Vlasov equation in terms of canonical variables

A new approach to the perturbation theory for the Vlasov equation is discussed. The approach is based on the expansion of the Hamiltonian in powers of the canonical variables about their equilibrium values. Unlike the traditional approach, the proposed perturbation theory provides energy conservation in every order. In particular, solutions to linearized equations are constructed that carry certain energy and momentum. The influence of decay processes on the kinetic beam-plasma instability is also discussed