Dynamics and conservation laws in electrostatic plasma turbulence

Abstract

We show how the Hamiltonian description of an ideal fluid can be used for a two fluid plasma. Translation to wave variables leads to a simple rule to obtain coupled-mode equations if the energy is known as a function of wave variables. In this context we discuss the intimate connexion between a particular dynamical model, specified by the interaction Hamiltonian, and the associated invariants of motion. By this method we derive an improved version of Zakharov's equations for Langmuir and ion sound waves with the correct invariants of motion. As a result of these corrections we find a stationary power law k−2 for the plasmon energy.