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Zur nichtlinearen Theorie der Strahl‐Plasma‐Wechselwirkung III. Vorbereitung der numerischen Rechnungen
Author(s) -
Leven Ronald
Publication year - 1969
Publication title -
beiträge aus der plasmaphysik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.531
H-Index - 47
eISSN - 1521-3986
pISSN - 0005-8025
DOI - 10.1002/ctpp.19690090403
Subject(s) - physics , dispersion relation , plasma , ordinary differential equation , amplitude , nonlinear system , differential equation , function (biology) , mathematical analysis , mathematical physics , atomic physics , mathematics , quantum mechanics , evolutionary biology , biology
In order to prepare the system of ordinary differential equations, describing approximately the non‐linear behaviour of a beam‐plasma system, for numerical solution, at first the dispersion relation is analized. In particular it is shown, that in the case of a three component plasma the complex wave number k = k r + i γ can be found without difficulties as a function of frequency ω and the plasma parameters, if the electron densities n b and n p are treated as the two dependent quantities. The expressions on the right hand sides of the differential equations are transformed in such a way, that all complex integrals can be found as functions of one basic integral, tabulated in the literature, not only for negative values of γ (amplification) but also for positive values of γ (evanescence). In this way it will be possible, to describe the behavior of the wave amplitude not only for short distances from the input, where amplification of the wave takes place, but also for larger distances, where nonlinear Landau‐damping may occur.