Wavebreaking amplitudes in warm, inhomogeneous plasmas revisited

Abstract

The effect of electron temperature on the space–time evolution of nonlinear plasma oscillations in an inhomogeneous plasma is studied using a one-dimensional particle-in-cell code. It is observed that, for an inhomogeneous plasma, there exists a critical value of electron temperature beyond which the wave does not break. These simulation results, which are in conformity with the purely theoretical arguments presented by Trines [Phys. Rev. E 79, 056406 (2009)], represent the first numerical elucidation of the effect of plasma pressure on wave breaking amplitude. The results presented are of relevance to experiments where moderate to large amplitude plasma waves are excited, e.g., laser–plasma interaction experiments.

Wave breaking limit in arbitrary mass ratio warm plasmas

“…[ 19,31–34 ] These critical velocities are respectively achieved at the critical points $$$ {\phi}_1 $$$ and $$$ {\phi}_2 $$$ (the range of $$$ {\phi}_{-} $$$, where the Sagdeev potential $$$ U\left({\phi}_{-}\right) $$$ is real), as may be seen from Equation (9) (and using the expressions for $$$ {\phi}_{\mp } $$$ at $$$ {\phi}_1 $$$ and $$$ {\phi}_2 $$$ , respectively). Substituting these in Equation (8), the peak density of the negative and positive species at the critical points $$$ {\phi}_1 $$$ and $$$ {\phi}_2 $$$, respectively, becomes $$$ {\hat{n}}_{\mp }={\beta}_{\mp}^{-1/4} $$$, [ 19,31,35 ] which clearly shows that at the wave breaking point density becomes infinite only in the cold plasma limit $$$ {\beta}_{\mp}\to 0 $$$.…”