ABSTRACT
This chapter describes the absorption and both spontaneous and stimulated emissions of Langmuir waves. It presents the description of the self-consistent dynamics in the case of waves with small amplitude. Averaging the second-order equations over the initial positions of the N particles yields an evolution equation for the wave energy. The chapter utilizes second-order perturbation analysis in ε of the canonical equations of the self-consistent Hamiltonian. Perturbation calculation is justified only if the particle and wave orbits do not wander too far away from free orbits. The calculation turns out to be simpler and to show its limits of validity better when using the action-angle variables for the electrostatic waves.
