The energy density of a Landau damped plasma wave

In this paper some theories about the energy of a Landau damped plasma wave are discussed and new initial conditions are proposed. Analysis of a wave packet, rather than an infinite wave, gives a clear picture of the energy transport from field to particles. Initial conditions are found which excite the Landau wave without transients causing spurious terms in the energy density and without secular terms in second order. The results agree with the Brillouin formula for energy density of a wave packet moving at the group velocity, if Landau damping is smalt The wave packet produces a forerunner of resonant electrons with enhanced energy, moving at the phase velocity. The total energy is conserved.