FMAP_Workshop - April 1, 2004 Frequency Map Calculation for the Advanced Light Source David Robin...
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![Page 1: FMAP_Workshop - April 1, 2004 Frequency Map Calculation for the Advanced Light Source David Robin Advanced Light Source work done in collaboration with.](https://reader035.fdocuments.net/reader035/viewer/2022062804/56649f465503460f94c68c70/html5/thumbnails/1.jpg)
FMAP_Workshop - April 1, 2004
Frequency Map Calculation
for the Advanced Light Source
David RobinAdvanced Light Source
work done in collaboration with
Christoph Steier (ALS), Ying Wu (Duke), Weishi Wan (ALS), Winfried Decking (DESY), James Safranek (SLAC/SSRL), Jacques Laskar (BdL),
Laurent Nadolski (SOLEIL), Scott Dumas (U. Cinc.)
with help from
Alan Jackson (LBNL), Greg Portmann (SLAC/SSRL), Etienne Forest (KEK), Amor Nadji (SOLEIL), Andrei Terebilo (SLAC/SSRL)
![Page 2: FMAP_Workshop - April 1, 2004 Frequency Map Calculation for the Advanced Light Source David Robin Advanced Light Source work done in collaboration with.](https://reader035.fdocuments.net/reader035/viewer/2022062804/56649f465503460f94c68c70/html5/thumbnails/2.jpg)
FMAP_Workshop - April 1, 2004
Outline
Motivation– Beam Lifetime– Injection Efficiency
Single Particle Beam Dynamics in the ALS– Importance of Periodicity– Example of Frequency Map with Lattice Errors
Frequency Map and Particle Loss
Injection– Superbend Example
Summary
![Page 3: FMAP_Workshop - April 1, 2004 Frequency Map Calculation for the Advanced Light Source David Robin Advanced Light Source work done in collaboration with.](https://reader035.fdocuments.net/reader035/viewer/2022062804/56649f465503460f94c68c70/html5/thumbnails/3.jpg)
FMAP_Workshop - April 1, 2004
Performance of the Advanced Light Source (ALS) is limited by the single particle electron beam dynamics
– Injection efficiency– Beam lifetime
Continue to strive for better understanding of the beam dynamics in order to
– Improve the performance of the ALS– Accurately predict what will happen when the ALS is
upgraded to include • Superbends, narrow gap insertion devices, elliptically
polarizing undulators, femtoslicing modifications, …
Motivation
![Page 4: FMAP_Workshop - April 1, 2004 Frequency Map Calculation for the Advanced Light Source David Robin Advanced Light Source work done in collaboration with.](https://reader035.fdocuments.net/reader035/viewer/2022062804/56649f465503460f94c68c70/html5/thumbnails/4.jpg)
FMAP_Workshop - April 1, 2004
The ALS is an interesting machine for studying the particle beam dynamics:
1. Simple Simple Magnetic Lattice 2. Very Nonlinear
In terms of single particle beam dynamics, the ALS is one of the most extensively studied storage rings
1. Theoretical investigations of the ALS began in the mid 1980s (Nishimura, Forest, Ruth, Bengtsson, …)
2. The ALS was used as the first example of frequency map analysis applied to accelerators (Laskar and Dumas in 1993)
Dynamics of the ALS
![Page 5: FMAP_Workshop - April 1, 2004 Frequency Map Calculation for the Advanced Light Source David Robin Advanced Light Source work done in collaboration with.](https://reader035.fdocuments.net/reader035/viewer/2022062804/56649f465503460f94c68c70/html5/thumbnails/5.jpg)
FMAP_Workshop - April 1, 2004
Dynamics in the ALS: Lattice
Typical ALS Sector
QF
1
QD
1 B 1 SD
1
QF
A 1
SF
1
B 2
SF
2
QF
A 2
SD
2
B 3
QD
2
QF
2
ALS consists of 12 sectors• 12-fold periodicity Suppression of resonances
mx + ny = 12 x q
where m, n, and q, are integers
![Page 6: FMAP_Workshop - April 1, 2004 Frequency Map Calculation for the Advanced Light Source David Robin Advanced Light Source work done in collaboration with.](https://reader035.fdocuments.net/reader035/viewer/2022062804/56649f465503460f94c68c70/html5/thumbnails/6.jpg)
FMAP_Workshop - April 1, 2004
Resonance Excitation
Resonances can lead to irregular and chaotic behavior for the orbits of particles which eventually will get lost by diffusion in the outer parts of the beam.
