupolar RDT with errors
Sextupolar RDT after optics correction
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The use of sextupole
independent power supplies
will allow to recover also the
residual distortion. Work is in
progress (N.Carmignani,
A.Franchi). More details in
Andrea Franchi’s Talk.
Many other techniques will be
applied and are under study to
improve the optics correction,
in particular focusing on the
correction of off energy beam
dynamics and resonant driving
terms.