Hamiltonian theory of the E778 nonlinear dynamics experiment
Conference
·
OSTI ID:6813746
Short, medium,a nd long time scale Hamiltonians describing the E778 experiment are presented, corresponding to smear, capture fraction, and tune modulation types of measurements. A one-turn discrete'' Hamiltonian representing motion in the presence of thin multipoles is derived from nonlinear projection maps, leading to expressions for distortion functions, Fourier spectra, normalized covariances, and smear. An N-turn Hamiltonian is derived representing motion at a tune near a rational fraction I/N, leading to expressions for detuning, resonance island width, resonance island tune, and persistent capture fraction. Generating functions appropriate to slow and fast tune modulation are presented, leading to four conditions which partition the tune modulation plane into four distinct phases'' of dynamical behavior. 9 refs., 2 figs.
- Research Organization:
- Lawrence Berkeley Lab., CA (USA). SSC Central Design Group
- Sponsoring Organization:
- DOE/ER
- DOE Contract Number:
- AC02-89ER40486
- OSTI ID:
- 6813746
- Report Number(s):
- SSC-175; CONF-8804111--7; ON: DE90013045
- Country of Publication:
- United States
- Language:
- English
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