| In this paper, based on the summary of controlling chaos, reviewing the formative mechanism of beam halo, dynamics equations and their properties and nonlinear controlling of beam halo, we study the effect of the changes of zero-current phase advance and tune depression,the transverse movement of particles, and a new nonlinear adaptive controlling method has been proposed in this paper.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 adaptive control. Halo-chaos controlling, which has already been a key issue for the development of new high-power accelerators, is becoming a hot research with more and more wide application of high-power beam. Considering this, Pro.Fang Jinqing, who works in the Institute of Atomic Energy of China, applied firstly the theory and methods of chaos controlling to control halos by using nonlinear functions and their works have solved the problems of halo regeneration. On the basis of their work and in view of some existing problems we do our study mainly from the following three aspects. Firstly, we have researched the effect of tune depression and zero-current phase advance which are two important parameters of the system. In the past, all of the researches had been made with the same and and the influence of their changes had not been considered. According to the relation of current and the two parameters, we adopt the wavelet function controller as follows: to study the influence of the change of tune depression and zero-current phase advance on controlling results, when the initial distribution is K-V. When the tune depression is changed and the zero-current phase advance unchanged,by comparising each statistic physical quantities after controlled, it has found that the better control on halo-chaos can still be realized if the tune depression is about 0.4. Then we researched the effect of change of the zero-current phase advance on halo-chaos control when different tune depressions are choosen, and the maximum zero-current phase advance was received and can control fairly, the findings which break the restriction of ,. According to the relation between current and tune depressin, zero-current phase advance: , we can calculate the maximum current can reach 3.228 times than the one when the nonlinear resonance would happen.The simulating results demonstrate that using nonlinear control not only can eliminate the regeneration of halo, but also is significant in increasing current in transportation systems.Secondly, we have applied delayed feedback controller: to study the change of particle movement and discoveried some particular laws: the movement of particles is restricted in a narrow region if the beam is controlled. The further study demonstrates that halo-chaos motions are a rather complicated process which is associated with the transverse energy exchange among particles as well as the nonlinear dependence of the space charges. The research demonstrates that the halo can be controlled completely by the controller quickly. There's no need to precisely calculate the coefficient of controller, and the controller can work well even if system parameters are changed. When the mismatched factor and zero-current phase advance are large, the chaotic movements of particles aggravate the transverse scatter of particles and serious results will happen if halo-chaos is not controlled. The simulated results also show that scraper can only scrape halos outside the core but can't hold back particles scattering from it, and halos regenerated. Therefore, we can make the conclusion that using controller control halo-chaos is an effective method. In the last part, in order to solve existed problems in the controllers, based on the proportional and differential controller which is a classical control in control theory, a new adaptive controller, whose form is has been proposed to control halo-chaos. In order to avoid too large controlling inte...
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