Zur nichtlinearen Theorie der Strahl‐Plasma‐Wechselwirkung IV. Numerische Ergebnisse: Elektronenschwingungen

The spatial variations of the electric field E and the electron distribution function f a for the case of beam plasma amplification are computed on the basis of a nonlinear approximation developed in the earlier parts of the present paper [1–3]. The essential results are: With increasing distance x from the point, where the beam enters the plasma, the amplitude à 1 of the first harmonic increases, reaches a maximum value at some point x m and than decreases monotonically without reaching a further maximum. In the region around x m we find a large increase of the higher harmonics, i.e. increasing nonlinearity, and also an increasing phase velocity, which soon approches the beam velocity. The non‐oscillating part of the distribution function of the beam electrons deformes, but not so much as the quasilinear theory predicts, so that amplitude settling must be interpreted as a nonlinear but not as a quasilinear effect. The results show a good agreement with some typical experiments on beam plasma interaction.