July 22, 2005 CESRc miniMAC 1

Introduction to CESRc Optics

M. Billing

July 22, 2005 CESRc miniMAC 2

Topology of CESRcTopology of CESRc

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Quad Dipole Wiggler Separator

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Normal Arc

Normal Arc

S IR S IR

N IR

HBs HBs

RF RF(Lattice Asymmetry)

July 22, 2005 CESRc miniMAC 3

Quad/Sextupole FamiliesQuad/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, 2005 CESRc miniMAC 4

Primary Optics ConstraintsPrimary Optics Constraints• Optics Design uses a Figure of Merit

– Based on weighted differences from Target Values (here called “Constraints”)

• General Parameters– Emittancesx

– Tunes, Qx, Qy

• Injection Parameters x, y, x at Injection Point

(x & x determine the injection oscillationamplitudes in the rest of CESRc)

July 22, 2005 CESRc miniMAC 5

Primary Optics ConstraintsPrimary Optics Constraints• 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: )

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C I

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Lab Coords Eigen Coords

C GA C GB 1

July 22, 2005 CESRc miniMAC 6

CESRc IR OpticsCESRc IR Optics

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quadadjustableskew quad

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QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

July 22, 2005 CESRc miniMAC 7

Pretzel ConstraintsPretzel Constraints• Basic Constraints

– Phase advance linked with parasitic crossing separation, xPr

– Pretzel efficiency = min/max( xPr/ √x )over all parasitic crossings in the arcs

e+beam

July 22, 2005 CESRc miniMAC 8

Horz Pretzel & SextupolesHorz Pretzel & Sextupoles• 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

k k

x 6

xPr

July 22, 2005 CESRc miniMAC 9

Pretzel ConstraintsPretzel Constraints• Sextupole effects - minimize e+/e- differences

(H separation in sextupole => differential quadrupole)so quadrupole & sextupole optics designed together

– In arcx, y, x - e+/e- differences

• General Parameters– Emittancesx

– Tunes, Qx, Qy (are used to adjust the e+/e- tunes)

– Chromaticities ( ), Q´x, Q´y

– Chromatic Betas & Phases in arcs - dx/d, dy/d, dx/d, dy/d

• IP Parameters x

*, y*, x

*

– Differences of Coupling matrix elements

p Q

p

July 22, 2005 CESRc miniMAC 10

Separation ConstraintsSeparation 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

B Ib y x

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4 xPr2

PCs

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July 22, 2005 CESRc miniMAC 11

Wiggler EffectsWiggler 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, 2005 CESRc miniMAC 12

Group ControlsGroup Controls• 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

July 22, 2005 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*