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Coupling Correction Through Beam Position
Data
J. Chavanne, P. Elleaume, F. Ewald, L. Farvacque, A. Franchi,
T. Perron, K. Scheidt
Low-emittance Rings workshop 2011 Heraklion, Crete, greece, 3rd to 5th October 2011
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Andrea Franchi Vertical Emittance reduction @ ESRF 2
Outlines
•Vertical emittances in the presence of coupling
•Coupling correction via Resonance Driving Terms
•2010: Application in the ESRF storage ring
•2010: Preserving small vertical emittance during beam delivery
•2011: Towards ultra-small vertical emittance
•PS: Indirect measurements of vertical emittance
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Andrea Franchi Vertical Emittance reduction @ ESRF 3
Outlines
•Vertical emittances in the presence of coupling
•Coupling correction via Resonance Driving Terms
•2010: Application in the ESRF storage ring
•2010: Preserving small vertical emittance during beam delivery
•2011: Towards ultra-small vertical emittance
•PS: Indirect measurements of vertical emittance
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Andrea Franchi Vertical Emittance reduction @ ESRF 4
Vertical emittance in the absence of coupling•Eigen-emittance E: constant along the ring, dependent on the linear lattice only. Ideally Ev≅0
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Andrea Franchi Vertical Emittance reduction @ ESRF 5
Vertical emittance in the absence of coupling•Eigen-emittance E: constant along the ring, dependent on the linear lattice only. Ideally Ev≅0
•Non measurable RMS emittance:
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Andrea Franchi Vertical Emittance reduction @ ESRF 6
Vertical emittance in the absence of coupling•Eigen-emittance E: constant along the ring, dependent on the linear lattice only. Ideally Ev≅0
•Non measurable RMS emittance:
•Measurable emittance from RMS beam size:
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Andrea Franchi Vertical Emittance reduction @ ESRF 7
Vertical emittance in the absence of coupling•Eigen-emittance E: constant along the ring, dependent on the linear lattice only. Ideally Ev≅0
•Non measurable RMS emittance:
•Measurable emittance from RMS beam size:
Ev=εy=Ey=const.
With zero vertical dispersion, Ev=εy=Ey≅0
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Andrea Franchi Vertical Emittance reduction @ ESRF 8
Meas. vertical emittance Ey from RMS beam size
ESRF SR equipment:•11 dipole radiation projection monitors (IAX) • 2 pinhole cameras
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Andrea Franchi Vertical Emittance reduction @ ESRF 9
Meas. vertical emittance Ey from RMS beam size
Ex=4.2 nm• Well corrected coupling• Low beam current (20 mA)
5.5 pm
2.8 pm
3.6 pm
1.4 pm2.8 pm
1.0 pm
2.3 pm
3.7 pm
4.2 pm
3.3 pm 1.8 pm
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Andrea Franchi Vertical Emittance reduction @ ESRF 10
Meas. vertical emittance Ey from RMS beam size
Ex=4.2 nm• Well corrected coupling• Low beam current (20 mA)
Εy=3.0 pm ±1.3 (STD)
±0.15 (fluctuation)
5.5 pm
2.8 pm
3.6 pm
1.4 pm2.8 pm
1.0 pm
2.3 pm
3.7 pm
4.2 pm
3.3 pm 1.8 pm
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Andrea Franchi Vertical Emittance reduction @ ESRF 11
Meas. vertical emittance Ey from RMS beam size
Ex=4.2 nm• Well corrected coupling• Low beam current (20 mA)
Εy=3.0 pm ±1.3 (STD)
±0.15 (fluctuation)
5.5 pm
2.8 pm
3.6 pm
1.4 pm2.8 pm
1.0 pm
2.3 pm
3.7 pm
4.2 pm
3.3 pm 1.8 pmAre vertical emittance and Ey/Ex
always good indicators of
coupling?
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Andrea Franchi Vertical Emittance reduction @ ESRF 12
Meas. vertical emittance Ey from RMS beam size
Stored beam current[mA]
Measured Vertical emittance [pm]
INCREASING ION TRAPPING
20 3.0 ± 1.5 (STD) ±0.15 (F)
100 5.7 ± 1.7 (STD) ±0.07 (F)160 10.1 ± 2.0 (STD) ±0.12 (F)200 17.2 ± 1.8 (STD) ±0.35 (F)
Fixed low coupling
• STD =standard deviation from 11 IAX monitors
• F=Fluctuation over 30 s from 1-Hz sampling
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Andrea Franchi Vertical Emittance reduction @ ESRF 13
Meas. vertical emittance Ey from RMS beam size
Stored beam current[mA]
Measured Vertical emittance [pm]
INCREASING ION TRAPPING
20 3.0 ± 1.5 (STD) ±0.15 (F)
100 5.7 ± 1.7 (STD) ±0.07 (F)160 10.1 ± 2.0 (STD) ±0.12 (F)200 17.2 ± 1.8 (STD) ±0.35 (F)
200* 4.2 ± 1.4 (STD) ±0.05 (F) with bunch-by-bunch feedback
• STD =standard deviation from 11 IAX monitors
• F=Fluctuation over 30 s from 1-Hz sampling
Fixed low coupling
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Andrea Franchi Vertical Emittance reduction @ ESRF 14
Meas. vertical emittance Ey from RMS beam size
Stored beam current[mA]
Measured Vertical emittance [pm]
INCREASING ION TRAPPING
Corrector skew quad (S13C1) current [A]
Measured Vertical emittance [pm]
INCREASING COUPLING
20 3.0 ± 1.5 (STD) ±0.15 (F) 0 3.1 ± 1.5 (STD) ±0.20 (F)
100 5.7 ± 1.7 (STD) ±0.07 (F) 0.08 5.7 ± 1.8 (STD) ±0.20 (F)160 10.1 ± 2.0 (STD) ±0.12 (F) 0.15 10.0 ± 2.7 (STD) ±0.20 (F)200 17.2 ± 1.8 (STD) ±0.35 (F) 0.18 17.2 ± 3.2 (STD) ±0.20 (F)
• STD =standard deviation from 11 IAX monitors
• F=Fluctuation over 30 s from 1-Hz sampling
Fixed low coupling Fixed low beam current
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Andrea Franchi Vertical Emittance reduction @ ESRF 15
Meas. vertical emittance Ey from RMS beam size
Stored beam current[mA]
Measured Vertical emittance [pm]
INCREASING ION TRAPPING
Corrector skew quad (S13C1) current [A]
Measured Vertical emittance [pm]
INCREASING COUPLING
20 3.0 ± 1.5 (STD) ±0.15 (F) 0 3.1 ± 1.5 (STD) ±0.20 (F)
100 5.7 ± 1.7 (STD) ±0.07 (F) 0.08 5.7 ± 1.8 (STD) ±0.20 (F)160 10.1 ± 2.0 (STD) ±0.12 (F) 0.15 10.0 ± 2.7 (STD) ±0.20 (F)200 17.2 ± 1.8 (STD) ±0.35 (F) 0.18 17.2 ± 3.2 (STD) ±0.20 (F)
• STD =standard deviation from 11 IAX monitors
• F=Fluctuation over 30 s from 1-Hz sampling
Fixed low coupling Fixed low beam current
2 different physical phenomena,
same average vertical emittance
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Andrea Franchi Vertical Emittance reduction @ ESRF 16
Meas. vertical emittance Ey from RMS beam size
Stored beam current[mA]
Measured Vertical emittance [pm]
INCREASING ION TRAPPING
Corrector skew quad (S13C1) current [A]
Measured Vertical emittance [pm]
INCREASING COUPLING
20 3.0 ± 1.5 (STD) ±0.15 (F) 0 3.1 ± 1.5 (STD) ±0.20 (F)
100 5.7 ± 1.7 (STD) ±0.07 (F) 0.08 5.7 ± 1.8 (STD) ±0.20 (F)160 10.1 ± 2.0 (STD) ±0.12 (F) 0.15 10.0 ± 2.7 (STD) ±0.20 (F)200 17.2 ± 1.8 (STD) ±0.35 (F) 0.18 17.2 ± 3.2 (STD) ±0.20 (F)
• STD =standard deviation from 11 IAX monitors
• F=Fluctuation over 30 s from 1-Hz sampling
Fixed low coupling Fixed low beam current
2 different physical phenomena,
same average vertical emittance
Are vertical emittance and Ey/Ex
always good indicators of
coupling?Maybe not
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Andrea Franchi Vertical Emittance reduction @ ESRF 17
Meas. vertical emittance Ey from RMS beam size
Stored beam current[mA]
Measured Vertical emittance [pm]
INCREASING ION TRAPPING
Corrector skew quad (S13C1) current [A]
Measured Vertical emittance [pm]
INCREASING COUPLING
