Kinetic theory of plasma waves

In this paper, I outline the solution of Vlasov-Maxwell's equations with given initial conditions. When transients have died out, the temporal evolution of each spatial Fourier component is completely determined by a dispersion relation. I derive the electrostatic dispersion relation and discuss the resonant interaction between particles and electrostatic waves. A new derivation of the wave energy density in a plasma with arbitary dissipation is given. The numerical solution of the dispersion relation of waves in a Maxwellian plasma is discussed, and finally I show some examples of numerically evaluated dispersion surfaces.