Quasilinear calculation of Langmuir wave generation and beam propagation in the presence of density fluctuations

The generation of beam-driven Langmuir waves and the propagation of an electron beam in the presence of ambient density fluctuations are numerically studied using quasilinear calculations in one spatial dimension. The random spatiotemporal density fluctuations are driven externally as ion-sound-like turbulence. The effects of Langmuir wave scattering off density inhomogeneities in three spatial dimensions are represented through effective damping of the Langmuir waves, and are included in the quasilinear model. The numerical results are explored for illustrative parameters, and Langmuir wave field statistics are compared with stochastic growth theory (SGT) predictions. Due to the combined effects of quasilinear interaction with the beam and scattering off density fluctuations, the Langmuir waves show burstiness and the levels are generally lower than when the density is homogeneous, qualitatively consistent with previous predictions. Apart from early evolution, the average beam speed is approximately the same as in the homogeneous case, but relaxation of the beam is significantly retarded. Both features are in qualitative agreement with earlier predictions. Moreover, the beam distribution function displays relatively smooth variations, which implies that the burstiness in the wave levels originates predominantly from the randomness in the damping rate due to density perturbations, rather than from the stochasticity in the beam growth rate. The statistics of the Langmuir wave field show good agreement with SGT predictions, thus indicating the beam-Langmuir wave system is in a SGT state. Furthermore, variations of the density fluctuation parameters are found to affect the evolution of both beam and Langmuir waves