fma workshop april 1st and 2nd, 2004 l. nadolski1 guiding lines for computing and reading a...
DESCRIPTION
FMA workshop April 1st and 2nd, 2004 L. Nadolski3 Tools Tracking codes –Simulation: Tracy II, Despot, MAD, AT, … –Nature: beam signal collected on BPM electrodes NAFF package (C, fortran, matlab) Turn number Selections –Choice dictated by Allows a good convergence near resonances Beam damping times (electrons, protrons) 4D/6D –AMD Opteron 2 GHz 0.7 s for tracking a particle over 2 x 1026 turns – 1h00 for 100x50 (enough for getting main caracteristics) – 6h45 for 400x100 (next fmap) Step size following a square root law (cf. Action)TRANSCRIPT
FMA workshop April 1st and 2nd, 2004 L. Nadolski 1
Guiding Lines for Computing and Reading a
Frequency Map
New FMA Calculations for SOLEIL including Insertion
Device EffectsLaurent S. Nadolski
Pascale Brunelle and Amor Nadji
FMA workshop April 1st and 2nd, 2004 L. Nadolski 2
z
z’
x
x’
x
z
x0
z0
x0’= 0z0’= 0
Frequency map
Configuration space Phase space
Phase spaceTracking T
NAFF
FT : (x0,z0) (x,z)
resonance
Frequency map:
NAFFTracking T
Computing a frequency map
x
z
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Tools• Tracking codes
– Simulation: Tracy II, Despot, MAD, AT, …– Nature: beam signal collected on BPM electrodes
• NAFF package (C, fortran, matlab)
• Turn number Selections– Choice dictated by
• Allows a good convergence near resonances• Beam damping times (electrons, protrons)• 4D/6D
– AMD Opteron 2 GHz• 0.7 s for tracking a particle over 2 x 1026 turns
– 1h00 for 100x50 (enough for getting main caracteristics)– 6h45 for 400x100 (next fmap)
• Step size following a square root law (cf. Action)
FMA workshop April 1st and 2nd, 2004 L. Nadolski 4
z
x
Regular areas
Resonances
Nonlinear or chaotic regionsFold
Reading a FMA
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5 10 15 201
510
1520
25
z (mm)
x (mm)
Mapping
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4th order5th order7th order9th order
Resonance network: a x + b z = c order = |a| + |b|
Higher orderresonance
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Rigid pendulum
Sampling effect
Hyperbolic Elliptic
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Diffusion D = (1/N)*log10(||||)
Color code:
||||< 10-10
||||> 10-2
Diffusion reveals as well slighted excited resonances
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Soleil Beam Dynamics investigations using FMA
• Working point 18.20 10.30– Lattice: bare, errors, IDs– Optimization schemes
• Design of a new working point taking into account what was discovered through FMA
• Conclusions
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Optimization Method• Tuneshift w/ amplitude• Tuneshift w/ energy• Robustness to errors
multipoles couplingIDs
Lattice designFine tuning
ImprovementNeeded
TrackingNAFF
NAFF suggestions
Yes
•(x-z) fmap injection eff. •(x-) fmap Lifetime•Touschek computation
Resonance identification
• 4D tracking• 6D tracking
Knobs10 quadrupole families 10 sextupole families
Dynamics analysis
Good WPNo
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x
z
x|z=1m
z| x=1m
X or z (m)
Flat vertical tune
No coupling resonance crossingx- z = 8 ( = 0.1).