20 3.0 ± 1.5 (STD) ±0.15 (F) 0 3.1 ± 1.5 (STD) ±0.20 (F)
100 5.7 ± 1.7 (STD) ±0.07 (F) 0.08 5.7 ± 1.8 (STD) ±0.20 (F)160 10.1 ± 2.0 (STD) ±0.12 (F) 0.15 10.0 ± 2.7 (STD) ±0.20 (F)200 17.2 ± 1.8 (STD) ±0.35 (F) 0.18 17.2 ± 3.2 (STD) ±0.20 (F)
• STD =standard deviation from 11 IAX monitors
• F=Fluctuation over 30 s from 1-Hz sampling
Fixed low coupling Fixed low beam current
20% larger STD
110% larger STD
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Andrea Franchi Vertical Emittance reduction @ ESRF 18
Meas. vertical emittance Ey from RMS beam size
Stored beam current[mA]
Measured Vertical emittance [pm]
Corrector skew quad (S13C1) current [A]
Measured Vertical emittance [pm]
INCREASING COUPLING
20 3.0 ± 1.5 (STD) ±0.15 (F) 0 3.1 ± 1.5 (STD) ±0.20 (F)
100 5.7 ± 1.7 (STD) ±0.07 (F) 0.08 5.7 ± 1.8 (STD) ±0.20 (F)160 10.1 ± 2.0 (STD) ±0.12 (F) 0.15 10.0 ± 2.7 (STD) ±0.20 (F)200 17.2 ± 1.8 (STD) ±0.35 (F) 0.18 17.2 ± 3.2 (STD) ±0.20 (F)
• STD =standard deviation from 11 IAX monitors
• F=Fluctuation over 30 s from 1-Hz sampling
Fixed low coupling Fixed low beam current
20% larger STD
110% larger STD
The spread among vertical emittance measurements along the ring increases
with coupling. Why?
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Andrea Franchi Vertical Emittance reduction @ ESRF 19
Vertical emittance in the absence of coupling•Eigen-emittance E: constant along the ring, dependent on the linear lattice only. Ideally Ev≅0
•Non measurable RMS emittance:
•Measurable emittance from RMS beam size:
Ev=εy=Ey=const.
With zero vertical dispersion, Ev=εy=Ey≅0
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Andrea Franchi Vertical Emittance reduction @ ESRF 20
Vertical emittances in the presence of coupling•Eigen-emittance E: still constant along the ring, but Ev≠0
•Non measurable projected s-dependent RMS emittance:
•Measurable apparent s-dependent emittance from RMS beam size:
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Andrea Franchi Vertical Emittance reduction @ ESRF 21
Vertical emittances in the presence of coupling•Eigen-emittance E: still constant along the ring, but Ev≠0
•Non measurable projected s-dependent RMS emittance:
•Measurable apparent s-dependent emittance from RMS beam size:
Ev=const ≠ εy(s) ≠ Ey(s)
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22
•Coupling sources (tilted quads, misaligned sextupoles, ID error fields, etc.) generate skew quad fields J1(s)
Vertical emittances in the presence of coupling
Andrea Franchi Vertical Emittance reduction @ ESRF
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23
•Coupling sources (tilted quads, misaligned sextupoles, ID error fields, etc.) generate skew quad fields J1(s)
Vertical emittances in the presence of coupling
Andrea Franchi Vertical Emittance reduction @ ESRF
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24
•Coupling sources (tilted quads, misaligned sextupoles, ID error fields, etc.) generate skew quad fields J1(s)
• J1(s) generate two Resonance Driving Terms (RDTs) f(s)
fa=Mab(β,φ) Jb,1
Linear dependence!
Vertical emittances in the presence of coupling
Andrea Franchi Vertical Emittance reduction @ ESRF
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25
•Coupling sources (tilted quads, misaligned sextupoles, ID error fields, etc.) generate skew quad fields J1(s)
• J1(s) generate two Resonance Driving Terms (RDTs) f(s)
fa=Mab(β,φ) Jb,1
Linear dependence!
Vertical emittances in the presence of coupling
Andrea Franchi Vertical Emittance reduction @ ESRF
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26
•Coupling sources (tilted quads, misaligned sextupoles, ID error fields, etc.) generate skew quad fields J1(s)
• J1(s) generate two Resonance Driving Terms (RDTs) f(s)
fa=Mab(β,φ) Jb,1
Linear dependence!
Vertical emittances in the presence of coupling
Andrea Franchi Vertical Emittance reduction @ ESRF
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27
Non measurable projected s-dependent emittance
Measurable apparent s-dependent emittance
Vertical emittances in the presence of coupling
Andrea Franchi Vertical Emittance reduction @ ESRF
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28
Non measurable projected s-dependent emittance
Measurable apparent s-dependent emittance
Vertical emittances in the presence of coupling
Andrea Franchi Vertical Emittance reduction @ ESRF
Nonlinear dependence on the RDTs and J1
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29
Non measurable projected s-dependent emittance
Measurable apparent s-dependent emittance
Vertical emittances in the presence of coupling
Andrea Franchi Vertical Emittance reduction @ ESRF
Vert. Eigen-emittance Hor. Eigen-emittance
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30
Non measurable projected s-dependent emittance
Measurable apparent s-dependent emittance
Vertical emittances in the presence of coupling
Andrea Franchi Vertical Emittance reduction @ ESRF
If |f1010| ~ |f1001| ( i.e. S+ ~ S-) [low-emitt. rings] εy(s) ≠ Ey(s)
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31
Non measurable projected s-dependent emittance
Measurable apparent s-dependent emittance
Vertical emittances in the presence of coupling
Andrea Franchi Vertical Emittance reduction @ ESRF
If |f1010|<<|f1001| ( i.e. S+<< S-) [hadron rings] εy(s) = Ey(s)
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32
Non measurable projected s-dependent emittance
Measurable apparent s-dependent emittance
Vertical emittances in the presence of coupling
Andrea Franchi Vertical Emittance reduction @ ESRF
In absence of coupling C=1, S-=S+=0 and Ey=Ev=εy=const
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Andrea Franchi Vertical Emittance reduction @ ESRF 33
Vertical emittances in the presence of couplingMeasurable apparent emittance:
Non measurable projected emittance:
Ev=
9 pm
Lattice errors from Orbit Response Matrix measurement + Accel. Toolbox
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Andrea Franchi Vertical Emittance reduction @ ESRF 34
Vertical emittances in the presence of couplingMeasurable apparent emittance:
Non measurable projected emittance:
Ev=
9 pm
100% overestimation
40% underestimation
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Andrea Franchi Vertical Emittance reduction @ ESRF 35
Vertical emittances in the presence of couplingMeasurable apparent emittance:
Non measurable projected emittance:
Ev=
9 pm
100% overestimation
40% underestimation300% overestimation Ey(apparent) Vs Ev (equilibrium)
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Andrea Franchi Vertical Emittance reduction @ ESRF 36
Vertical emittances in the presence of couplingMeasurable apparent emittance:
Non measurable projected emittance:
Ev=
9 pm
100% overestimation
40% underestimation300% overestimation Ey(apparent) Vs Ev (equilibrium)
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Andrea Franchi Vertical Emittance reduction @ ESRF 37
Vertical emittances in the presence of couplingMeasurable apparent emittance:
Non measurable projected emittance:
Ev=
9 pm
100% overestimation
40% underestimation300% overestimation Ey(apparent) Vs Ev (equilibrium)
Which “vertical
emittance” shall we choose, then?
