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Classical hamiltonian perturbation theory formulated in terms of action-angle variables is applied to develop a general and systematic method for calculating the influence of anharmonic perturbations on the motion of a charged particle in a Penning trap. Action-angle variables are ideally suited to determine the shifts of the characteristic frequencies in a perturbed orbit. The application of the method is demonstrated by several case studies
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Martin Kretzschmar (1990) studied this question.
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