Chaotic Phenomena in Unstable System

不稳定系统中的混沌现象

基本信息

批准号：
08458110
负责人：
KAWAI Yoshinobu
金额：
$ 1.22万
依托单位：
KYUSHU UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
1996
资助国家：
日本
起止时间：
1996 至 1997
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-08458110/
关键词：
unstable system drift velocity period doubling intermittent chaos type-1 corelation dimension ion acoustic instability electron beam plasma instability 電子ブーム・プラズマ不安定性プラズマカオスダブルプラズマ

项目摘要

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

为了研究不稳定系统中的混沌现象，我们通过向双等离子体注入电子束或通入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率来调整系统以使其变得混沌。使用双等离子体装置，压力范围为10^-4至3*10^-4托。等离子体参数为：n_e=(1-5)。 *10^8cm_<-3>和Te=1eV。获得的主要结果如下：[1]电子束等离子体系统：(1)通过将能量为10-100eV的电子束注入等离子体中，激发电子束流等离子体不稳定，频率在200MHz左右。(2)当电子束密度增加时，出现周期倍增现象，表现为周期2和周期3的分岔。 (3) 通过嵌入方法计算相关维数 D，发现第 3 周期 D=2.5，第 4 周期 D=3.3。(4) 最大李亚普诺夫指数为正，表明该系统是混沌的。(5)由(3)(4)得出电子束等离子体系统处于混沌状态。[2]离子声不稳定系统：(1)为了通过一个电流在等离子体中，我们在等离子体中安装了两个网格，并向其中一个网格施加直流电势，当电流超过一定值时，离子声学不稳定性被激发，其中上限截止频率在离子等离子体频率附近。用探针测量电子漂移速度，结果为 40Cs（Cs：离子声速）。（2）上述结果是从电流驱动的离子声学不稳定性的色散关系来理解的。（3）观察的时间序列表明：当超过阈值时，系统变为间歇性混沌，相关维数为非整数且大于2。最大李雅普诺夫指数为正，表明系统处于间歇性混沌状态。(4)谱的形式为f。 ^<-1>，因此观察到的间歇性为 Type-1。