Introduction to CESRc Optics

1. Introduction to CESRc Optics M. Billing CESRc miniMAC

2. Topology of CESRc (Lattice Asymmetry) S IR RF Normal Arc Normal Arc RF S IR N IR HBs HBs CESRc miniMAC

3. There are no families! All quadrupoles Independently powered in FODO configuration Unipolar power supplies Current resolution: 1.5x10-5 of full scale All sextupoles Independently powered Bipolar power supplies Current resolution: 2.4x10-3 of full scale => Great flexibility in optics designs Quad/Sextupole Families CESRc miniMAC

4. Optics Design uses a Figure of Merit Based on weighted differences from Target Values (here called “Constraints”) General Parameters Emittancesx Tunes, Qx, Qy Injection Parameters x, y, x at Injection Point(x & x determine the injection oscillation amplitudes in the rest of CESRc) Primary Optics Constraints CESRc miniMAC

5. IP Parameters x*, y*, x* Coupling matrix elements(Solenoid compensation: To keep y* small, want C12 & C22 small) See following plots (Plot C-matrix in -normalized units: ) Lab Coords Eigen Coords Primary Optics Constraints CESRc miniMAC

6. CESRc IR Optics ) ) adjustableskew quad quad CESRc miniMAC

7. Basic Constraints Phase advance linked with parasitic crossing separation, xPr Pretzel efficiency = min/max( xPr/ √x )over all parasitic crossings in the arcs Pretzel Constraints e+beam CESRc miniMAC

8. Horizontal Pretzel Differential displacement 2 xPr between e+/e- Sextupole effects xPr in sextupole => quad ( ) for e+/e- => Pretzel dependant parameters Tunes, Qx, Qy (tonality) Twiss parameters,x, y, x, y, x (e.g. y* moves y*minimum in opposite directions!) Initially-Linear Effects, but can become non-linear as’s ’s are perturbed Horz Pretzel & Sextupoles CESRc miniMAC

9. Sextupole effects - minimize e+/e- differences (H separation in sextupole => differential quadrupole)so quadrupole & sextupole optics designed together In arcx, y, x - e+/e- differences General Parameters Emittancesx Tunes, Qx, Qy (are used to adjust the e+/e- tunes) Chromaticities ( ), Q´x, Q´y Chromatic Betas & Phases in arcs - dx/d, dy/d, dx/d, dy/d IP Parameters x*, y*, x* Differences of Coupling matrix elements Pretzel Constraints CESRc miniMAC

10. Additional Constraints for minimum Pretzel separation at Parasitic Crossings B Parameter - Form: Each term represents the RMS vertical kick from its parasitic crossing Phenomenological / Experimental Justification from Lifetime Considerations Long range tune shift at parasitic crossings Minimize the worst tune shift Separation Constraints CESRc miniMAC

11. Linear Focusing in the vertical plane only Q=0.1/wiggler (significant optics issue,but not really a problem) Small skew quadrupole errors (locally compensated & not part of design) Non-Linear Vert odd order multipoles Other multipoles from field non-uniformity Model 3-D Design field model for the magnet Model’s fields fit to an analytic functional expansion Optics designs based on analytic expansion Wiggler Effects CESRc miniMAC

12. Basic Idea Software control of a large number of elements Control for specific functions “Common” Knob Controls QTUNEING (quads) [5] Qy [6] Qx XQUNEING (sextupoles) /=== “Tonality” ===\ [1] Qy´ [2] Qx´ [3] ∂Qy/∂xPr [4] ∂Qx/∂xPr PRETZING (H separators) [1] Pretzel Ampl [13] S IP separation Group Controls CESRc miniMAC

13. More “Common” Knob Controls VNOSEING (NIR quads: phase advance change within Vert separation bump in NIR)(launches vertical separation wave from NIR to SIR) [1] SIR V separation [2] SIR Diff V angle BETASING (quads & skew quads) [1] y* [2] x* SCMATING (quads & skew quads) [1] y* [2] c12* [3] c21* [4] c22* [5] c11* [6] y* CESRc miniMAC