The Simulation On The Time For Achieving Beam Halo-chaos On High Intensity Ion Beam

Based on the particle-core model, as well as the beam halo-chaos control theory, and reviewing the results of controlling beam halo-chaos by four typical nonlinear controllers, as well as the particles tracking of high intensity ion beam with five initial distributions, we study the time for achieving controlling beam halo-chaos on high intensity ion beam with K-V distribution ,under four typical nonlinear controllers, analyze the reasons for the different time under different controllers'controlling ,and found on the results above, we find the methods to develop logarithm-function controller. The simulative results demonstrate that the ameliorated logarithm-function controller achieves controlling quicker and more effective than before.High-intensity accelerators and high-intensity ion beam have extensive application and developing foreground. But the beam halo-chaos produced by high intensity ion beam results in serious dangers, which has raised wide attraction in the world. Considering this, Prof.Fang Jin-qing, who works in the Institute of Atomic Energy of China, applied firstly the theory and methods of chaos controlling to control beam halo-chaos by using nonlinear functions. On the basis of their work, the former people had found Wavelet function controller,delayed-feedback controller and self-adaptive controller at first. But these controllers select root-mean-square radius as controlling variable, which is very difficult to measure. So later a new controller----logarithm-function controller was presented, which selects ions number ratio that can be measured in experiment as controlling variable. The simulative results show that these nonlinear controllers are all able to achieve controlling beam halo-chaos effectively in theory. If the beam halo-chaos can be controlled quickly, then there will be less damages to the body and the environment around. So there are more questions needed to be considered for the application of controllers, for example the efficiency of the controllers. We mainly study the following two aspects by using Particle-In-Cell simulations procedure in this paper.(1) The time for Wavelet function controller, delayed-feedback controller, self-adaptive controller and logarithm-function controller to achieve controlling beam halo-chaos is investigated, on two conditions as following: when the beam mismatches too much(M=2.0),the beam halo-chaos appears at the very start, so the controllers are joined at the beginning; when the beam mismatches less(M=1.5),the beam halo-chaos appears after a short time, so the controllers are joined when the halo-chaos strength factor H reaches the initial H of the first condition. The simulative results indicate that when the mismatch factor M=2.0 and the filling factorΓ=0.8,or the mismatch factor M=1.5 and the filling factorΓ=0.4, self-adaptive controller is the first to suppress halo-chaos, delayed-feedback controller and Wavelet function controller are in the next place, while logarithm-function controller needs more time than others, and can achieve controlling just when the filling factor is large. But, if the conditions are satisfied, the beam halo-chaos can be controlled at the beginning when the filling factor is large (Γ= 0.8) and the logarithm-function controller is joined before the beam halo-chaos appears.(2)The second work is to find another method to ameliorate logarithm-function controller when the beam halo-chaos appears in the very start. We firstly perform the PIC simulation procedure to track one ion randomly selected in a beam with KV distribution, and then analyze the change of the ion's force and movement along with r that denotes the distance from the ion to origin, and finally investigate the reasons for different time under different controllers'controlling. The simulative results show the reasons why logarithm-function controller needs more time in controlling beam halo-chaos is that the controlling force offered by logarithm-function controller just has repellent effect and doesn't has focused effect on the ion in every phase of the contrail. The results also indicate why Wavelet function controller and delayed-feedback controller have not only repellent effect but also focused effect is that their controlling functions have plus as well as negative values, namely, G>0 and G<0 in the four processes of the contrail; and why self-adaptive controller has focused effect all the time is that its controlling function just has negative values, namely, G<0 in the four processes of the contrail. Grounded on the results above, we can ameliorate logarithm-function controller through removing the coordinate of it, so that its controlling force takes place such like that of Wavelet function controller and delayed-feedback controller or self-adaptive controller. Consequently, we apply the ameliorated logarithm-function controller to control halo-chaos, when the halo-chaos appear at the very start. The simulative results indicate that the ameliorated logarithm-function controller achieves controlling quicker than before. Furthermore, when the filling factor is small, it also acquires effectual controlling outcome. Because the controlling force of the second ameliorated logarithm-function controller just has focused effect like the magnetic field, we substitute it for the magnetic field. In this way, not only the time is reduced, but also the material can be economized.In this paper, according to the investigation of the time for achieving beam haol-chaos under four typical controllers and the analysis on the reasons for the fast control and slow control, we have found methods to ameliorate logarithm-function controller. When the ameliorated logarithm-function controller is used to control beam haol-chaos, the time for achieving controlling is cut down and the focused materials can be saved, too. However, more researches are needed to do. If the beam halo-chaos can be controlled effectively without magnetic in reality, the practicability of logarithm-function controller is further advanced, and it will offer the consult to the design of the high-intensity accelerators.