Rule of thumb Avoid low order resonances
![Page 7: FMAP_Workshop - April 1, 2004 Frequency Map Calculation for the Advanced Light Source David Robin Advanced Light Source work done in collaboration with.](https://reader035.fdocuments.net/reader035/viewer/2022062804/56649f465503460f94c68c70/html5/thumbnails/7.jpg)
FMAP_Workshop - April 1, 2004
9.0
8.8
8.6
8.4
8.2
8.0
Vert
ical
Tun
e15.014.814.614.414.214.0
Horizontal Tune
9.0
8.8
8.6
8.4
8.2
8.0
Vert
ical
Tun
e
15.014.814.614.414.214.0
Horizontal Tune
Benefits of Periodicity
All resonances Allowed resonancesTune plane - resonances up to 5th order
working point
Unfortunately there is no simple way to forecast the real strength of a resonances without a realistic model of the ring
and a tracking code.
![Page 8: FMAP_Workshop - April 1, 2004 Frequency Map Calculation for the Advanced Light Source David Robin Advanced Light Source work done in collaboration with.](https://reader035.fdocuments.net/reader035/viewer/2022062804/56649f465503460f94c68c70/html5/thumbnails/8.jpg)
FMAP_Workshop - April 1, 2004
ALS : Ideal Lattice versus Calibrated Model
![Page 9: FMAP_Workshop - April 1, 2004 Frequency Map Calculation for the Advanced Light Source David Robin Advanced Light Source work done in collaboration with.](https://reader035.fdocuments.net/reader035/viewer/2022062804/56649f465503460f94c68c70/html5/thumbnails/9.jpg)
FMAP_Workshop - April 1, 2004
Ideal versus Calibrated Model
Introducing linear errors fundamentally changes the beam dynamics
Ideal ring– The dynamic aperture is large– Small chaotic zone at large amplitudes– Particle loss is fast– Particle loss is due to high order resonances
Ring with calibrated linear errors– Dynamic aperture is smaller– Large chaotic zone at large amplitudes– Particle loss is slow– Particle loss is due to lower order unallowed resonances
![Page 10: FMAP_Workshop - April 1, 2004 Frequency Map Calculation for the Advanced Light Source David Robin Advanced Light Source work done in collaboration with.](https://reader035.fdocuments.net/reader035/viewer/2022062804/56649f465503460f94c68c70/html5/thumbnails/10.jpg)
FMAP_Workshop - April 1, 2004
Ideal versus Calibrated Model
Introducing linear errors fundamentally changes the beam dynamics
Ideal ring– The dynamic aperture is large– Small chaotic zone at large amplitudes– Particle loss is fast– Particle loss is due to high order resonances
Ring with calibrated linear errors– Dynamic aperture is smaller– Large chaotic zone at large amplitudes– Particle loss is slow– Particle loss is due to lower order unallowed resonances
![Page 11: FMAP_Workshop - April 1, 2004 Frequency Map Calculation for the Advanced Light Source David Robin Advanced Light Source work done in collaboration with.](https://reader035.fdocuments.net/reader035/viewer/2022062804/56649f465503460f94c68c70/html5/thumbnails/11.jpg)
FMAP_Workshop - April 1, 2004
Vertical orbit diffusion – On-energy example
Particle are lost in the vertical plane• via nonlinear coupling and diffusion of the trajectory.
Example : Particle launched at 12 mm horizontally and 1 mm vertically and tracked with damping and synchrotron oscillations.
