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Exact Classical Model of Distributions of Ions in Collisionally Evolving Axisymmetric Traps

Classical dynamics is used to analyze the motion of individual ions in axisymmetric traps subject to charge-changing and momentum-changing collisions. By means of a series of transformations, equilibrium distributions of the ions are determined for arbitrary radial and axial trap potentials, under the assumption that the radial and axial motions are independent. These calculations will be useful for interpreting experiments on trapped ions and for understanding the behavior of confinement ion sources.