Oscillatory growth behavior of multistream instabilities
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LASMA INSTABILITY
Oscillatory Growth Behavior of Multistream Instabilities1 Y. W. Houa, *, M. X. Chenb, M. Y. Yuc, d, and B. Wue a Key
Laboratory of Neutronics and Radiation Safety, Institute of Nuclear Energy Safety Technology, Chinese Academy of Sciences, Hefei, 230031 China b School of Electronic Science and Applied Physics, Hefei University of Technology, Hefei, China c Institute for Fusion Theory and Simulation, Department of Physics, Zhejiang University, Hangzhou, 310058 China d Institute for Theoretical Physics I, Ruhr University, Bochum, 44780 Germany e Institute of Plasma Physics, Chinese Academy of Sciences, Anhui, 230031 China *e-mail: [email protected] Received February 18, 2016
Abstract—Multistream instabilities in the one-dimensional Vlasov−Poisson system are studied numerically by using plasmas with multi-humped electron distributions. The evolution of the total wave energy of the plasma oscillations excited by (numerical) noise consists of transient, growth, and nonlinear saturation stages. It is found that, in the growth stage, the total wave energy oscillates for odd number of streams, but it does not oscillate for even number of streams. It is also found that different spectral (Fourier) modes can dominate different stages of the “linear” growth and nonlinear saturation stages. DOI: 10.1134/S1063780X1609004X
1. INTRODUCTION Instability can take place when one or more electron beams propagate in plasma. Experiments [1–6] showed that when a beam is injected into the plasma, spatially unstable waves are excited and the wave power grows exponentially with the distance until it saturates. The linear instability condition can be predicted theoretically by the Nyquist criterion [7, 8]. Since the 1950s there have been many analytical and numerical investigations of instabilities and their saturation involving beam–plasma and beam–beam interactions [9–18]. In particular, electron beams at different densities were analyzed in [9]. Simulations using one-dimensional (1D) particle-in-cell (PIC) [10] and quasilinear diffusion equation [11] were carried out to see the effect of velocity space diffusion on the beam instabilities. The two-stream instability was also studied theoretically [12, 13] and numerically [14–18]. More recently, simulations found that the change of growth rate of the two-stream instability during the growth stage can be attributed to contributions from the different modes excited from the thermal fluctuations [19]. On the other hand, study on multistream interactions remains rather limited [20, 21]. In this paper, we reconsider multistream instabilities by simulating plasmas with multi-humped electron distributions in more detail. It is found that the growth and saturation behavior of initial distributions with odd and even number of streams can be quite different. 1 The article is published in the original.
This paper is organized as follows. In the next section, the simulation model and numerical method are given. Section 3 gives the simulation results on the evolution of the wave
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