The bispectrum is used to demonstrate that wave–wave coupling occurs when ponderomotive forces due to wave fields in the ion cyclotron range of frequencies are used to stabilize a magnetized plasma column against magnetohydrodynamic (MHD) interchange instabilities. The three waves that interact resonantly are an applied wave, a MHD wave, and the nonlinearly coupled sideband wave. The net ponderomotive forces contain partially canceling and augmenting contributions from each induced sideband field.