High-frequency emissions during the propagation of an electron beamin high-density plasma

A relativistic annular electron beam passing through a high-density plasma excites Langmuir waves via Cerenkov interaction. The Langmuir waves are backscattered off ions via nonlinear ion Landau damping. At moderately high amplitudes these waves are parametrically up-converted by the beam into high-frequency electromagnetic radiation, as observed in some recent experiments. A nonlocal theory of this process is developed in a cylindrical geometry. It is seen that the growth rate of the Langmuir wave scales as one-third the power of beam density. The growth rate of parametric instability scales as one-fourth the power of beam density and the square root of beam thickness