![Page 12: FMAP_Workshop - April 1, 2004 Frequency Map Calculation for the Advanced Light Source David Robin Advanced Light Source work done in collaboration with.](https://reader035.fdocuments.net/reader035/viewer/2022062804/56649f465503460f94c68c70/html5/thumbnails/12.jpg)
FMAP_Workshop - April 1, 2004
Frequency Map AnalysisV
erti
cal
Tu
ne
Horizontal Tune Horizontal Amplitude [mm]
Ver
tica
l A
mp
litu
de
[mm
]
14.0 14.258.0
8.2
0 15 0
4
Frequency Space Amplitude Space
![Page 13: FMAP_Workshop - April 1, 2004 Frequency Map Calculation for the Advanced Light Source David Robin Advanced Light Source work done in collaboration with.](https://reader035.fdocuments.net/reader035/viewer/2022062804/56649f465503460f94c68c70/html5/thumbnails/13.jpg)
FMAP_Workshop - April 1, 2004
Frequency Map AnalysisV
erti
cal
Tu
ne
Horizontal Tune Horizontal Amplitude [mm]
Ver
tica
l A
mp
litu
de
[mm
]
14.0 14.258.0
8.2
0 15 0
4
Frequency Space Amplitude Spaceworking point
![Page 14: FMAP_Workshop - April 1, 2004 Frequency Map Calculation for the Advanced Light Source David Robin Advanced Light Source work done in collaboration with.](https://reader035.fdocuments.net/reader035/viewer/2022062804/56649f465503460f94c68c70/html5/thumbnails/14.jpg)
FMAP_Workshop - April 1, 2004
Tools and Techniques
![Page 15: FMAP_Workshop - April 1, 2004 Frequency Map Calculation for the Advanced Light Source David Robin Advanced Light Source work done in collaboration with.](https://reader035.fdocuments.net/reader035/viewer/2022062804/56649f465503460f94c68c70/html5/thumbnails/15.jpg)
FMAP_Workshop - April 1, 2004
Tools and Techniques
![Page 16: FMAP_Workshop - April 1, 2004 Frequency Map Calculation for the Advanced Light Source David Robin Advanced Light Source work done in collaboration with.](https://reader035.fdocuments.net/reader035/viewer/2022062804/56649f465503460f94c68c70/html5/thumbnails/16.jpg)
FMAP_Workshop - April 1, 2004
Frequency Map AnalysisV
erti
cal
Tu
ne
Horizontal Tune Horizontal Amplitude [mm]
Ver
tica
l A
mp
litu
de
[mm
]
14.0 14.258.0
8.25
0 15 0
4
Frequency Space Amplitude Space
![Page 17: FMAP_Workshop - April 1, 2004 Frequency Map Calculation for the Advanced Light Source David Robin Advanced Light Source work done in collaboration with.](https://reader035.fdocuments.net/reader035/viewer/2022062804/56649f465503460f94c68c70/html5/thumbnails/17.jpg)
FMAP_Workshop - April 1, 2004
On-energy dynamic aperture - frequency map (left) versus induced amplitude (right)
Induced AmplitudeFrequency Map
![Page 18: FMAP_Workshop - April 1, 2004 Frequency Map Calculation for the Advanced Light Source David Robin Advanced Light Source work done in collaboration with.](https://reader035.fdocuments.net/reader035/viewer/2022062804/56649f465503460f94c68c70/html5/thumbnails/18.jpg)
FMAP_Workshop - April 1, 2004
Injection efficiency
Like to have a good injection efficiency– Minimize fill times– Minimize radiation levels
• Top-off• Insertion devices
At the ALS the injected beam is horizontally offset by ~10mm from the stored beam when it enters the ring.
The injected beam oscillates about the stored beam and slowly damps down.
If particles in the injected beam encounter regions of high diffusion they can be lost.