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Andrea Franchi Vertical Emittance reduction @ ESRF 38
Vertical emittances in the presence of couplingMeasurable apparent emittance:
Non measurable projected emittance:
Ev=
9 pm
Average over the ring< >
< >
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Andrea Franchi Vertical Emittance reduction @ ESRF 39
Vertical emittances in the presence of couplingMeasurable apparent emittance:
Non measurable projected emittance:
Ev=
9 pm
Average over the ring< >
< >
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Andrea Franchi Vertical Emittance reduction @ ESRF 40
Vertical emittances in the presence of couplingMeasurable apparent emittance:
Non measurable projected emittance:
Ev=
9 pm
Average over the ring< >
< >
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Andrea Franchi Vertical Emittance reduction @ ESRF 41
Vertical emittances in the presence of couplingMeasurable apparent emittance:
Non measurable projected emittance:
Ev=
9 pm
< >
< >
Definition of vertical emittance @ ESRF:
More details in PRSTAB-14-012804 (2011)
Average over the ring
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Andrea Franchi Vertical Emittance reduction @ ESRF 42
Outlines
•Vertical emittances in the presence of coupling
•Coupling correction via Resonance Driving Terms
•2010: Application in the ESRF storage ring
•2010: Preserving small vertical emittance during beam delivery
•2011: Towards ultra-small vertical emittance
•PS: Indirect measurements of vertical emittance
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Andrea Franchi Vertical Emittance reduction @ ESRF 43
Vertical emittance reduction in the storage ring•Coupling (x-y & y-δ) correction @ ESRF SR is carried out with independent skew quadrupoles (V=J1xy) distributed along the machine.
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Andrea Franchi Vertical Emittance reduction @ ESRF 44
Vertical emittance reduction in the storage ring•Coupling (x-y & y-δ) correction @ ESRF SR is carried out with independent skew quadrupoles (V=J1xy) distributed along the machine.
•Until 2009 their currents were computed by trying to minimize the apparent vertical emittance along the machine non-linear fitting
- time consuming - may get stuck into a local minimum value
Details and formulas in PRSTAB-14-012804 (2011)
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Andrea Franchi Vertical Emittance reduction @ ESRF 45
Vertical emittance reduction in the storage ring•Coupling (x-y & y-δ) correction @ ESRF SR is carried out with independent skew quadrupoles (V=J1xy) distributed along the machine.
•As of 2010 their currents are computed by trying to minimize other quantities: Resonance Driving Terms, obtained from orbit measurements (for x-y) and vert. disp. (for y-δ). This automatically minimizes vertical emittance linear fitting
- faster- gets directly to absolute minimum value
Details and formulas in PRSTAB-14-012804 (2011)
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Coupling correction via Resonance Driving Terms
The lower the vertical dispersion and the coupling RDTs, the smaller the
vertical emittances
Procedure [already independently developed by R. Tomas (for ALBA)]:1.Build an error lattice model (quad tilts, etc. from Orbit Response Matrix
or turn-by-turn BPM data) => RDTs and Dy F = (a1*f1001, a1*f1010, a2*Dy) , a1+a2=1
2.Evaluate response matrix of the available skew correctors M3.Find via SVD a corrector setting J that minimizes both RDTs and Dy
J =-M F to be pseudo-inverted
Andrea Franchi Vertical Emittance reduction @ ESRF
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47
Coupling correction via Resonance Driving Terms
Procedure [already independently developed by R. Tomas (for ALBA)]:1.Build an error lattice model (quad tilts, etc. from Orbit Response Matrix
or turn-by-turn BPM data) => RDTs and Dy F = (a1*f1001, a1*f1010, a2*Dy) , a1+a2=1
2.Evaluate response matrix of the available skew correctors M3.Find via SVD a corrector setting J that minimizes both RDTs and Dy
J =-M F to be pseudo-inverted
Andrea Franchi Vertical Emittance reduction @ ESRF
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48
Coupling correction via Resonance Driving Terms
1.Build an error lattice model (quad tilts, etc. from Orbit Response Matrix or turn-by-turn BPM data) => RDTs and Dy
F = (a1*f1001, a1*f1010, a2*Dy) , a1+a2=1 2.Evaluate response matrix of the available skew correctors M3.Find via SVD a corrector setting J that minimizes both RDTs and Dy
J =-M F to be pseudo-inverted
Orbit Response Matrix at 224 BPMs after exciting 16x2 steerers (H,V)
Andrea Franchi Vertical Emittance reduction @ ESRF
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49
Coupling correction via Resonance Driving Terms
1.Build an error lattice model (quad tilts, etc. from Orbit Response Matrix or turn-by-turn BPM data) => RDTs and Dy
F = (a1*f1001, a1*f1010, a2*Dy) , a1+a2=1 2.Evaluate response matrix of the available skew correctors M3.Find via SVD a corrector setting J that minimizes both RDTs and Dy
J =-M F to be pseudo-inverted
Fitting measured diagonal blocks from ideal ORM => focusing errors ΔK1 .
