On Langmuir oscillations breaking driven by ion motion and relativistic effects

The nonlinear evolution of Langmuir oscillations (LOs) is studied in a cold plasma including the ion motion and (weakly) relativistic mass variation of electrons. For the purposes, a simple perturbation technique is used to solve the governing one-dimensional fluid-Maxwell's equations. The solutions show that the Langmuir mode frequency acquires spatial dependencies due to the finite ion inertia and relativistic effects. As a result, excited LOs mix up in phase and break at arbitrarily low amplitudes. An approximate expression for the phase-mixing time of LOs is then obtained, thus improving some earlier results. Phase-mixing time is found to decrease with the increase of both the electron-to-ion mass ratio parameter and relativistic factor. A comparative analysis between these two effects is also carried out to clarify which effect contributes more to the phase-mixing time. It is revealed that phase-mixing is induced more quickly due to the ion motion than the relativistic effects. (paper)