Parametric decay of an upper-hybrid wave in a plasma cylinder

A large-amplitude upper-hybrid wave in a plasma cylinder is susceptible to parametric decay into a lower-hybrid wave and an upper-hybrid wave. The perpendicular and parallel motions of electrons play equally important roles in the nonlinear interaction. The coupled-mode equations are solved using a perturbation technique. The growth rate of the instability is less sensitive to the radial mode number of the sideband. However, for higher-order radial modes it falls off as the overlap of the interacting wave functions decreases.