Transverse phase-space dynamics of mismatched charged-particle beams

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Abstract
The transverse dynamics of a nonrelativistic, mismatched charged-particle beam propagating through a continuous, linear focusing channel is calculated using the Fokkker-Planck equation to represent the evolution of a coarse-grained distribution function in the phase space of a single beam particle. The relaxation rate and diffusion coefficient are determined from a simple model of turbulence resulting from charge redistribution. The solution for the distribution function enables calculation of all transverse beam properties as a function of time, including the halo.