| 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...
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