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An advanced spectral analysis of a mis-matched charged particle beam propagating through a periodic focusing transport lattice is utilized in particle-in-cell (PIC) simulations. It is found that the betatron frequency distribution function of a mismatched space-charge-dominated beam has a bump-on-tail structure attributed to the beam halo particles. Based on this observation, a new spectral method for halo particle definition is proposed that provides the opportunity to carry out a quantitative analysis of halo particle production by a beam mismatch. In addition, it is shown that the spectral analysis of the mismatch relaxation process provides important insights into the emittance growth attributed to the halo formation and the core relaxation processes. Finally, the spectral method is applied to the problem of space-charge transport limits.

New Spectral Method for Halo Particle Definition in Intense Mis-matched Beams