Saturation of two-stream instability of an electron beam in plasma
- PDF / 366,815 Bytes
- 8 Pages / 612 x 792 pts (letter) Page_size
- 8 Downloads / 182 Views
MA INSTABILITY
Saturation of TwoStream Instability of an Electron Beam in Plasma K. V. Lotov, A. V. Terekhov, and I. V. Timofeev Budker Institute of Nuclear Physics, Siberian Branch, Russian Academy of Sciences, pr. Akademika Lavrent’eva 11, Novosibirsk, 630090 Russia Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090 Russia Received February 1, 2008, in final form November 20, 2008
Abstract—The development and nonlinear saturation of twostream instability of a warm nonrelativistic electron beam in a cold plasma are investigated numerically in the framework of a onedimensional model. It is shown that, for a sufficiently large velocity spread of the electron beam, instability develops and saturates according to a universal law, the wave phase velocity remains the same in the saturation stage, and the maxi mum field is somewhat lower than that predicted by classical estimates and depends in a different way on the growth rate. The damping of plasma oscillations not only changes the instability growth rate, but also sub stantially decreases the maximum wave field. PACS numbers: 52.35.Qz DOI: 10.1134/S1063780X09060099
1. INTRODUCTION The longitudinal (twostream) instability of an electron beam propagating in a dense plasma is one of the classical problems of plasma physics. The first publications on this problem appeared more than half a century ago [1, 2]. The main features of this instabil ity have been thoroughly described in reviews, mono graphs, and textbooks (see, e.g., [3−8]). Nevertheless, sometimes it becomes necessary to consider one or another aspect of this physical phenomenon in greater detail in the context of new applications or theoretical models. In the present paper, we will focus on the instability saturation caused by the trapping of beam electrons by the excited wave. The necessity of returning to the classical problem is motivated by successful experiments on plasma heating by highpower electron beams in the GOL3 facility at the Budker Institute of Nuclear Physics (Novosibirsk) [9−11]. Analysis of experimental results indicates that, in this and similar facilities [12−15], the energy of resonant Langmuir waves, which determines the beam deceleration rate, nearly corresponds to the saturation level of beam−plasma instability. Specifi cally, the calculated distribution of the energy released by the beam along the plasma column in the regime of instability saturation is in good quantitative agreement with the experimental data [16]. Moreover, the energy of resonant waves measured in the similar GOLL facility [13, 17] is close to the calculated energy of a wave saturated due to trapping effects. We will consider the interaction of a nonrelativistic electron beam with plasma in the framework of a one dimensional model and assume that the beam density
is much smaller than the plasma density. Of course, in such a formulation, the problem is far from actual experiments. Nevertheless, it allows us to compare the results of numerical simulations with simple analytical models, de
Data Loading...