Andrea Franchi Vertical Emittance reduction @ ESRF
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50
Coupling correction via Resonance Driving Terms
1.Build an error lattice model (quad tilts, etc. from Orbit Response Matrix or turn-by-turn BPM data) => RDTs and Dy
F = (a1*f1001, a1*f1010, a2*Dy) , a1+a2=1 2.Evaluate response matrix of the available skew correctors M3.Find via SVD a corrector setting J that minimizes both RDTs and Dy
J =-M F to be pseudo-inverted
Fitting measured off-diagonal blocks from ideal ORM => effective quadrupole tilts θ (accounting for sextupole ver. misalignments )
Andrea Franchi Vertical Emittance reduction @ ESRF
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51
Coupling correction via Resonance Driving Terms
1.Build an error lattice model (quad tilts, etc. from Orbit Response Matrix or turn-by-turn BPM data) => RDTs and Dy
F = (a1*f1001, a1*f1010, a2*Dy) , a1+a2=1 2.Evaluate response matrix of the available skew correctors M3.Find via SVD a corrector setting J that minimizes both RDTs and Dy
J =-M F to be pseudo-inverted
Fitting measured off-diagonal blocks from ideal ORM => effective quadrupole tilts θ (accounting for sextupole ver. misalignments )
Andrea Franchi Vertical Emittance reduction @ ESRF
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52
Coupling correction via Resonance Driving Terms
1.Build an error lattice model (quad tilts, etc. from Orbit Response Matrix or turn-by-turn BPM data) => RDTs and Dy
F = (a1*f1001, a1*f1010, a2*Dy) , a1+a2=1 2.Evaluate response matrix of the available skew correctors M3.Find via SVD a corrector setting J that minimizes both RDTs and Dy
J =-M F to be pseudo-inverted
Fitting measured off-diagonal blocks from ideal ORM => effective quadrupole tilts θ (accounting for sextupole ver. misalignments )
Andrea Franchi Vertical Emittance reduction @ ESRF
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53
Coupling correction via Resonance Driving Terms
1.Build an error lattice model (quad tilts, etc. from Orbit Response Matrix or turn-by-turn BPM data) => RDTs and Dy
F = (a1*f1001, a1*f1010, a2*Dy) , a1+a2=1 2.Evaluate response matrix of the available skew correctors M3.Find via SVD a corrector setting J that minimizes both RDTs and Dy
J =-M F to be pseudo-inverted
Fitting measured off-diagonal blocks from ideal ORM => effective quadrupole tilts θ (accounting for sextupole ver. misalignments )
Andrea Franchi Vertical Emittance reduction @ ESRF
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54
Coupling correction via Resonance Driving Terms
1.Build an error lattice model (quad tilts, etc. from Orbit Response Matrix or turn-by-turn BPM data) => RDTs and Dy
F = (a1*f1001, a1*f1010, a2*Dy) , a1+a2=1 2.Evaluate response matrix of the available skew correctors M3.Find via SVD a corrector setting J that minimizes both RDTs and Dy
J =-M F to be pseudo-inverted
Vertical dispersion Dy is measured at all 224 BPMs
Andrea Franchi Vertical Emittance reduction @ ESRF
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55
Coupling correction via Resonance Driving Terms
1.Build an error lattice model (quad tilts, etc. from Orbit Response Matrix or turn-by-turn BPM data) => RDTs and Dy
F = (a1*f1001, a1*f1010, a2*Dy) , a1+a2=1 2.Evaluate response matrix of the available skew correctors M3.Find via SVD a corrector setting J that minimizes both RDTs and Dy
J =-M F to be pseudo-inverted
Andrea Franchi Vertical Emittance reduction @ ESRF
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56
Coupling correction via Resonance Driving Terms
1.Build an error lattice model (quad tilts, etc. from Orbit Response Matrix or turn-by-turn BPM data) => RDTs and Dy
F = (a1*f1001, a1*f1010, a2*Dy) , a1+a2=1 2.Evaluate response matrix of the available skew correctors M3.Find via SVD a corrector setting J that minimizes both RDTs and Dy
J =-M F to be pseudo-inverted
Andrea Franchi Vertical Emittance reduction @ ESRF
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57
Coupling correction via Resonance Driving Terms
1.Build an error lattice model (quad tilts, etc. from Orbit Response Matrix or turn-by-turn BPM data) => RDTs and Dy
F = (a1*f1001, a1*f1010, a2*Dy) , a1+a2=1 2.Evaluate response matrix of the available skew correctors M3.Find via SVD a corrector setting J that minimizes both RDTs and Dy
J =-M F to be pseudo-inverted
Andrea Franchi Vertical Emittance reduction @ ESRF
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58
Coupling correction via Resonance Driving Terms
1.Build an error lattice model (quad tilts, etc. from Orbit Response Matrix or turn-by-turn BPM data) => RDTs and Dy
F = (a1*f1001, a1*f1010, a2*Dy) , a1+a2=1 2.Evaluate response matrix of the available skew correctors M3.Find via SVD a corrector setting J that minimizes both RDTs and Dy
J =-M F to be pseudo-inverted
Andrea Franchi Vertical Emittance reduction @ ESRF
From MADX or AT
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59
Coupling correction via Resonance Driving Terms
1.Build an error lattice model (quad tilts, etc. from Orbit Response Matrix or turn-by-turn BPM data) => RDTs and Dy
F = (a1*f1001, a1*f1010, a2*Dy) , a1+a2=1 2.Evaluate response matrix of the available skew correctors M3.Find via SVD a corrector setting J that minimizes both RDTs and Dy
J =-M F to be pseudo-inverted
From MADX or AT
Andrea Franchi Vertical Emittance reduction @ ESRF
From MADX or AT
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60
Coupling correction via Resonance Driving Terms
1.Build an error lattice model (quad tilts, etc. from Orbit Response Matrix or turn-by-turn BPM data) => RDTs and Dy
F = (a1*f1001, a1*f1010, a2*Dy) , a1+a2=1 2.Evaluate response matrix of the available skew correctors M3.Find via SVD a corrector setting J that minimizes both RDTs and Dy
J =-M F to be pseudo-inverted
Andrea Franchi Vertical Emittance reduction @ ESRF
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61
Coupling correction via Resonance Driving Terms
1.Build an error lattice model (quad tilts, etc. from Orbit Response Matrix or turn-by-turn BPM data) => RDTs and Dy
F = (a1*f1001, a1*f1010, a2*Dy) , a1+a2=1 2.Evaluate response matrix of the available skew correctors M3.Find via SVD a corrector setting J that minimizes both RDTs and Dy
J =-M F to be pseudo-inverted
a2=0.7 (2010) , 0.4 (2011)
a1+a2=1
Different weights on f1001 and f1010 tried, best if equal.
Andrea Franchi Vertical Emittance reduction @ ESRF
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Andrea Franchi Vertical Emittance reduction @ ESRF 62
Outlines
•Vertical emittances in the presence of coupling
•Coupling correction via Resonance Driving Terms
•2010: Application in the ESRF storage ring
•2010: Preserving small vertical emittance during beam delivery
•2011: Towards ultra-small vertical emittance
•PS: Indirect measurements of vertical emittance
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Andrea Franchi Vertical Emittance reduction @ ESRF 63
2010: Application in the ESRF storage ring
First RDT correction: January 16th 2010 All skew correctors OFF: εy ±δεy = 237 ± 122 pm
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Andrea Franchi Vertical Emittance reduction @ ESRF 64
2010: Application in the ESRF storage ringFirst RDT correction: January 16th 2010
After ORM measur. and RDT correction: εy ±δεy = 11.5 ± 4.3 pm
~20 min. for ORM a few seconds for RDT correction
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Andrea Franchi Vertical Emittance reduction @ ESRF 65
2010: Application in the ESRF storage ringFirst RDT correction: January 16th 2010
After ORM measur. and RDT correction: εy ±δεy = 11.5 ± 4.3 pm
~20 min. for ORM a few seconds for RDT correction
|f1010| ~ |f1001| ( i.e. S+ ~ S-) => sum resonance may not be neglected
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Andrea Franchi Vertical Emittance reduction @ ESRF 66
2010: Application in the ESRF storage ringESRF 2010 temporary record-low vertical emittance: June 22nd
At ID gaps open: εy ±δεy = 4.4 ± 0.7 pm
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Andrea Franchi Vertical Emittance reduction @ ESRF 67
Outlines
•Vertical emittances in the presence of coupling
•Coupling correction via Resonance Driving Terms
•2010: Application in the ESRF storage ring
•2010: Preserving small vertical emittance during beam delivery
•2011: Towards ultra-small vertical emittance
•PS: Indirect measurements of vertical emittance
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Andrea Franchi Vertical Emittance reduction @ ESRF 68
2010: Preserving vertical emittance during beam delivery
• Low coupling may not be preserved during beam delivery because of continuous changes of ID gaps that vary coupling along the ring
Apparent emittance measured at 13 monitors (red) on Jan. 20th 2010, during beam delivery and movements of two ID gaps (black & green)
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Andrea Franchi Vertical Emittance reduction @ ESRF 69
2010: Preserving vertical emittance during beam delivery
• H-V steerers at the ends of an ID straight section were cabled so as to provide skew quad fields.
• Look-up tables (corrector currents Vs ID gap aperture) were defined so as to preserve the vertical emittance at any gap value.
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• H-V steerers at the ends of an ID straight section were cabled so as to provide skew quad fields.
• Look-up tables (corrector currents Vs ID gap aperture) were defined so as to preserve the vertical emittance at any gap value.
Andrea Franchi Vertical Emittance reduction @ ESRF 70
2010: Preserving vertical emittance during beam delivery
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• H-V steerers at the ends of an ID straight section were cabled so as to provide skew quad fields.
• Look-up tables (corrector currents Vs ID gap aperture) were defined so as to preserve the vertical emittance at any gap value.
Andrea Franchi Vertical Emittance reduction @ ESRF 71
2010: Preserving vertical emittance during beam delivery
This scheme is being implemented on other IDs
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Andrea Franchi Vertical Emittance reduction @ ESRF 72
2010: Preserving vertical emittance during beam delivery
32 corrector skew quads
• Coupling may be represented by two complex vectors (for the sum and difference resonances respectively) C±=|A±|eiφ± .
