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This work presents a fully analytic way of determining relevant equilibrium quantities of a high-intensity charged particle beam submitted to magnetic focusing while inside a linear channel. Through the current approach, some intermediate steps of our original hybrid model which had to be solved numerically can now be eliminated, leading to the obtainment of a fully analytic expression. This expression relates the initial beam parameters with those at equilibrium, allowing beam macroscopicdoi:10.1017/s0022377809990079 fatcat:6jbrafaqondhfkwsjivdm6xwaa