Propagation of a cloud of hot electrons through a plasma in the presence of Langmuir scattering by ambient density fluctuations

Gas-dynamic theory is generalized to incorporate the effects of beam-driven Langmuir waves scattering off ambient density fluctuations, and the consequent effects on the propagation of a cloud of hot electrons in an inhomogeneous plasma. Assuming Langmuir scattering as the limit of nonlinear three-wave interactions with fluctuations that are weak, low-frequency, long-wavelength ion-sound waves, the net effect of scattering is equivalent to effective damping of the Langmuir waves. Under the assumption of self-similarity in the evolution of the beam and Langmuir wave distribution functions, gas-dynamic theory shows that the effects of Langmuir scattering on the beam distribution are equivalent to a perturbation in the injection profile of the beam. Analytical expressions are obtained for the height of the plateau of the beam distribution function, wave spectral number density, total wave and particle energy density, and the beam number density. The main results of gas-dynamic theory are then compared with simulation results from numerical solutions of quasilinear equations. The relaxation of the beam in velocity space is retarded in the presence of density fluctuations and the magnitude of the upper velocity boundary is less than that in the absence of fluctuations. There are four different regimes for the height of the plateau, corresponding to different stages of relaxation of the beam in velocity space. Moreover, Langmuir scattering results in transfer of electrons from moderate velocity to low velocity; this effect produces an enhancement in the beam number density at small distances near the injection site and a corresponding decrease at large distances. There are sharp decreases in the profiles of the beam and total wave energy densities, which are related to dissipation of energy at large phase velocities. Due to a slower velocity space diffusion of the beam distribution in the presence of scattering effects, the spatial width of the beam is reduced while its mean velocity of propagation increases slightly.