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

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

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

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.

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.

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.

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.

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:

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

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

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.

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.

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.

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.

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.

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.

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