July 22, 2005CESRc miniMAC1 Introduction to CESRc Optics M. Billing

July 22, 2005CESRc miniMAC2 Topology of CESRc Normal Arc S IR N IR HBs RF (Lattice Asymmetry)

July 22, 2005CESRc miniMAC3 Quad/Sextupole Families 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

July 22, 2005CESRc miniMAC4 Primary Optics Constraints Optics Design uses a Figure of Merit –Based on weighted differences from Target Values (here called “Constraints”) General Parameters –Emittances  x –Tunes, Q x, Q y Injection Parameters –  x,  y,  x at Injection Point (  x &  x determine the injection oscillation amplitudes in the rest of CESRc)

July 22, 2005CESRc miniMAC5 Primary Optics Constraints IP Parameters –  x *,  y *,  x * –Coupling matrix elements (Solenoid compensation: To keep  y * small, want C 12 & C 22 small) –See following plots (Plot C-matrix in  -normalized units: ) Lab Coords Eigen Coords

July 22, 2005CESRc miniMAC6 CESRc IR Optics quad adjustable skew quad ) )

July 22, 2005CESRc miniMAC7 Pretzel Constraints Basic Constraints –Phase advance linked with parasitic crossing separation,  x Pr –Pretzel efficiency = min/max(  x Pr / √  x ) over all parasitic crossings in the arcs e+ beam

July 22, 2005CESRc miniMAC8 Horz Pretzel & Sextupoles Horizontal Pretzel –Differential displacement 2  x Pr between e+/e- Sextupole effects –  x Pr in sextupole =>  quad ( ) for e+/e- => Pretzel dependant parameters –Tunes,  Q x,  Q y (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

July 22, 2005CESRc miniMAC9 Pretzel Constraints 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,  Q x,  Q y (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

July 22, 2005CESRc miniMAC10 Separation Constraints 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

July 22, 2005CESRc miniMAC11 Wiggler Effects 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

July 22, 2005CESRc miniMAC12 Group Controls Basic Idea –Software control of a large number of elements –Control for specific functions “Common” Knob Controls –QTUNEING (quads) [5] Q y [6] Q x –XQUNEING (sextupoles) /=== “Tonality” ===\ [1] Q y ´[2] Q x ´[3] ∂Q y /∂x Pr [4] ∂Q x /∂x Pr –PRETZING (H separators) [1] Pretzel Ampl[13] S IP separation

July 22, 2005CESRc miniMAC13 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] c 12 *[3] c 21 * [4] c 22 *[5] c 11 * [6]  y *