  A kinetic theory is developed to describe radiating electrons whose motion is
governed by the Lorentz-Dirac equation. This gives rise to a generalized Vlasov
equation coupled to an equation for the evolution of the physical submanifold
of phase space. The pathological solutions of the 1-particle theory may be
removed by expanding the latter equation in powers of $\tau := q^2/ 6\pi m$.
The radiation-induced change in entropy is explored, and its physical origin is
discussed. As a simple demonstration of the theory, the radiative damping rate
of longitudinal plasma waves is calculated.