• In the ESRF storage ring, on top of the RDT static correction, C± may be dynamically varied in order to catch up coupling variations induced by ID gap movements.
• A new software automatically minimizes C± by looking at the average vertical emittance
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• Coupling may be represented by two complex vectors (for the sum and difference resonances respectively) C±=|A±|eiφ± .
• In the ESRF storage ring, on top of the RDT static correction, C± may be dynamically varied in order to catch up coupling variations induced by ID gap movements.
• A new software automatically minimizes C± by looking at the average vertical emittance
Andrea Franchi Vertical Emittance reduction @ ESRF 73
2010: Preserving vertical emittance during beam delivery
32 corrector skew quads
C± loop OFF, manual correction
C± loop ON, automatic hourly correction
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Andrea Franchi Vertical Emittance reduction @ ESRF 74
Outlines
•Vertical emittances in the presence of coupling
•Coupling correction via Resonance Driving Terms
•2010: Application in the ESRF storage ring
•2010: Preserving small vertical emittance during beam delivery
•2011: Towards ultra-small vertical emittance
•PS: Indirect measurements of vertical emittance
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Andrea Franchi Vertical Emittance reduction @ ESRF 75
2011: Towards ultra-small vertical emittance
2010, with 32 skew quad correctors
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Andrea Franchi Vertical Emittance reduction @ ESRF 76
2011: Towards ultra-small vertical emittance
2011, with 64 skew quad correctors
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Andrea Franchi Vertical Emittance reduction @ ESRF 77
Conclusion• The Resonance Driving Terms (RDT) formalism helps to
clarify the various definitions of “vertical emittance” in the presence of coupling and allows a straightforward linear correction algorithm.
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Andrea Franchi Vertical Emittance reduction @ ESRF 78
Conclusion• The Resonance Driving Terms (RDT) formalism helps to
clarify the various definitions of “vertical emittance” in the presence of coupling and allows a straightforward linear correction algorithm.
• Applications in the ESRF storage ring led to vertical emittance of εy = 2.6 ± 1.1 pm, a record low for this machine (εx=4.2 nm => εy/εx≈ 0.06%, a factor 10 lower than in the past).
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Andrea Franchi Vertical Emittance reduction @ ESRF 79
Conclusion• The Resonance Driving Terms (RDT) formalism helps to
clarify the various definitions of “vertical emittance” in the presence of coupling and allows a straightforward linear correction algorithm.
• Applications in the ESRF storage ring led to vertical emittance of εy = 2.6 ± 1.1 pm, a record low for this machine (εx=4.2 nm => εy/εx≈ 0.06%, a factor 10 lower than in the past).
• Two procedures to preserve small vertical emittance during beam delivery were successfully tested: as of spring 2011 stable εy = 3.2-4.5 pm delivered to users (lifetime of 45 hours after refilling @ 200 mA, 10 hours less than in the past only).
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Andrea Franchi Vertical Emittance reduction @ ESRF 80
Conclusion• The Resonance Driving Terms (RDT) formalism helps to
clarify the various definitions of “vertical emittance” in the presence of coupling and allows a straightforward linear correction algorithm.
• Applications in the ESRF storage ring led to vertical emittance of εy = 2.6 ± 1.1 pm, a record low for this machine (εx=4.2 nm => εy/εx≈ 0.06%, a factor 10 lower than in the past).
• Two procedures to preserve small vertical emittance during beam delivery were successfully tested: as of spring 2011 stable εy = 3.2-4.5 pm delivered to users (lifetime of 45 hours after refilling @ 200 mA, 10 hours less than in the past only).
• Final goal: to deliver a beam of εy = 2 pm.
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Andrea Franchi Vertical Emittance reduction @ ESRF 81
Outlines
•Vertical emittances in the presence of coupling
•Coupling correction via Resonance Driving Terms
•2010: Application in the ESRF storage ring
•2010: Preserving small vertical emittance during beam delivery
•2011: Towards ultra-small vertical emittance
•PS: Indirect measurements of vertical emittance
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Andrea Franchi Vertical Emittance reduction @ ESRF 82
The coupling sum resonance Lepton machine => low hor. emittance => hor. focusing stronger than vertical => Qx >> Qy (@ ESRF Qx=36.44 , Qy=13.39 , Qx-Qy=23.05 ) Low-emitt. Rings: |f1010| ~ |f1001| ( i.e. S+ ~ S- )=> |C+|~|C- |
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Andrea Franchi Vertical Emittance reduction @ ESRF 83
The coupling sum resonance Lepton machine => low hor. emittance => hor. focusing stronger than vertical => Qx >> Qy (@ ESRF Qx=36.44 , Qy=13.39 , Qx-Qy=23.05 )
Hadron machine => almost “round” beam (Ex~Ey) => similar hor. & ver. focusing => Qx ~ Qy (like the CERN SPS Qx=26.18 , Qy=26.22 , Qx-Qy=-0.04 )
Low-emitt. Rings: |f1010| ~ |f1001| ( i.e. S+ ~ S- )=> |C+|~|C- |
Hadron Rings: |f1010| << |f1001| ( i.e. S+ << S- )=> |C+|<<|C- |
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Lepton machine => low hor. emittance => hor. focusing stronger than vertical => Qx >> Qy (@ ESRF Qx=36.44 , Qy=13.39 , Qx-Qy=23.05 )
Hadron machine => almost “round” beam (Ex~Ey) => similar hor. & ver. focusing => Qx ~ Qy (like the CERN SPS Qx=26.18 , Qy=26.22 , Qx-Qy=-0.04 )
WHY?Andrea Franchi Vertical Emittance reduction @ ESRF 84
The coupling sum resonance
Low-emitt. Rings: |f1010| ~ |f1001| ( i.e. S+ ~ S- )=> |C+|~|C- |
Hadron Rings: |f1010| << |f1001| ( i.e. S+ << S- )=> |C+|<<|C- |
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Andrea Franchi Vertical Emittance reduction @ ESRF 85
The coupling sum resonance
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Andrea Franchi Vertical Emittance reduction @ ESRF 86
The coupling sum resonance
