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.

Automated summary

The nonlinear evolution of Langmuir oscillations in a cold plasma with ion motion and (weakly) relativistic mass variation of electrons has been studied. The results show that Langmuir mode frequency acquires spatial dependencies, leading to phase mixing and breaking at low amplitudes. The phase-mixing time is found to decrease with an increase in the electron-to-ion mass ratio parameter and relativistic factor, with ion motion inducing phase-mixing more quickly than relativistic effects.