Simulation Investigation On Control Of Beam Halo-chaos By Selecting Ion Numbers Ratio As Controlling Variable And Broadening The Spectrum Of Zero-current Phase Advance

The physics of beam halo-chaos and its controlling methods are summarized , and some problems unsolved and outlooks are offered in this paper. Based on these , the main two parts research work of this dissertation are as follows: In the first part , the problem on the control of beam halo-chaos by selecting ion numbers ratio as controlling variable is investigated .The control of beam halo-chaos has been a key issue for the development of new high-power accelerators .Many nonlinear controllers have been constructed since the method of controlling beam halo-chaos by using nonlinear functions was offered in ref.[1] .Most of the controllers control beam halo-chaos effectively by simulation ,which enhanced people's interest in the nonlinear controlling method .The maximum radius r_max, root-mean-square radius r_rms , envelope radius r_b of ion beams ,and so on are chosen as controlling variable to simulate the control of beam halo-chaos in high intensity accelerator. Wavelet-function controller , delayed feedback controller , adaptive controller and some others choosing r_rms or r_b as controlling variable depress beam halo-chaos better ( ref.[2-5] ),while it's very difficult and not operational in experiment to probe several times all ions'positions of the beams every single period for calculating the rr ms or rb . In order to solve the problems on the controllers , the ratio of the number of ions outside the match radius to the total ion number λ( λ=NNa,here N a denotes the number of ions outside the match radius , N denotes the total ion number ) is selected as controlling variable to simulate the control of beam halo-chaos in high intensity accelerator by using multi-particle code (PIC code ) .The main rational for choosing λas controlling variable is that probing λonly needs to probe how many ions are outside the match radius ,not need to probe anything about ions inside the match radius and not need to probe the positions of ions outside the match radius , which means probing λmay be operational in experiment as compared with calculating rr ms and rb . A sine-function controller is constructed firstly: G = gsinλ(1) Simulation results show that the controller control halo-chaos for beams of K-V initial distribution fairly well ,which means that it may be operational to depress beam halo-chaos in simulation by selecting λas controlling variable .But further investigation shows that the controller can't depress halo-chaos for beams of other distributions . A logarithm-function controller is proposed after analysis and much simulation in order to control beams of several initial diatributions: G = gln(1 ?λ) (2) Simulation results show that the controller control halo-chaos for beams of five different initial distributions fairly well, respectively. It's effective as other controllers ,and the controlling variable λis easier to probe than rr ms and rb , so the nonlinear controlling method may be applied at last by selecting the controlling variable which is easier to be probed . In the other part , the problem on broadening the spectrum of zero-current phase advance σ0 is researched in this paper . Much research on the effect of parameters on beams has been made by using single controller and the difference of beams induced by the different controllers has not beenconsidered and the controlling variable applied by the controllers is rr ms, which is difficult and not operational in experiment . Based on the research , the problem on broadening the spectrum of zero-current phase advance σ0 is investigated by adopting the logarithm-function controller and wavelet-function controller to investigate the influence of σ0 on ion beams of K-V initial distribution ,respectively . The conclusions from the simulation are as follows. First , the spectrum of σ0 is broadened significantly when controllers are used to control the beams as compared with that of σ0when no controllers are used ,which means the electric current maybe be increased .Secondly , there are difference between the spectrums of σ0 when the controllers are different even if the initial beams there are no difference , and that one controller can't control beam halo-chaos under a particular σ0 doesn't means that other controllers can't control beam halo-chaos under the same σ0. So it's very necessary to find new controllers and controlling methods in order to increse the electric current as significantly as possible .