1. Improvement of PEP-II Linear Optics with a MIA-Derived Virtual Accelerator
Ben Cerio
Office of Science, SULI Program 2006
Stanford Linear Accelerator Center
August 16, 2006

2. Outline of Talk PEP-II Collider at SLAC Accelerator Physics
Linear Optics and Betatron Motion
Beam Position Monitor (BPM) Measurements
Model Independent Analysis (MIA)
Construction of Virtual PEP-II
Improvement of Linear Optics

3. PEP-II Two storage rings: linac
2 mi.
Two storage rings:
e+ stored at 3.1 GeV in low energy ring (LER)
e- stored at 9 GeV in high energy ring (HER)
linac
interaction point (IP)
PEP-II tunnel

4. What does an accelerator physicist do?
Designs new accelerators
Improves existing accelerators
Ultimate goal: Increase collider luminosity—particle interactions per unit cross section.
Luminosity:
Stategy 1) Increase beam current.
Strategy 2) Decrease transverse beam size at IP.
Done by improving linear optics
PEP-II parameters from yesterday Blue is luminosity.

5. Transverse Linear Beam Optics
Dipole magnets bend charged particles into closed orbits.
Quadrupole magnets focus and defocus beam.
Nonlinear magnetic elements are not considered.
Coordinate system: y
Bunch of particles s x
Quadrupoles focus in one transverse direction and defocus in the other.
defocusing magnet
focusing magnets
bend (dipole) magnets
Focusing and defocusing of beam results in betatron motion.

6. What is betatron motion?
Motion of charged particle in transverse plane due to quadrupoles.
- example) motion in one dimension
β gives information about amplitude and phase of motion.
Useful to examine betatron motion in phase space.
is the initial phase space coordinate. x F D F s
Each lattice element can be represented by a matrix.

7. Linear Maps a b
Between two arbitrary points in lattice (a and b), we can define a linear map M, where
M can be factorized:
- (one dimensional case). Transforms into normalized phase space, where particle motion resembles simple harmonic motion. Gives the betatron function value at location a.
- (one dimensional case). Rotation matrix that rotates in normalized phase space by betatron phase advance.

8. My Research
Problem: PEP-II LER beta functions deviated from the ideal (design) lattice functions (called beta beat).
s (m)
Beta functions from PEP-II LER derived from measurement taken on August 9, 2006.
Goal: Reduce beta beat of PEP-II LER (and increase luminosity?).
remember:

9. Beam Position Monitor (BPM) Measurements
Double view BPM:
gives y position of centroid (center of mass)
319 BPMs in LER
293 BPMs in HER
gives x position of centroid (center of mass)
Excite beam vertically and horizontally with a kicker magnet.
Beam position measured at every BPM location for 1024 beam revolutions (turns).
FFT(BPM data)
Four independent beam orbits

10. Linear Green’s Functions and Betatron Phase Advances
From 4 orbits, we obtain Green’s functions and betatron phase advances between every BPM location.
MATH!
Green’s Functions
Transfer matrix elements:
Model Independent Analysis (MIA) Program:
Goal: Construct accelerator model.
Start with ideal lattice as initial model, vary model lattice and update model linear Green’s Functions and betatron phase advances until these parameters match those derived from measurement.
We have then obtained a model that matches the linear optics of PEP-II at the time that BPM measurements were taken.
remember:
Phase Advance

11. Comparison of Phase Advances
The following results were obtained from BPM measurements taken on August 9.
SVD-enhanced fitting
Red: measurement-derived phase advance Blue: phase advance of model before fitting (design lattice)
Red: measurement-derived phase advance Blue: phase advance of model after fitting.
When the phase advances and Green’s functions of model match the corresponding quantities derived from measurement, we have obtained a lattice that matches the linear optics of PEP-II, called the virtual accelerator.

12. Beta Functions of PEP-II LER
Once virtual accelerator is obtained, use one turn maps to find beta functions of the ring.
remember:
, where
red: virtual accelerator blue: ideal lattice
Plots on bottom characterize linear optics at IP. Remember: beta function at IP is important for luminosity.
Note high beta beat.
Manipulate virtual accelerator to reduce beta beat.

13. Manipulation of Virtual Accelerator
Problem: HIGH BETA BEAT Attack: Manipulate virtual accelerator lattice (i.e. change quadrupole strengths) and find a new lattice that more closely matches the linear optics of the design lattice. Call the new lattice solution the improved accelerator.
Red: improved virtual accelerator, blue: design lattice
Change quadrupole strengths
Note reduction of beta beat by a factor of ~3.
New magnet configuration was dialed into the real PEP-II on August 10.

14. Post-Solution Virtual Accelerator
After new magnet configuration is dialed into PEP-II, BPM measurements were taken again, and a post-solution virtual accelerator is constructed.
Beta beat was reduced.
Not a surprise. The virtual accelerator, a very accurate model, predicted this behavior.

15. In case I blew your mind…
Diagrammatic recapitulation:
Calculate Green’s Functions and Phase Advances
4 independent orbits
BPM data
FFT
Dial new magnet configuration into real machine.
Calculate Green’s functions and phase advances of initial model
Fit model quantities (GF and PA) to measurement- derived quantities
New magnet configuration.
Virtual accelerator lattice
Improve virtual optics by changing strengths of select quadrupoles.

16. So you improved linear beam optics. BIG DEAL. Did luminosity increase?
Yes, average luminosity integration has increased (luminosity integrated over time). Projected 7 day luminosity will break the current record for PEP-II.
Solution dialed in here.

17. Acknowledgements Yiton Yan William Colocho
Adam Edwards and Stephanie Majewski
Mike Woods and DOE Office of Science