Abstract
A theory of particle trapping and transport during a single passage through a high-order nonlinear resonance is developed. The main result is an expression for the trapping efficiency as a function of two scaling variables which are related to the resonance excitation width, the nonlinear detuning and the speed of passage through the resonance. The question of what phase-space region trapped particles are drawn from and the question of adiabaticity are discussed. The theory is then verified with a computer simulation for crossing a fifth order resonance.
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