On the viability of the single-wave model for the beam plasma instability

¹ ENEA, FSN-FUSPHY-TSM, R.C. Frascati - Via E. Fermi, 45, I-00044 Frascati (RM), Italy
² L.T. Calcoli - Via Bergamo, 60, I-23807 Merate (LC), Italy
³ Department of Physics, “Sapienza” University of Rome - P.le Aldo Moro, 5, I-00185 Roma, Italy
⁴ Department of Physics, University of Naples “Federico II” - Via Cinthia, I-80126 Napoli, Italy

Received: 26 April 2016
Accepted: 2 September 2016

Abstract

We analyze the interaction of a cold fast electron beam with a thermalized plasma, in the presence of many Langmuir modes. The work aims at characterizing the deviation of the system behavior from the single-mode approximation, both with respect to a consistent spectral analysis of the most unstable mode harmonics and with respect to the presence of a dense spectrum, containing linearly unstable and stable modes. We demonstrate how, on the one hand, the total energy fraction absorbed by the harmonics is negligible at all (by evaluating its total amount) and, on the other hand, the additional Langmuir modes can be excited via an avalanche mechanism, responsible for a transport in the particle velocity space. In particular, we show that the spectral broadening outlines a universal shape and the distribution function, associated to the avalanche mechanism, has an asymptotic plateau, differently from the coherent structures characterizing the single-wave model.