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Reduction of the 6-dimensional phase-space of a muon beam by 6 orders of magnitude is a key requirement for a Muon Collider. Recently, a 12-stage rectilinear ionization cooling channel has been proposed to achieve that goal. In this paper, we establish the mathematical framework to predict and evaluate the cooling performance of the proposed channel. We predict the system effectiveness, by deriving key lattice parameters such as the lattice quality factor which describes the rate of coolingdoi:10.18429/jacow-ipac2014-tupme021 fatcat:ez2jnbljm5c45kbi27iyljprem