Non-linear Modulational Interactions

Abstract

Non-linear modulational interactions occur when the energy input into the system is sufficiently large and the frequency broadening due to the nonlinear interactions is larger than the difference in the frequencies of the interacting waves. The physics of this interaction consists in the modulation of the plasma parameters by one of the interacting waves which leads to the above-mentioned frequency broadening and to interactions with other waves. The physics of most non-linear interactions is the same-the modulation of the plasma properties by one of the waves and the propagation of other waves through the modulated system. In this sense, the nature of the decay and scattering processes is the same as that of the modulational interactions. The important point for the modulational interactions is that they are sufficiently strong to include the other interacting waves in the non-linear broadening. Earlier, in Chap.5, we have already estimated this broadening using a dimensional analysis and found a critical density of the waves above which the stimulated scattering processes and the decay processes become modulational interactions. We shall now start directly with a calculation of this broadening. The broadening is related to the total non-linear frequency shift, including both its real and its imaginary parts. Earlier we studied the imaginary part in detail-it is due to the non-linear processes we discussed above.