Different k$\lambda _{D}$ Regimes for Nonlinear Langmuir Wave Behavior

As Langmuir waves (LW) are driven to large amplitudes in plasmas, they are affected by nonlinear mechanisms. Significant effort at LANL has resulted in a theoretical model of nonlinear Langmuir wave behavior based on the dimensionless parameter k$\lambda _{D}$ ($k$ is the Langmuir wave number and $\lambda _{D}$ is the Debye length), as well as an experimental platform to test the model without spurious effects. Experiments conducted over a range of k$\lambda _{D}$ are consistent with and support the model. k$\lambda _{D}$ physically represents the ratio of the electron thermal to the LW phase velocity. When k$\lambda _{D}$ is large, the LW phase velocity is near the electron thermal velocity and wave-particle kinetic effects such as electron trapping tend to dominate the nonlinear LW behavior. When k$\lambda _{D}$ is small, the LW phase velocity is much greater than the electron thermal velocity where little wave-particle interaction can take place and wave-wave effects tend to dominate. One such mechanism is the Langmuir Decay instability where the Primary LW can parametrically decay into an oppositely propagating LW and a co-propagating ion acoustic wave, a process that can cascade with each successive daughter LW. Collective Thomson scattering measurements of LWs driven by Stimulated Raman Scattering in a diffraction limited single laser focal spot have been used to study both wave-wave and wave-particle nonlinearities [Kline \textit{et al.}, \textit{PRL}, \textbf{94}, 175003 (2005)]. For k$\lambda _{D}<\sim $ 0.29, multiple waves are detected and are attributed to Langmuir decay instability, the wave-wave regime. For k$\lambda _{D}>\sim $ 0.29, a single wave, frequency-broadened spectrum is observed associated with electron trapping, the wave-particle regime. The transition from the wave-wave to the wave-particle regime is qualitatively consistent with quasi-2D particle-in-Cell simulations and with crossing of the Langmuir decay instability amplitude threshold above that for LW self-focusing.