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Andrea Franchi Vertical Emittance reduction @ ESRF 87
The coupling sum resonance
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Andrea Franchi Vertical Emittance reduction @ ESRF 88
The coupling sum resonance
Σϕ
Δϕ
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Andrea Franchi Vertical Emittance reduction @ ESRF 89
Low-emittance rings [Qx>Qy]
ϕx=2.55
ϕx=5.11
ϕx=7.66
ϕx=10.22
ϕx=12.77
ϕx=15.33
ϕx=17.88
Qx=20.44
ϕy=1.29
ϕy=2.58
ϕy=3.87
ϕy=5.16
ϕy=6.45
ϕy=7.74
ϕy=9.03
Qy=10.32Σϕ=3.84Δϕ=1.26
Σϕ=7.69Δϕ=2.53
Σϕ=11.53Δϕ= 3.79
Σϕ=15.38Δϕ= 5.06
Σϕ=19.22Δϕ= 6.32
Σϕ=23.07Δϕ= 7.49
Σϕ=26.91Δϕ= 8.85
ΣQ=30.76ΔQ=10.12
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Andrea Franchi Vertical Emittance reduction @ ESRF 90
Low-emittance rings [Qx>Qy]
ϕx=2.55
ϕx=5.11
ϕx=7.66
ϕx=10.22
ϕx=12.77
ϕx=15.33
ϕx=17.88
Qx=20.44
ϕy=1.29
ϕy=2.58
ϕy=3.87
ϕy=5.16
ϕy=6.45
ϕy=7.74
ϕy=9.03
Qy=10.32Σϕ=3.84Δϕ=1.26
Σϕ=7.69Δϕ=2.53
Σϕ=11.53Δϕ= 3.79
Σϕ=15.38Δϕ= 5.06
Σϕ=19.22Δϕ= 6.32
Σϕ=23.07Δϕ= 7.49
Σϕ=26.91Δϕ= 8.85
ΣQ=30.76ΔQ=10.12
![Page 91: Coupling Correction Through Beam Position Data](https://reader038.vdocument.in/reader038/viewer/2022110215/568156c4550346895dc455ea/html5/thumbnails/91.jpg)
Andrea Franchi Vertical Emittance reduction @ ESRF 91
Low-emittance rings [Qx>Qy]Qx=20.44
ϕy=2.58ϕy=7.74
Qy=10.32ΣQ=30.76ΔQ=10.12
Σϕ
Δϕ
![Page 92: Coupling Correction Through Beam Position Data](https://reader038.vdocument.in/reader038/viewer/2022110215/568156c4550346895dc455ea/html5/thumbnails/92.jpg)
Andrea Franchi Vertical Emittance reduction @ ESRF 92
Low-emittance rings [Qx>Qy]Qx=20.44
ϕy=2.58ϕy=7.74
Qy=10.32ΣQ=30.76ΔQ=10.12
Σϕ
Δϕ
The same for both
![Page 93: Coupling Correction Through Beam Position Data](https://reader038.vdocument.in/reader038/viewer/2022110215/568156c4550346895dc455ea/html5/thumbnails/93.jpg)
Andrea Franchi Vertical Emittance reduction @ ESRF 93
Low-emittance rings [Qx>Qy]Qx=20.44
ϕy=2.58ϕy=7.74
Qy=10.32ΣQ=30.76ΔQ=10.12
Σϕ
Δϕ
The same for both
The sum Σ-term oscillates 3 times faster than
difference Δ-term, only
![Page 94: Coupling Correction Through Beam Position Data](https://reader038.vdocument.in/reader038/viewer/2022110215/568156c4550346895dc455ea/html5/thumbnails/94.jpg)
Andrea Franchi Vertical Emittance reduction @ ESRF 94
Low-emittance rings [Qx>Qy]Qx=20.44
ϕy=2.58ϕy=7.74
Qy=10.32ΣQ=30.76ΔQ=10.12
Σϕ
Δϕ
The same for both
The sum Σ-term oscillates 3 times faster than
difference Δ-term, only|C+|~|C-|
![Page 95: Coupling Correction Through Beam Position Data](https://reader038.vdocument.in/reader038/viewer/2022110215/568156c4550346895dc455ea/html5/thumbnails/95.jpg)
Andrea Franchi Vertical Emittance reduction @ ESRF 95
Hadron rings [Qx~Qy]
ϕx=3.27
ϕx=6.55
ϕx=9.82
ϕx=13.09
ϕx=16.36
ϕx=19.62
ϕx=22.89
Qx=26.18
ϕy=3.28
ϕy=6.56
ϕy=9.84
ϕy=13.11
ϕy=16.39
ϕy=19.58
ϕy=22.86
Qy=26.22Σϕ= 6.55Δϕ=-0.01
Σϕ=13.10Δϕ=-0.01
Σϕ=19.66Δϕ=-0.02
Σϕ=26.20Δϕ=-0.02
Σϕ=32.75Δϕ=-0.03
Σϕ=39.20Δϕ=-0.03
Σϕ=45.75Δϕ=-0.03
ΣQ=52.40ΔQ=-0.04
![Page 96: Coupling Correction Through Beam Position Data](https://reader038.vdocument.in/reader038/viewer/2022110215/568156c4550346895dc455ea/html5/thumbnails/96.jpg)
Andrea Franchi Vertical Emittance reduction @ ESRF 96
Hadron rings [Qx~Qy]
ϕx=3.27
ϕx=6.55
ϕx=9.82
ϕx=13.09
ϕx=16.36
ϕx=19.62
ϕx=22.89
Qx=26.18
ϕy=3.28
ϕy=6.56
ϕy=9.84
ϕy=13.11
ϕy=16.39
ϕy=19.58
ϕy=22.86
Qy=26.22Σϕ= 6.55Δϕ=-0.01
Σϕ=13.10Δϕ=-0.01
Σϕ=19.66Δϕ=-0.02
Σϕ=26.20Δϕ=-0.02
Σϕ=32.75Δϕ=-0.03
Σϕ=39.20Δϕ=-0.03
Σϕ=45.75Δϕ=-0.03
ΣQ=52.40ΔQ=-0.04
![Page 97: Coupling Correction Through Beam Position Data](https://reader038.vdocument.in/reader038/viewer/2022110215/568156c4550346895dc455ea/html5/thumbnails/97.jpg)
Andrea Franchi Vertical Emittance reduction @ ESRF 97
Hadron rings [Qx~Qy]Qx=26.18Qy=26.22
ΣQ=52.40ΔQ=-0.04
ϕy=2.58ϕy=7.74
Σϕ
Δϕ
The same for both
The sum Σ-term oscillates 52 times, while the
difference Δ-term does not|C+|<<|C-|
=1
![Page 98: Coupling Correction Through Beam Position Data](https://reader038.vdocument.in/reader038/viewer/2022110215/568156c4550346895dc455ea/html5/thumbnails/98.jpg)
Andrea Franchi Vertical Emittance reduction @ ESRF 98
Caution with Guignard’s formula• At very low coupling εy may be smaller than monitor/camera
resolution and hence non measurable.
![Page 99: Coupling Correction Through Beam Position Data](https://reader038.vdocument.in/reader038/viewer/2022110215/568156c4550346895dc455ea/html5/thumbnails/99.jpg)
Andrea Franchi Vertical Emittance reduction @ ESRF 99
Caution with Guignard’s formula• At very low coupling εy may be smaller than monitor/camera
resolution and hence non measurable.• One may be then tempted to use Guignard’s formula
The “large” εx easier to measure and “g” evaluated from tune measurements (closest tune approach). Δ = Qx-Qy (fractional part, |C-| is the difference resonance stop band.
![Page 100: Coupling Correction Through Beam Position Data](https://reader038.vdocument.in/reader038/viewer/2022110215/568156c4550346895dc455ea/html5/thumbnails/100.jpg)
Andrea Franchi Vertical Emittance reduction @ ESRF 100
Caution with Guignard’s formula• At very low coupling εy may be smaller than monitor/camera
resolution and hence non measurable.• One may be then tempted to use Guignard’s formula
The “large” εx easier to measure and “g” evaluated from tune measurements (closest tune approach). Δ = Qx-Qy (fractional part, |C-| is the difference resonance stop band.
• But the formula is only valid for: sum resonance negligible, i.e. |C-| >> |C+| Vert. dispersion Dy contribution to εy << betatron
coupling contribution
![Page 101: Coupling Correction Through Beam Position Data](https://reader038.vdocument.in/reader038/viewer/2022110215/568156c4550346895dc455ea/html5/thumbnails/101.jpg)
Andrea Franchi Vertical Emittance reduction @ ESRF 101
Caution with Guignard’s formula• At very low coupling εy may be smaller than monitor/camera
resolution and hence non measurable.• One may be then tempted to use Guignard’s formula
The “large” εx easier to measure and “g” evaluated from tune measurements (closest tune approach). Δ = Qx-Qy (fractional part, |C-| is the difference resonance stop band.
