Hamiltonian Resonance Theory
Particle resonances in circular accelerators occur as a result of perturbation terms involving particular Fourier harmonics. That approach is based on the common knowledge that periodic perturbations of a harmonic oscillator can cause a resonance when the perturbation frequency is equal to an eigenfrequency of the oscillator. In the realm of Hamiltonian resonance theory we will be able to derive not only obvious resonant behavior but also resonant dynamics which does not necessarily lead to a loss of the beam but to a significant change of beam parameters. We also will be able to determine the strength of resonances, effectiveness, escape mechanisms, and more.
KeywordsResonance Condition Stop Band Resonance Pattern Perturbation Term Resonant Term
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