Numerical and analytical demonstration of the interaction of a wave with a free-streaming perturbation

The interaction of a plasma wave with a long wavelength free-streaming perturbation is considered in the case of a one-dimensional electron plasma. A demonstration of this interaction is provided by means of both numerical simulation and analytical theory. The initial distribution function is so chosen as to give rise to an ordinary plasma wave together with a long wavelength disturbance containing a free-streaming portion. Satellites of the plasma wave are shown to be excited in agreement with earlier work of Morales and Malmberg on the ''linear sideband'' effect. This result is found to hold when the initial long wavelength disturbance is close to a pure free-streaming perturbation. In order to have an observable effect in the numerical simulation, it is necessary to increase the density of resonant particles by adding a warm beam to the Maxwellian plasma, in such a way though, as to avoid beam plasma instability. The predictions of analytical theory on the amplitudes of the satellites are compared with the results of numerical simulation and a fair amount of agreement is found both in absolute magnitude and in time evolution