Nonlinear resonance islands and modulational effects in a proton synchrotron

Thesis/Dissertation · Fri Jan 01 04:00:00 EST 1993

OSTI ID:7235053

Satogata, T J

The authors examine one-dimensional and two-dimensional nonlinear resonance islands created in the transverse phase space of a proton synchrotron by nonlinear magnets. The authors examine application of the theoretical framework constructed to the phenomenon of modulational diffusion in a collider model of the Fermilab Tevatron. For the one-dimensional resonance island system, the authors examine the effects of two types of modulational perturbations on the stability of these resonance islands: Tune modulation and beta function modulation. Hamiltonian models are presented which predict stability boundaries that depend on only three parameters: The strength and frequency of the modulation and the frequency of small oscillations inside the resonance island. The tune modulation model is successfully tested in experiment, where frequency domain analysis coupled with tune modulation is demonstrated to be useful in measuring the strength of a nonlinear resonance. Nonlinear resonance islands are examined in two transverse dimensions in the presence of coupling and linearly independent crossing resonances. The authors present a first-order Hamiltonian model which predicts fixed point locations, but does not reproduce small oscillation frequencies seen in tracking. Particle tracking is presented which shows evidence of two-dimensional persistent signals, and the authors make suggestions on methods for observing such signals in future experiment. The authors apply the tune modulation stability diagram to the explicitly two-dimensional phenomenon of modulational diffusion in the Fermilab Tevatron with beam-beam kicks as the source of nonlinearity. The amplitude growth created by this mechanism in simulation is exponential rather than root-time as predicted by modulational diffusion models. The authors comment upon the luminosity and lifetime limitations such a mechanism implies in a proton storage ring.

• Research Organization: Northwestern Univ., Chicago, IL (United States)
• OSTI ID: 7235053
• Country of Publication: United States
• Language: English

Related Subjects

43 PARTICLE ACCELERATORS
430200* -- Particle Accelerators-- Beam Dynamics
Field Calculations
& Ion Optics
ACCELERATORS
BEAM OPTICS
BEAMS
CYCLIC ACCELERATORS
ELECTRICAL EQUIPMENT
ELECTROMAGNETS
EQUIPMENT
FERMILAB TEVATRON
KICKER MAGNETS
MAGNETS
MODULATION
NONLINEAR PROBLEMS
NUCLEON BEAMS
PARTICLE BEAMS
PROTON BEAMS
RESONANCE
SYNCHROTRONS