Nonlinear interaction of electromagnetic waves in bounded plasmas

A method is presented for the solution of second-order electromagnetic fields in a bounded plasma which is excited by two high-frequency electromagnetic waves. Due to nonlinearities inherent in any plasma, incoming waves are mixed, creating sum and difference frequencies. The signal from the difference frequencyomega_{1}-omega_{2}, whereomega_{1}andomega_{2}are source frequencies, can be of considerable consequence whenomega_{1}-omega_{2}is sufficiently low to cause a significant reaction in a plasma as resonant conditions develop. In particular, the problem considered in this paper is the optimization of second-order fields in a uniform plasma confined to a circular waveguide including reference to diagnostic applications.