• But the formula is only valid for: sum resonance negligible, i.e. |C-| << |C+| Vert. dispersion Dy contribution to εy > betatron
coupling contribution
@ ESRF SR9E-4 3E-3
0.94 pm 0.65 pm
![Page 102: Coupling Correction Through Beam Position Data](https://reader038.vdocument.in/reader038/viewer/2022110215/568156c4550346895dc455ea/html5/thumbnails/102.jpg)
Andrea Franchi Vertical Emittance reduction @ ESRF 102
Caution with lifetime measurement (1)• At very low coupling εy may be smaller than monitor/camera
resolution and hence non measurable.• One may use the reduction of the Touschek lifetime
![Page 103: Coupling Correction Through Beam Position Data](https://reader038.vdocument.in/reader038/viewer/2022110215/568156c4550346895dc455ea/html5/thumbnails/103.jpg)
Andrea Franchi Vertical Emittance reduction @ ESRF 103
Caution with lifetime measurement (1)• At very low coupling εy may be smaller than monitor/camera
resolution and hence non measurable.• One may use the reduction of the Touschek lifetime
This approach is valid under the assumption that the lifetime reduction is exclusively induced by the Touschek effect.
However, the sum resonance ( |C+| ) is unstable and may account for lower-than-expected lifetime with larger εy , if inadvertently enhanced during coupling correction.
![Page 104: Coupling Correction Through Beam Position Data](https://reader038.vdocument.in/reader038/viewer/2022110215/568156c4550346895dc455ea/html5/thumbnails/104.jpg)
• At very low coupling εy may be smaller than monitor/camera resolution and hence non measurable.
• One may use the reduction of the Touschek lifetime
This approach is valid under the assumption that the lifetime reduction is exclusively induced by the Touschek effect.
However, the sum resonance ( |C+| ) is unstable and may account for lower-than-expected lifetime with larger εy , if inadvertently enhanced during coupling correction.
Andrea Franchi Vertical Emittance reduction @ ESRF 104
Caution with lifetime measurement (1)
At the ESRF, while trimming skews, it has been sometimes observed that:
![Page 105: Coupling Correction Through Beam Position Data](https://reader038.vdocument.in/reader038/viewer/2022110215/568156c4550346895dc455ea/html5/thumbnails/105.jpg)
• At very low coupling εy may be smaller than monitor/camera resolution and hence non measurable.
• One may be then tempted to use Touschek-lifetime reduction
This approach is valid under the assumption that the lifetime reduction is exclusively induced by the Touschek effect.
However, the sum resonance ( |C+| ) is unstable and may account for lower-than-expected lifetime with larger εy , if inadvertently enhanced during coupling correction.
Andrea Franchi Vertical Emittance reduction @ ESRF 105
Caution with lifetime measurement (1)
At the ESRF, while trimming skews, it has been sometimes observed that:1. reducing |C-|, both Ey and lifetime
decrease (stronger Touschek)
![Page 106: Coupling Correction Through Beam Position Data](https://reader038.vdocument.in/reader038/viewer/2022110215/568156c4550346895dc455ea/html5/thumbnails/106.jpg)
• At very low coupling εy may be smaller than monitor/camera resolution and hence non measurable.
• One may be then tempted to use Touschek-lifetime reduction
This approach is valid under the assumption that the lifetime reduction is exclusively induced by the Touschek effect.
However, the sum resonance ( |C+| ) is unstable and may account for lower-than-expected lifetime with larger εy , if inadvertently enhanced during coupling correction.
Andrea Franchi Vertical Emittance reduction @ ESRF 106
Caution with lifetime measurement (1)
At the ESRF, while trimming skews, it has been sometimes observed that:1. reducing |C-|, both Ey and lifetime
decrease (stronger Touschek)2. increasing |C+|, Ey increases whereas
lifetime decreases (sum resonance stronger than Touschek ?)
![Page 107: Coupling Correction Through Beam Position Data](https://reader038.vdocument.in/reader038/viewer/2022110215/568156c4550346895dc455ea/html5/thumbnails/107.jpg)
Andrea Franchi Vertical Emittance reduction @ ESRF 107
Caution with lifetime measurement (2)• At very low coupling εy may be smaller than monitor/camera
resolution and hence non measurable.• One may infer the average εy via Touschek-lifetime measurement.
€
1τ tot
= Aεy
+ 1τ Vac
![Page 108: Coupling Correction Through Beam Position Data](https://reader038.vdocument.in/reader038/viewer/2022110215/568156c4550346895dc455ea/html5/thumbnails/108.jpg)
Andrea Franchi Vertical Emittance reduction @ ESRF 108
Caution with lifetime measurement (2)• At very low coupling εy may be smaller than monitor/camera
resolution and hence non measurable.• One may infer the average εy via Touschek-lifetime measurement.
• A depends on several RF-related parameters (bunch length, RF acceptance, dynamic aperture).
€
1τ tot
= Aεy
+ 1τ Vac
![Page 109: Coupling Correction Through Beam Position Data](https://reader038.vdocument.in/reader038/viewer/2022110215/568156c4550346895dc455ea/html5/thumbnails/109.jpg)
Andrea Franchi Vertical Emittance reduction @ ESRF 109
Caution with lifetime measurement (2)• At very low coupling εy may be smaller than monitor/camera
resolution and hence non measurable.• One may infer the average εy via Touschek-lifetime measurement.
• A depends on several RF-related parameters (bunch length, RF acceptance, dynamic aperture).
• The emittance in the formula shall be the apparent one, not the model eigen-emittance Ev
€
1τ tot
= Aεy
+ 1τ Vac
![Page 110: Coupling Correction Through Beam Position Data](https://reader038.vdocument.in/reader038/viewer/2022110215/568156c4550346895dc455ea/html5/thumbnails/110.jpg)
Andrea Franchi Vertical Emittance reduction @ ESRF 110
Caution with lifetime measurement (2)• At very low coupling εy may be smaller than monitor/camera
resolution and hence non measurable.• One may infer the average εy via Touschek-lifetime measurement.
• A depends on several RF-related parameters (bunch length, RF acceptance, dynamic aperture) and β-functions
• Actually, it shall be the apparent emittance averaged along the low-beta regions of the ring (those with the high scattering rate contributing the most the lifetime integral), not the model eigen-emittance Ev
€
1τ tot
= Aεy
+ 1τ Vac
![Page 111: Coupling Correction Through Beam Position Data](https://reader038.vdocument.in/reader038/viewer/2022110215/568156c4550346895dc455ea/html5/thumbnails/111.jpg)
• At very low coupling εy may be smaller than monitor/camera resolution and hence non measurable.
• One may infer the average εy via Touschek-lifetime measurement.
• A depends on several RF-related parameters (bunch length, RF acceptance, dynamic aperture).
• Actually it shall be the apparent emittance averaged along the low-beta regions of the ring (those with the high scattering rate contributing the most the lifetime integral) , not the model eigen-emittance Ev
Andrea Franchi Vertical Emittance reduction @ ESRF 111
Caution with lifetime measurement (2)
€
1τ tot
= Aεy
+ 1τ Vac
![Page 112: Coupling Correction Through Beam Position Data](https://reader038.vdocument.in/reader038/viewer/2022110215/568156c4550346895dc455ea/html5/thumbnails/112.jpg)
• At very low coupling εy may be smaller than monitor/camera resolution and hence non measurable.
• One may infer the average εy via Touschek-lifetime measurement.
• A depends on several RF-related parameters (bunch length, RF acceptance, dynamic aperture).
• Actually, it shall be the apparent emittance averaged along the low-beta regions of the ring (those with the high scattering rate contributing the most the lifetime integral) , not the model eigen-emittance Ev
Andrea Franchi Vertical Emittance reduction @ ESRF 112
Caution with lifetime measurement (2)
Eigen-emittance Ev= 9 pm [from the model] Vs
Av. apparent emittance <Ey>=16 pm [measured]
€
1τ tot
= Aεy
+ 1τ Vac
![Page 113: Coupling Correction Through Beam Position Data](https://reader038.vdocument.in/reader038/viewer/2022110215/568156c4550346895dc455ea/html5/thumbnails/113.jpg)
Andrea Franchi Vertical Emittance reduction @ ESRF 113
Caution with lifetime measurement (2)• At very low coupling εy may be smaller than monitor/camera
resolution and hence non measurable.• One may infer the average εy via Touschek-lifetime measurement.
