Chaotic Phenomena in Unstable System

为了研究不稳定系统中的混沌现象，我们通过在双等离子体中注入电子束或通过电流来激发两种类型的不稳定性。然后，通过控制不稳定性的增长速度，使系统处于混沌状态。实验采用双等离子体装置进行。使用氩气，压力范围为10^<-4> ~ 3*10^<-4> Torr。等离子体参数为：n_e= (1-5) *10^8cm_<-3>, Te=1eV。得到的主要结果如下：[1]电子束等离子体系统：(1)通过向等离子体中注入能量为10-100eV的电子束，激发频率在200MHz左右的电子束等离子体不稳定。(2)随着电子束密度的增大，周期加倍。周期2和周期3的分叉发生了，表明有一个窗口。(3)通过嵌入法计算相关维数D，发现周期3的D=2.5，周期4的D= 3.3。(4)最大和更大Lyapunov指数为正，表明系统是混沌的。(5)由(3)(4)可知，电子束等离子体系统处于混沌状态离子声不稳定系统：(1)为了在等离子体中传递电流，我们在等离子体中安装了两个网格，并在其中一个网格上施加直流电位。当电流超过一定值时，离子声不稳定性被激发，其中上截止频率在离子等离子体频率附近。用探针测量了电子漂移速度，达到40Cs （Cs：离子声速）。(2)以上结果可以从电流驱动离子声不稳定性的色散关系来理解。(3)观测时间序列表明，系统在一定阈值以上成为间歇性混沌。相关维数非整数且大于2。最大Lyapunov指数为正，表明系统处于一个间歇混沌状态。(4)光谱形式为f^<-1>，因此观测到的间歇为1型。少

To study chaotic phenomen in unstable systems, we excited two types of instabilities by injecting an electron beam or passing a current into a Double plasma. Then, we adjusted to make the system chaotic by controlling the growth rate of the instabilities. The experiments were performed using a Double-Plasma Device. Argon gas was used and the pressure was ranged from 10^<-4> to 3*10^<-4> Torr. The Plasma parameters were : n_e= (1-5) *10^8cm_<-3> and Te=1eV.Obtained main results were as follows :[1] Electron beam plasma system :(1) By injecting an elecron beam whose energy is 10-100eV into the plasma, we excited the electron beam plasma instability whose frequency is around 200MHz.(2) When the electron beam density was increased, the period doubling appeared. The period-2 and period-3's bifurcation took place, showing that there is a window.(3) We calcurated the correlation dimension D by the embeding method and found that D=2.5 for period-3 and 3.3 for period-4, respectively.(4) The max … More imum Lyapunov exponent was positive, suggesting that the system is chaotic.(5) It is concluded from (3) (4) that the electron beam plasma system is in the chaotic state.[2] Ion acoustic instability system :(1) In order to pass a current in the plasma, we installed two grid meshes in the plasma and applied DC potentials to one of the grids. When the current exceeded a certain value, the ion acouistic instability was excited, where the upper cut off frequency was around the ion plasma frequency. The electron drift velocity was measured with the probe and amounted to 40Cs (Cs : ion acoustic velocity).(2) Above results are understood from the dispersion relation of the current-driven ion acoustic instability.(3) Observed time series showed that the system becomes intermittent chaos above a threshold. The correlation dimension was non-integer and larger than 2. The maximum Lyapunov exponent was positive, which suggests that the system is in an intemittent chaotic state.(4) The spectrum took a form of f^<-1>, so that observed intemittency is Type-1. Less