Lagrangian studies of plasma wave interactions. I

Abstract

A study of wave-wave interactions in plasmas is made using a lagrangian formulation developed by Low. Coupled mode equations are derived. The method offers distinct advantages over the conventional approach starting from the Vlasov- Maxwell equations. Two examples of the lagrangian method are considered: (i) the nonlinear interaction of transverse waves in a warm field-free plasma to produce plasma oscillations and (ii) the interaction of three- electromagnetic waves in a cold magnetized plasma. Its application to waves in warm magnetized plasmas and to explosive instabilities is considered in part II.