Nonlinear mode coupling between waves in a nonneutral plasma

Nonlinear mode coupling is observed to create striking patterns of frequency splitting in waves excited on a nonneutral plasma column. The patterns are caused by the nonlinear interaction of a diocotron mode with up to five other magnetized plasma modes. The explanation of these patterns has led to the development of a novel and general eigenmode analysis for ideal fluid and plasma systems, involving inner products based on the wave energy or wave angular momentum, and with respect to which the modes form an orthogonal basis. The theory employs and clarifies the connection between conservation laws and the Hermitian (or anti-Hermitian) properties of the linearized dynamics. Consequently, the general approach to nonlinear mode coupling presented here is applicable to any ideal nonlinear inhomogeneous fluid or plasma system.