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Phase-Dependent Quadrupole Skew Coupling Effects in CEBAF-ER

This study explores the impact of phase-dependent skew quadrupoles on transverse beam oscillations in a particle accelerator, suggesting correction schemes to minimize coupling effects. Different correction strategies are evaluated to improve beam stability and reduce coupling-induced distortions. Simulation methods are used to analyze the behavior of the coupled beam envelopes, beam spot sizes, and emittance under various correction scenarios. Recommendations include investigating distributed decoupling schemes proposed by Chao to address coupling effects effectively.

charlesryan
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Phase-Dependent Quadrupole Skew Coupling Effects 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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