  We present a generalization of Vlasov-Maxwell kinetic theory that accounts
for intense electromagnetic fields. A strongly-radiating, possibly
optically-thick plasma is decomposed into fragments, each comprising a charged
particle together with its self-generated electromagnetic field. Assuming weak
inter-fragment correlations, but strong intra-fragment correlations, a
mean-field evolution equation for the single-fragment distribution functional
is derived. We also identify the equation's Hamiltonian formulation. By
incorporating strong correlations between a charged particle and the field it
generates, the new model captures the effects of strong radiation reaction
non-perturbatively. The fragment kinetic formalism offers an attractive
approach to modeling exotic light-matter interactions such as nonlinear and
multiple Compton scattering.