• A depends on several RF-related parameters (bunch length, RF acceptance, dynamic aperture).
• It actually shall be the apparent emittance averaged along the low-beta regions of the ring (those with the high scattering rate contributing the most the lifetime integral), not the model eigen-emittance Ev 0
0.005
0.01
0.015
0.02
0.025
0 0.1 0.2 0.3 0.4 0.5IAX Vert Emittance e -1/2 [pm- 1/2 ]
1/ Li
etim
e [
h-1]
Fit Measurement
€
1τ tot
= Aεy
+ 1τ Vac
Measured <Ey> not model eigen-emittance Ev !!
![Page 114: Coupling Correction Through Beam Position Data](https://reader038.vdocument.in/reader038/viewer/2022110215/568156c4550346895dc455ea/html5/thumbnails/114.jpg)
Andrea Franchi Vertical Emittance reduction @ ESRF 114
Caution with lifetime measurement (2)• At very low coupling εy may be smaller than monitor/camera
resolution and hence non measurable.• One may infer the average εy via Touschek-lifetime measurement.
• A depends on several RF-related parameters (bunch length, RF acceptance, dynamic aperture).
• It actually shall be the apparent emittance averaged along the low-beta regions of the ring (those with the high scattering rate contributing the most the lifetime integral), not the model eigen-emittance Ev 0
0.005
0.01
0.015
0.02
0.025
0 0.1 0.2 0.3 0.4 0.5IAX Vert Emittance e -1/2 [pm- 1/2 ]
1/ Li
etim
e [
h-1]
Fit Measurement
€
1τ tot
= Aεy
+ 1τ Vac
1/ Vacuum Lifetime
![Page 115: Coupling Correction Through Beam Position Data](https://reader038.vdocument.in/reader038/viewer/2022110215/568156c4550346895dc455ea/html5/thumbnails/115.jpg)
Andrea Franchi Vertical Emittance reduction @ ESRF 115
Caution with lifetime measurement (2)• At very low coupling εy may be smaller than monitor/camera
resolution and hence non measurable.• One may infer the average εy via Touschek-lifetime measurement.
• A depends on several RF-related parameters (bunch length, RF acceptance, dynamic aperture).
• It actually shall be the apparent emittance averaged along the low-beta regions of the ring (those with the high scattering rate contributing the most the lifetime integral), not the model eigen-emittance Ev 0
0.005
0.01
0.015
0.02
0.025
0 0.1 0.2 0.3 0.4 0.5IAX Vert Emittance e -1/2 [pm- 1/2 ]
1/ Li
etim
e [
h-1]
Fit Measurement
€
1τ tot
= Aεy
+ 1τ Vac
A inferred from lifetime measurement at large
emittance (with white noise, rather than with coupling) => no need of RF-related parameters
![Page 116: Coupling Correction Through Beam Position Data](https://reader038.vdocument.in/reader038/viewer/2022110215/568156c4550346895dc455ea/html5/thumbnails/116.jpg)
Andrea Franchi Vertical Emittance reduction @ ESRF 116
Caution with lifetime measurement (2)• At very low coupling εy may be smaller than monitor/camera
resolution and hence non measurable.
Conditions 200 mA m 7/8 no Single Bunch 01-Feb-11
MeasurementsModel eigen-emittance [pm] 2.4Vert Emitt. <IAX> [pm] 4.2±1.2Vert Emitt. ID25-b [pm] 3.64Vert Emitt. ID25-XRL [pm] 3.75Vert Emitt. D9-a [pm] 7.1Total Lifetime [h] 51.5
ProcessingTouschek Prolongated Vert Emitt [pm] 3.9Vacuum Lifetime [h] 170Touschek Lifetime [h] 74
EstimationTotal Lifetime @ 2pm [h] 40.4
![Page 117: Coupling Correction Through Beam Position Data](https://reader038.vdocument.in/reader038/viewer/2022110215/568156c4550346895dc455ea/html5/thumbnails/117.jpg)
Andrea Franchi Vertical Emittance reduction @ ESRF 117
Caution with lifetime measurement (2)• At very low coupling εy may be smaller than monitor/camera
resolution and hence non measurable.
Conditions 200 mA m 7/8 no Single Bunch 01-Feb-11
MeasurementsModel eigen-emittance [pm] 2.4Vert Emitt. <IAX> [pm] 4.2±1.2Vert Emitt. ID25-b [pm] 3.64Vert Emitt. ID25-XRL [pm] 3.75Vert Emitt. D9-a [pm] 7.1Total Lifetime [h] 51.5
ProcessingTouschek Prolongated Vert Emitt [pm] 3.9Vacuum Lifetime [h] 170Touschek Lifetime [h] 74
EstimationTotal Lifetime @ 2pm [h] 40.4
OK!
![Page 118: Coupling Correction Through Beam Position Data](https://reader038.vdocument.in/reader038/viewer/2022110215/568156c4550346895dc455ea/html5/thumbnails/118.jpg)
Andrea Franchi Vertical Emittance reduction @ ESRF 118
Caution with lifetime measurement (2)• At very low coupling εy may be smaller than monitor/camera
resolution and hence non measurable.
Conditions 200 mA m 7/8 no Single Bunch 01-Feb-11
MeasurementsModel eigen-emittance [pm] 2.4Vert Emitt. <IAX> [pm] 4.2±1.2Vert Emitt. ID25-b [pm] 3.64Vert Emitt. ID25-XRL [pm] 3.75Vert Emitt. D9-a [pm] 7.1Total Lifetime [h] 51.5
ProcessingTouschek Prolongated Vert Emitt [pm] 3.9Vacuum Lifetime [h] 170Touschek Lifetime [h] 74
EstimationTotal Lifetime @ 2pm [h] 40.4
NO!!
![Page 119: Coupling Correction Through Beam Position Data](https://reader038.vdocument.in/reader038/viewer/2022110215/568156c4550346895dc455ea/html5/thumbnails/119.jpg)
Andrea Franchi Vertical Emittance reduction @ ESRF 119
Caution with lifetime measurement (2)• At very low coupling εy may be smaller than monitor/camera
resolution and hence non measurable.
Conditions 200 mA m 7/8 no Single Bunch 01-Feb-11
MeasurementsModel eigen-emittance [pm] 2.4Vert Emitt. <IAX> [pm] 4.2±1.2Vert Emitt. ID25-b [pm] 3.64Vert Emitt. ID25-XRL [pm] 3.75Vert Emitt. D9-a [pm] 7.1Total Lifetime [h] 51.5
ProcessingTouschek Prolongated Vert Emitt [pm] 3.9Vacuum Lifetime [h] 170Touschek Lifetime [h] 74
EstimationTotal Lifetime @ 2pm [h] 40.4
NO!!
0
0.005
0.01
0.015
0.02
0.025
0 0.1 0.2 0.3 0.4 0.5IAX Vert Emittance e -1/2 [pm- 1/2 ]
1/ Li
etim
e [
h-1]
Fit Measurement
Measured <Ey> not model eigen-emittance Ev !!
Touschek lifetime measurement @ ESRF
large <Ey> with white noise rather than with coupling to keep βx, βy & δEy constant
![Page 120: Coupling Correction Through Beam Position Data](https://reader038.vdocument.in/reader038/viewer/2022110215/568156c4550346895dc455ea/html5/thumbnails/120.jpg)
Andrea Franchi Vertical Emittance reduction @ ESRF 120
EXTRA: Brilliance @ εy = 3 pm @200 mA
Solid curve: Brilliance of the X-ray beam emitted from the two in-vacuum undulators installed on ID27 (High Pressure beamline). Each undulator segment has a period of 23 mm, a length of 2 m and is operated with a minimum gap of 6 mm.