Transport of energy and momentum due to spatial Landau damping and growth of electrostatic waves

It is shown that Landau damping in space (LDS), occuring for time-periodic electrostatic waves, does not lead to any deposition of energy in plasmas. A steady-state balance and a steady-state transport of energy, momentum and particles take place both for damped and growing waves. Because of the phase interference of coherent free and forced particle oscillations, the oscillatory energy of particles increases in the direction of wave propagation; the time-averaged flow of plasma kinetic energy being constant in space for these waves, the LDS must take place for a Maxwellian plasma in order to compensate for the growth of the particle oscillatory energy in space. (Author)