【作者】 田敬北；

【导师】 翁甲强；

【作者基本信息】 广西师范大学 ， 理论物理， 2005， 硕士

【摘要】 本文分别综述了混沌控制原理及几种与本文相关的控制方法,强流离子束中束晕-混沌的基本动力学行为及特性、几种主要形成机制,束晕-混沌控制现状和束密度研究现状。在此基础上研究了五种不同初始分布的强流离子束在束晕—混沌控制前后的束离子径向密度分布变化情况和离子径向运动情况,并进一步对形成晕的离子在径向的概率分布进行研究。所得到的结果表明:我们可以运动束晕-混沌控制方法来消除束晕-混沌,并定性地说明了束晕-混沌控制的有效性。人们在研究研究混沌控制中提出了许多种控制方法,在综述部分选取了与本文相关的一些混沌控制反馈方法:OGY 方法、时间延迟反馈法、时空混沌控制方法。强流离子束有着广泛的应用和发展前景。强流离子束在使用过程中产生的束晕—混沌现象也日益引起国内外的广泛关注并且成为研究的热点问题。本文首先介绍了束晕—混沌的特性及其产生的物理机制,再介绍了束晕—混沌的控制策略和几种有效控制方法比较,并且对强流离子束离子密度研究状况做了简要介绍,最后对束晕—混沌的研究做了总结和展望。强流离子束产生的束晕—混沌现象会造成很大的危害,因此将束晕—混沌消除是十分必要的。中国原子能科学研究院的方锦清研究员提出了非线性反馈的控制策略,即在单离子径向所受的空间电荷力方程的右边加上一个非线性控制器G: F_r = -q(?)Φ~s( x,y,s)+G 通过改变G 就可以达到控制束晕—混沌的目的。关于初始分布满足K-V 分布的离子束在控制前后束离子性质的变化[1]和离子运动情况[2]已有研究,但对于不同初始分布的离子束,这方面的工作还未见有文章报道。本文运用PIC 模拟程序和已提出的延迟反馈控制方法,对初始分布分别满足水袋分布,抛物线分布,3-sigma 高斯分布和全高斯分布的离子束的情况,主要做以下两个方面的研究工作。(1) 控制前后的离子束径向密度分布的有关规律。对于这方面的工作,文献[1]已对初始分布满足K-V 分布情形,研究了束晕—混沌控制前后离子束离子径向密度分布变化情况。更多还原

【Abstract】 The principle of chaos control and its control methods, the essence of dynamical equations of high-intensity beams and theirs properties, the halo-chaos formation mechanism and its control methods, and the ion density distribution has investigated in high-intensity beams are differently summarized in this paper. Based on those, the ionic radial density situation and ionic transverse motion of high intensity ion beams which are controlled or not are studied in five different initial distributions. And carry on research to the radial probability distribution of halo ion. The results are shown that halo-chaos is eliminated by chaos control methods. And the validity of Halo-chaos control is approved from the qualitative description. A lot of kinds of control methods have been proposed on studying the chaos control. In the part of the summary about controlling chaos, we selectively introduce three methods related with this paper. They are OGY control, time delayed feedback control and spatiotemporal chaos control. The acceleration of intense beams has become very relevant due to a number of important applications. The phenomenon of halo-chaos formation has been attracted attention when intense beams are used. Firstly, the properties and formation mechanisms of halo-chaos are stated; secondly, control strategy and methods of halo-chaos are described, and investigation of ion density distribution is introduced; finally is halo-chaos study summarized in this paper. The halo-chaos will cause damage to accelerator etc, so it is necessary to remove halo-chaos. Researcher. Fang Jin-qing in China institute of Atomic Energy has proposed the nonlinear control strategy; the approach is to apply a nonlinear feedback controller G to the right-hand side of the single ion forced equation, that is, F_r = -q(?)Φ~s( x,y,s)+G Halo-chaos is controlled in terms of controller G.. About initial distribution to is it satisfied with K-V , the character of the beam and its ion transverse motion has already studied beforewhen the beam is under control or without control[1,2]. But to different initial distribution, work of in this respect don’t meet in any other papers. We mainly study two works by using using Particle-In-Cell simulations procedure and delay feedback control in this paper. The initial distribution of a beam injected into a linac to be different distribution such as waterbag, parabolic, 3-sigma Gaussian and full Gaussian. (1) Studying he radial density of high intensity ion beams with before control and after control. The work has been studied on the beam with the initial distribution of K-V in the paper[1]. However, considering that initial beam is nonuniform density profile propagating through a periodic focusing magnetic field, we study the radial density of high intensity ion beams which are controlled or not in different initial distributions of a beam injected into linac. The initial distribution is adopted to be some sufficiently realistic distributions such as waterbag, parabolic, 3-sigma Gaussian and full Gaussian. Without control, the simulation results show that the radial density of ion beams are all changed when the high intensity ion beam with nonuniform density profile propagate through a periodic focusing magnetic field. The overall situation that the density changes is that most ions are focused to a beam’s center, small amount of ion distribute in halo district. But unlike K-V distribution, nonuniform density distribution doesn’t change strongly. Under control, the curve of density distribution gained improvement and halo-chaos is controlled. But a different one is to some extent. The change of radial density distribution of K-V not only relate to the controller, but to the filling factor. As there is no evidence to other distributions such as waterbag, parabolic, 3-sigma Gaussian and full Gaussian. The change of radial density distribution is similar to that without control. But halo-chaos is controlled. (2) Investigating the transverse motion of beam halo ion by randomly chosen in different initial distributions of a beam injected into linac. The result is shown that ionic transverse motion is very complex. With the ranges of ion transverse motion, we divide the beam halo ion into two kinds. The first one is that ion repeatedly moves between the core and the halo district all the time in the evolution of 1 to 2000 periods. The second one is that ion is in the core or can regard as in the core in the evolution of 1 to 2000 periods. In the two kinds, one that can’t ignore in the core plays a key role in the halo formation. Then we investigate the ion leading halo formation by using its probability distribution on the radial channel. The result shows that the transverse motion of the halo ion without control is between the area of halo and the core when there is no control. But introducing nonlinear feedback controller can control it. Halo-chaos control is approved from the qualitative description. The change of density distribution, the transverse motion of the ion, and the radial probability distribution of the halo ion in different initial distribute of intensity ion beam are studied from above when the beam is under control and without control. The results of study can be us in the course of using ion beam, how to utilize ion beam to offer certain reference value effectively. halo-Chaos control ion更多还原