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Coupling in CEBAF-ER

Coupling in CEBAF-ER. HOM coupler introduces phase dependent skew quad, which couples beam transverse oscillations gradient integral ~4 g on crest @ 5 MV/m sinusoidal phase dependence linear gradient dependence

charlesryan
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Coupling in CEBAF-ER

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  1. Coupling in CEBAF-ER • HOM coupler introduces phase dependent skew quad, which couples beam transverse oscillations • gradient integral ~4 g on crest @ 5 MV/m • sinusoidal phase dependence • linear gradient dependence • In CEBAF, can locally correct coupling effects by using a DC magnetic skew quad between modules providing compensatory gradient integral • Correction more complex in CEBAF-ER, as sign of HOM-induced skew quad changes from pass to pass • DC external skew quad can locally correct only a single pass, doubles coupling on the other

  2. Proposed Correction Schemes • Correct accelerated beam, leave recovered beam uncorrected • used in IR Demo; left significant coupling at end of machine • Correct accelerated beam in NL, decelerated beam in SL • “up-down” • correction in periodic lattice/at low energy, double coupling on aperiodic beam at high energy (where relative effect is weaker) • Correct decelerated beam in NL, accelerated beam in SL • “down-up” • correct aperiodic beams with large envelopes, double coupling on lower energy, periodic motion (where it may phase-average out) • Leave coupling uncorrected • in principle, things get out of hand only during/after 3rd pass • Use nonlocal/global coupling correction (Chao)

  3. Simulation • DIMAD based • gradient & phase dependent skew quad simulated at each HOM coupler position; nominal values used - in principle/with some agony “real” values can be used • DC magnetic skew quad at each quad position adjacent to module • Checked cosine-like, sine-like rays in each transverse plane on each pass • Injected decoupled, nominally matched, asymmetric (ex=2 ey=2 nm-rad) phase space & propagated s-matrix through entire acceleration/recovery cycle evaluating • coupled spot sizes • projected emittances • Can also easily check H/V correlations in s-matrix, cross-plane coupling terms in transfer matrix (not yet done)

  4. Ideal Machine Beam envelopes

  5. Coupled, no correction

  6. Coupled, no correction

  7. Coupled, up-up correction

  8. Coupled, up-up correction

  9. Coupled, up-down correction

  10. Coupled, up-down correction

  11. Coupled, down-up correction

  12. Coupled, down-up correction

  13. Observations & Recommendation • All schemes manifest significant coupling in at least part of machine • Uncorrected system has best spot size behavior • Up-up has worst emittance behavior & bad 2nd pass spots • Down-up, uncorrected have “smoothest” emittance behavior; down-up & up-down recover projected emittances - but beam is still coupled • Chao’s distributed decoupling schemes should be investigated (auto-steer coupled orbits with skew trims)

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