Goal is to ensure that the particle motion is stable in the region where injected particles may travel
![Page 19: FMAP_Workshop - April 1, 2004 Frequency Map Calculation for the Advanced Light Source David Robin Advanced Light Source work done in collaboration with.](https://reader035.fdocuments.net/reader035/viewer/2022062804/56649f465503460f94c68c70/html5/thumbnails/19.jpg)
FMAP_Workshop - April 1, 2004
Example : Superbend Upgrade
Normal ALS Sector
Modified ALS Sector
QD
A 1
QD
A 2
In three of the twelve ALS Sectors • Replaced the central combined function dipole with
a Superbend and two quadrupoles
![Page 20: FMAP_Workshop - April 1, 2004 Frequency Map Calculation for the Advanced Light Source David Robin Advanced Light Source work done in collaboration with.](https://reader035.fdocuments.net/reader035/viewer/2022062804/56649f465503460f94c68c70/html5/thumbnails/20.jpg)
FMAP_Workshop - April 1, 2004
Frequency Maps without Superbends (Top) versus with Superbends (Bottom)
Horizontal Amplitude [mm]
Ver
tica
l A
mp
litu
de
[mm
]V
erti
cal
Am
pli
tud
e [m
m]
Amplitude Space
Ver
tica
l T
un
e
Horizontal Tune
Frequency Space
Ver
tica
l T
un
e
8.0
8.25
8.0
8.25
0 1514.0 14.25
0
4
0
4
![Page 21: FMAP_Workshop - April 1, 2004 Frequency Map Calculation for the Advanced Light Source David Robin Advanced Light Source work done in collaboration with.](https://reader035.fdocuments.net/reader035/viewer/2022062804/56649f465503460f94c68c70/html5/thumbnails/21.jpg)
FMAP_Workshop - April 1, 2004
Momentum Aperture and Lifetime
Frequency Map Analysis has been extended to study the momentum aperture and the effect on lifetime
In the case of the Superbends the predictions agreed with the result to within 5%
The off energy frequency maps will be discussed in the next talk.
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FMAP_Workshop - April 1, 2004
Other Results
Frequency Map Analysis has been an important technique for optimizing and predicting the performance of future upgrades
In addition to the Superbend Upgrade we have used FMA for studying– Effect of Insertion Devices with Complicated Field Profiles– Smaller Gap Insertion Devices– Femtosecond Slicing Upgrade– Higher Tune Lattice– …
![Page 23: FMAP_Workshop - April 1, 2004 Frequency Map Calculation for the Advanced Light Source David Robin Advanced Light Source work done in collaboration with.](https://reader035.fdocuments.net/reader035/viewer/2022062804/56649f465503460f94c68c70/html5/thumbnails/23.jpg)
FMAP_Workshop - April 1, 2004
Some References
1. H. Dumas and J. Laskar, Phys. Rev. Lett. 70, 2975-2979
2. J. Laskar and D. Robin, “Application of Frequency Map Analysis to the ALS”, Particle Accelerators, 1996, Vol 54 pp. 183-192
3. D. Robin and J. Laskar, “Understanding the Nonlinear Beam Dynamics of the Advanced Light Source”, Proceedings of the 1997 Computational Particle Accelerator Conference
4. D. Robin, J. Safranek, and W. Decking, “Realizing the benefits of restored periodicity in the advanced light source”, PRST, Vol 2, 044001 (1999)
5. D. Robin, C. Steier, J. Laskar, and L. Nadolski, “Global Dynamics of the Advanced Light Source Revealed through Experimental Frequency Map Analysis”, Phys. Rev. Lett. Vol. 85, No. 3 (2000)
6. C. Steier, et. al.,”Measuring and optimizing the momentum aperture in a particle accelerator”,Phys. Rev. E. Vol. 65, 056506
7. D. Robin and C. Steier, W. Wan, and A. Wolski, “Impact of Narrow Gap Undulators on the Advanced Light Source”, Proceedings of the 2003 Particle Accelerator Conference
8. D. Robin, “Superbend Upgrade of the Advanced Light Source”, Proceedings of the 2003 Particle Accelerator Conference
9. Y. Wu, E. Forest, and D. Robin, “Explicit symplectic integrator for s-dependent static magnetic field”, Phys Rev. E. Vol 68 046502 (2003)