Abstract
Abstract The problem of the amplitude growth of a particle executing a betatron oscillation, caused by crossing a resonance line either once or several times (repetitive resonance crossing), is analyzed from a unified formulation. We assume that the particles in a beam are independent and the motion has one degree of freedom, i.e. it is described by one coordinate-momentum or action-angle pair, Both amplitude-independent tune and amplitude-dependent tune cases are studied for easy comparison and the effects of detuning on amplitude growth have been explicitly presented. Explicit analytic expressions and computer tracking results demonstrating the dependence of the amplitude growth on the parameters governing the motion are presented and the connection with the results of analyses by other authors are discussed.
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