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This paper provides a systematic derivation of a guiding-center kinetic model that describes intense beam propagation through a periodic focusing lattice with axial periodicity length S, valid for sufficiently small phase advance (say, σ<60°). The analysis assumes a thin (a,b≪S) axially continuous beam, or very long charge bunch, propagating in the z direction through a periodic focusing lattice with transverse focusing coefficients κ_{x}(s+S)=κ_{x}(s) and κ_{y}(s+S)=κ_{y}(s), where S=const is the lattice period. By averaging over the (fast) oscillations occurring on the length scale of a lattice period S, the analysis leads to smooth-focusing Vlasov-Maxwell equations that describe the slow evolution of the guiding-center distribution function f[over ¯]_{b}(x[over ¯],y[over ¯],x[over ¯]^{′},y[over ¯]^{′},s) and (normalized) self-field potential ψ[over ¯](x[over ¯],y[over ¯],s) in the four-dimensional transverse phase space (x[over ¯],y[over ¯],x[over ¯]^{′},y[over ¯]^{′}). In the resulting kinetic equation for f[over ¯]_{b}(x[over ¯],y[over ¯],x[over ¯]^{′},y[over ¯]^{′},s), the average effects of the applied focusing field are incorporated in constant focusing coefficients κ_{x sf}>0 and κ_{y sf}>0, and the model is readily accessible to direct analytical investigation. Similar smooth-focusing Vlasov-Maxwell descriptions are widely used in the accelerator physics literature, often without a systematic justification, and the present analysis is intended to place these models on a rigorous, yet physically intuitive, foundation.