Quasilinear dynamics of a cloud of hot electrons propagating through a plasma in the presence of an externally applied uniform electric field

The propagation of a cloud of hot electrons through a plasma and the generation of Langmuir waves are investigated in the presence of an externally applied uniform electric field. Using numerical simulations of the quasilinear equations the evolution of the electron distribution function and the spectral density of Langmuir waves are monitored in coordinate and velocity space. It is found that the Langmuir waves are enhanced in the presence of the electric field and the distribution functions of the beam and Langmuir waves diffuse toward large velocities. The overall self-similar characteristic of the system is preserved in the presence of the electric field. The average beam velocity is no longer constant and increases with time along its trajectory, but the acceleration is much less than that of free streaming particles. The beam number density plateaus in coordinate space and large scale, small amplitude fluctuations develop on the top of this plateau. The level of the fluctuations depends on the strength of the electric field. We also investigated the influence of the external electric field on the evolution of gas-dynamical parameters such as the height of the plateau in the beam distribution function in velocity space, its upper velocity boundary, and the local velocity spread of the beam. Due to the finite quasilinear relaxation time and spatial inhomogeneity of the electron beam, different parts of the beam are in different states of relaxation. In the region of partial relaxation the plateau is specified by both upper and lower velocity boundaries. The upper boundary of plateau increases linearly with the strength of the electric field but the lower boundary is independent of it. Contrary to the free streaming of a beam in an electric field or quasilinear relaxation in the absence of the electric field, the local velocity spread of the beam increases during its propagation. Some of the electrons at the back of the beam are also transferred by the electric field to its front, so that the height of plateau increases at large distances