Non-linear interaction of hydromagnetic waves

It is well known that a magnetized cylindrical plasma can sustain the propagation of low frequency, torsional hydromagnetic waves. In particular the linear dispersion relation of the azimuthally symmetric mode (m = 0) has been extensively studied, both theoretically and experimentally. It is predicted that weakly non-linear interaction of two such waves propagating in opposite directions can lead to the generation of oscillations at twice the frequency of the torsional waves. Details of the theory and of the experiments designed to confirm the predictions are presented. (author)