IMPACT Simulation of the Montague Resonance at PS

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Presentation transcript:

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

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. 68-38, CERN, 1968. E. Metral et al., Proc. of EPAC 2004, p. 1894. I. Hofmann et al., Proc. of EPAC 2004, p. 1960.

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

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

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

(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

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

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

(fully 3D self-consistent simulation) X-delE phase space correlation at the beginning and the end of 12800 turns (fully 3D self-consistent simulation) (horizontal tune = 6.20)

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

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.