1. IMPACT Simulation of the Montague Resonance at PS
(understand the absence of emittance overshoot inside the static resonance stopband)

2. PS Montague Resonance Studies
Physical parameters:
Vrf = ramping with f = 39.5 MHz
Ek = 1.4 GeV
Emit_x = 7.5 mm-mrad
Emit_y = 2.5 mm-mrad
Rms bunch length = 45 ns
Rms dp/p = 1.7 x 10-3
Horizontal tune: 6.15 – 6.245
Vertical tune: 6.21
Synchrotron period: 1.5 ms
Half Aperture = 7cm x 3.5cm
I = 1.0x1012
Montague Resonance:
2 Qx – 2 Qy = 0
can cause particle due to
unequal aperture size in
horizontal and vertical
dimensions.
Refs: B. W. Montague, CERN-Report No , CERN, 1968.
E. Metral et al., Proc. of EPAC 2004, p
I. Hofmann et al., Proc. of EPAC 2004, p

3. Static Montague Resonance Crossing at PS
measurements
2004 results
IMPACT simulation: fully 3D+nonlinear lattice (2011)

4. RMS emittance evolution of a longitudinally frozen beam
(nonzero dp/p, with dispersion effects)
(with different horizontal tunes)

5. Center slice emittance evolution of a longitudinally frozen beam
(with different horizontal tunes)

6. (longitudinally frozen beam)
X-delE phase space correlation at the beginning and the end of 512 turns
(longitudinally frozen beam)
(horizontal tune = 6.197)
Initial delE – X phase space distribution
delE – X phase space distribution 512 turns

7. RMS emittance evolution of a longitudinal frozen beam
(0 dp/p, 0 dispersion effects)
(with different horizontal tunes)

8. (with different horizontal tunes)
RMS emittance evolution with a fully 3D self-consistent simulation beam
(with different horizontal tunes)

9. (fully 3D self-consistent simulation)
X-delE phase space correlation at the beginning and the end of turns
(fully 3D self-consistent simulation)
(horizontal tune = 6.20)

10. RMS emittance evolution of an initial upright Gaussian beam
(with different horizontal tunes)

11. Preliminary Conclusions
It seems that the final emittance exchange inside the Montague
resonance depends on the dispersion match and the synchrotron motion.
Synchrotron motion help enhance the emittance exchange towards equipartition.
Dispersion mismatch preclude the reach of the full horizontal-vertical equipartition.