Intuitive and rigorous derivation of spontaneous emission and Landau damping of Langmuir waves through classical mechanics

Abstract

Classical mechanics provides the intuitive and unified description of spontaneous emission, Landau growth and damping of Langmuir waves, the cold beam–plasma instability, and van Kampen modes. This is done by studying the interaction between M weak modes of a plasma without resonant particles and N quasiresonant particles, which leads to an exactly solvable high-dimensional Floquet problem. Growth corresponds to an eigenmode of the system, whereas damping requires statistical averaging. Both imply synchronization of near-resonant particles with waves, and the corresponding force on individual particles is computed explicitly.