Reference working point (18.2, 10.3)
See M. Belgroune’s talk
Just looking at these curves, it seems very clean …
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Bare lattice(no errors)
WP sitting onResonance node
x + 6z = 805x = 91
x - 4z = -232x + 2z = 57
9x=164 x-4z=-234x=73
x+6z=80x+5z=88
x+4z=96
5x=91
x+2z=57
x+z=65
On-momentum Dynamics --Working point: (18.2,10.3)
x
z
4x=73x-4z=-23 9x=164
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Randomly rotating 160
Quads
•Map fold Destroyed
•Coupling strongly impacts
3x + z = 65
•Resonance node excited
PhysicalAperture
On-momentum dynamics with 1.9% coupling (18.2,10.3)
x+z=65
Resonance islandx+z=65
x-4z=-234x=73
x+6z=80x+5z=88
x+4z=96
5x=91
x+2z=57
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Importance of including vaccum chamber
Injection @ 14mm
x+z=65 4x=73
x
z
Skew resonance excited by coupling
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Adding effect of 3 in-vacuum IDsx+z=65
z = 4.5 10- 3
IDOctupole term
deeper
Injection trouble if stronger
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Particle behavior after
Touschek scattering Chromatic orbitChromatic orbit
Closed orbit 01
x
x Ax
2'
00
'
000
2
02
0
xxx xA
ALS ExampleWP
WP
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1 = 4.38 10-04
2 = 4.49 10-03
Non-linear synchrotron motion
Tracking 6D required
ds
1
2
2 2
ds1
+3.8% -6%
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Off momentum dynamics w/o IDs
4x=73excited
4x=73
3x+z=65
3x- 2z=34
3z=31
3z=313z=313x+z=65
3x- 2z=34
>0 <0
z0 = 0.3mm
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Off momentum dynamics w/ 3 x U20
U20
B-Roll offx = 18 mg = 5mm
4x=73
3x+z=65
What’s about Effect of synchrotron radiation and damping?
Very narrow resonances
Synchrotron140 turns
Damping5600 turns
Loss over >400 turnsStable in 6D
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Coupling reduction by a factor 2 with 3 x U20
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Optimization of a New PointEnhanced philosophy
• On momentum – 3 x + z = 65 to be avoided (not shown w/o fmap)– WP to be shifted from resonance node: locus of most particles– Control of tune shift with amplitude using sextupole knobs
• x (Jx, Jz) = a Jx + b Jz
• z (Jx, Jz) = b Jx + c Jz
• Off momentum x()• Large energy acceptance • Control of the tune shift with energy using sextupoles• The 4 x = 73 resonance has to be avoided for insertion devices
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Energy tune shift for the new WP 18.19 / 10.29
x
z
dp/px
z
dp/p
18.19 / 10.2918.20 / 10.30
Tune shift w/ energy optimised with sextupoles to avoid in addition the 4x = 73 resonance for negative energy offset
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On momentum fmap for the WP 18.19 / 10.29
3x- 2z=34
3x- 2z=34
WP to be slightly shifted
Clean DA
1% coupling
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On momentum fmap for the WP 18.19 / 10.29 with 3 x U20
Map Torsion
Strong diffusion related to ID roll off
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Off momentum fmap for the WP 18.19 / 10.29
Off-momentum map
comparable to the
nominal WP
2x+2z=57
2x+2z=57
3x-z=26
3x-z=26
1% coupling
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Off momentum fmap for the WP 18.19 / 10.29 with 3 x U20
Effect of the 2x+2z=57 resonance becomes
« dangerous »
with the 3xU20
2x+2z=57
2x-z=26
2x-z=26
2x+2z=57
Smoothing by synchrotron oscillations
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ConclusionsFMA at design stage for the SOLEIL lattice
– Gives us a global view (footprint of the dynamics)– Dynamics sensitiveness to quads, sextupoles and IDs – Reveals nicely effect of coupled resonances, specially cross
term z(x)– Enables us to modify the working point to avoid resonances or
regions in frequency space– Importance of coupling correction to small values (below 1%)– 4D/6D …
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Aknowledgements and references
• Institutes– IMCCE, ALS, SOLEIL
• Codes– BETA (Loulergue -- SOLEIL)– Tracy II (Nadolski -- SOLEIL, Boege -- SLS)– AT (Terebilo http://www-ssrl.slac.stanford.edu/at/welcome.html)
• Papers– Frequency map analysis and quasiperiodic decompositions, J. Laskar,
Proceedings of Porquerolles School, sept. 01– Global Dynamics of the Advanced Light Source Revealed through
Experimental Frequency Map Analysis, D. Robin et al., PRL (85) 3– Measuring and optimizing the momentum aperture in a particle
accelerator, C. Steier et al., Phys. Rev. E (65) 056506– Review of single particle dynamics of third generation light sources through
frequency map analysis, L. Nadolski and J. Laskar, Phys. Rev. AB (6) 114801