caa a22 4500 386367469 CHVBK 20180307111941.0 cr unu---uuuuu 161130e198902 xx s 000 0 eng 10.1017/S0022377800013593 doi S0022377800013593 pii (NATIONALLICENCE)cambridge-10.1017/S0022377800013593 Abdel-Gawad H. I. Department of Mathematics, Faculty of Science, Cairo University, Egypt Dynamical evolution of three-dimensional kinetic electron-beam instabilities [Elektronische Daten] [H. I. Abdel-Gawad] We present a method of solution of the quasi-linear diffusion equation for the averaged distribution function. The criterion for its validity is discussed. Using the solution obtained, we study the dynamics of the relaxation of a weak kinetic electron-beam instability and show that it saturates asymptotically at zero energy level. In a self-consistent manner, the distribution function for the beam particles will be shown to deform to a flat shape. Copyright © Cambridge University Press 1989 Journal of Plasma Physics Cambridge University Press 41/1(1989-02), 1-11 0022-3778 41:1<1 1989 41 PLA https://doi.org/10.1017/S0022377800013593 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0022377800013593 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Abdel-Gawad H. I. Department of Mathematics, Faculty of Science, Cairo University, Egypt NATIONALLICENCE 773 0- Journal of Plasma Physics Cambridge University Press 41/1(1989-02), 1-11 0022-3778 41:1<1 1989 41 PLA CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge