Numerical modeling of electron beam-plasma interactions

by Löfgren, Torbjörn

Beam plasma interactions in density gradients can produce narrow hf structures. The \hf spikes " are seen in experiments with a hot cathode as electron source, and in particle in cell simulations. Using a new parameterization technique for non-Maxwellian distribution functions in homogeneous plasmas, it is found that the spatial growth in the spike cannot be explained by a kinetic beam-plasma instability. Waves entering denser plasma are reected. The interference, of a forward wave and a backward wave, produce a narrow region of standing waves surrounded by regions dominated by travelling waves. A dynamic uid model, incorporating the static electric eld and the inhomogeneous electron density, is solved by numerical methods. The solution reproduces a standing wave pattern with the maximum amplitude at a position with a local plasma frequency close to, but below, the oscillation frequency. The oscillation frequency is found to be a normal mode of a short-circuited diode. The amplitude of the eld in the diode, and thus the amplitude at the spike, is determined by the total ac current, which is limited by the dc electron density level close to the cathode. To incorporate kinetic e ects as the driving instability in the beam and resonant damping, a new method for eigenmode analysis in inhomogeneous diodes is developed. No applications of this method for the spike are reported but it is shown that singular space charge structures, producing corners in the electric eld, can form in the re ection regions.