Abstract

We review recent progresses in the study of linear beam dynamics of the ionization cooling in solenoidal focusing channels. The topics included are: understanding of the solenoidal focusing in the rotating frame; beam parameterization in terms of the envelope functions, emittance, and angular momentum; the coupled equation for emittance and angular momentum in periodic focusing channels; general solution and comparison with simulation; analytic approach for calculating the stability criteria and envelope function in periodic focusing channels.

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