The transverse motion of beam halo particles is described by a particle-core model which uses the space-charge field of a continuous cylindrical oscillating beam core in a uniform linear focusing channel to provide the force that drives particles to large amplitudes. The model predicts a maximum amplitude for the resonantly-driven particles as a function of the initial mismatch. We have calculated these amplitude limits and have estimated the growth times for extended-halo formation as a function of both the space-charge tune-depression ratio and a mismatch parameter. We also present formulas for the scaling of the maximum amplitudes as a function of the beam parameters. The model results are compared with multiparticle simulations and we find very good agreement for a variety of initial particle distributions. [S1098-4402(98)00022-6]

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INTRODUCTION 1 I. GENERAL DESCRIPTION 3 III. COORDINATE SYSTEM AND UNITS 4 IV. TRANSPORT-SYSTEM ELEMENTS 5 V. DYNAMICS CALCULATIONS 8 A. Elements Having Zero Length 9 B. Elements Having Constant Fields and No Energy Gain 9 C. Elements Causing Energy Change or Having Varying Fields 9 VI. TRANSFER MATRICES 9 A. Drift (ft) 10 B. Thin Lens (f , f , f) 10 x v z C. Quadripole

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