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3D versus 2D in structure resonances

This study confirms a scaling law for 3D versus 2D resonances in structure using MICROMAP simulations. The ansatz for the scaling law was verified and the coefficient determined. The paper explores the "ring notation" and "linac notation" for the 3D problem, specifically focusing on the adiabatic crossing and adiabaticity parameter. Different regimes such as scattering and trapping are analyzed, along with the impact on RMS emittance growth. Experimental evidence and limitations are also discussed.

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3D versus 2D in structure resonances

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  1. 3D versus 2D in structure resonances

  2. This ansatz for a scaling law was clearly confirmed by MICROMAP simulations determine coefficient! "ring notation" "linac notation  3D problem" ~ S1 S: scaling or "similarity" parameter reversed crossing normal: adiabatic crossing L: focusing cell length

  3. S is adiabaticity parameter • S large: adiabatic behavior with slow tune change in 2D coasting beam limit • 3D: S < Ssynch ~ DQ2/(DQ/nsynch) = DQ nsynch • Example: DQ = -0.2 nsynch = 20  Ssynch ~ 4  loss of adiabatic condition for S > 4! • no full exchange for Montague (experimental evidence at CERN PS!) • no trapping with 4th or 6th order structure resonance • probably no trappping in linac (S^2 or S^3 power law suppressed)

  4. Searched for expression containing again S Ξ(DQ)2/dQ/dn and found two regimes: scattering - trapping RMS emittance growth due to substantial fraction of total number of particles growing in amplitude "trapping" regime 90% 100% reverse crossing "scattering" regime fast or reverse crossing

  5. Negligible quantitative emittance growth only few % of particles in ring halo rms emittance growth irrelevant rms emittance growth: 100% o: 90% emittance only ~ 1% growth

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