Second-harmonic generation in the presence of an instability of resonant absorption

Besides second-harmonic generation by coupling of the incident wave with the directly driven plasma wave in resonance absorption, the incident wave can couple to a wave scattered from the critical surface which is rippled by ion-acoustic waves resulting from an instability of resonance absorption. This results in additional red shift corresponding to the frequency of the ion-acoustic waves, which, being sensitive to the plasma density-gradient scale length, has been evaluated for a self-consistent modified plasma-density profile