Three-wave interaction and Manley–Rowe relations in quantum hydrodynamics

Abstract

The theory for nonlinear three-wave interaction in magnetized plasmas is reconsidered using quantum hydrodynamics. The general coupling coefficients are calculated for the generalized Bohm de Broglie term. It is found that the Manley–Rowe relations are fulfilled only if the form of the particle dispersive term coincides with the standard expression. The implications of our results are discussed.