3D versus 2D in structure resonances

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 lt Ssynch DQ2/(DQ/nsynch) DQ nsynch
• Example DQ -0.2 nsynch 20 ?
  Ssynch 4 ? loss of adiabatic condition for S
  gt 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 (S2 or S3 power
  law suppressed)

4
Searched for expression containing again S ?
(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