Chaotic Phenomena in Unstable System

为了研究不稳定系统中的混沌现象，我们用电子束或电流注入双等离子体来激发两种不稳定性。然后通过控制不稳定性的增长率使系统达到混沌状态。使用双等离子体装置进行实验。使用氩气，并且压力范围为10 - 3 * 10 - 4托。<-4><-4>等离子体参数为：n_e =（1 - 5）× 10^8cm_2，Te = 1eV。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，激发出频率为200MHz左右的电子束等离子体不稳定性。<-3>(2)当电子束密度增加时，出现了倍周期现象。第2周期和第3周期发生了分叉，表明存在一个窗口。(3)我们用嵌入方法计算了关联维数D，发现D = 2.5，周期-3和3.3，分别为周期-4。(4)最大 ...更多信息 系统的最小李雅普诺夫指数为正值，说明系统是混沌的. (5)由（3）（4）可知电子束等离子体系统处于混沌状态。[2]离子声不稳定性系统：（1）为了在等离子体中通过电流，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势。当电流超过一定值时，离子声不稳定性被激发，其上限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，其值为40 Cs（Cs：离子声速）。(2)上述结果是从电流驱动离子声不稳定性的色散关系理解的。(3)观察到的时间序列表明，系统成为间歇性的混沌超过一个阈值。关联维数为非整数且大于2。系统的最大李雅普诺夫指数为正值，表明系统处于间歇混沌状态。(4)频谱采用f ^的形式，因此观察到的间歇性是类型1。<-1>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