Controlling Beam Halo-Chaos Using Wavelet Function Feedback Method

Abstract

The wavelet function feedback method is proposed for controlling beam halo-chaos for high intensity proton beam in a periodic-focusing channel.After control for four different primary proton distributions,the halo intensity factor become zero,other statistical physical quantities (such as rrms and P2av) and relative average emittances are more than doubly reduced.Simulation results show that the method is very effective and has its prospect for application.

Controlling beam halo-chaos via backstepping design

“…In order to characterize the effects of halo-chaos under control, we adopt some statistical physical quantities as follows: [10,13] the halo-chaos strength factor H, which is defined as the ratio of the number of particles whose positions are larger than 1.75 r b0 to the number of total particles; the statistical average value of beam halo-chaos strength factor in each period, H av ; the maximum value of the average relative emittance ε av max corresponding to transverse direction; the transverse mean-square momentum P 2 av ; the maximal value of the ion beam radius r max . Table 1 summarizes the main results of controlling the beam halo-chaos with five types of initial ion distributions.…”

“…The root-mean-square radius of beam, r rms , as a measurable feedback variable, replaces the envelope radius r b in expression (19). Choosing a statistical physical quantity as a feedback variable has been reported in References [10,11]. Considering the actual time-lag between the observed input and the feedback response, and reducing the control cost, the control strategy is carried in each half of the period.…”

“…[3] How to suppress and control the beam halo-chaos is a very important and challenging subject in the sense of theory and practice. Fang and Chen [9] proposed a set of nonlinear feedback control methods based on the mechanism of control chaos, and the measurability to variables of complex system such as the wavelet-based function feedback, [10] the sample function feedback, [11] variables delayed feedback and variable structure method. [12,13] It will be valuable and realizable in engineering application if some external parameters (for example the exterior field) can be used to control the beam halo-chaos in a high-current accelerator.…”

Control of Beam Halo-Chaos with Sinc Function in a Uniform-Focusing Channel

“…Previous work has realized effective control on beam halo -chaos, using nonlinear feedback control method [1,2], variable structure control method [3], delayed feedback control method [4,5], parameter adaptive control method [6] and a series of methods [7,8] .Literature [9] uses nonlinear function to construct nonlinear function controller and to suppress beam halo -chaos, but it's not perating easily in actual project. Considering about project implementation and practical operation, this paper tries to use non-linear sinc function to realize effective control on beam halo -chaos.…”

Control of beam halo-chaos by Gauss function in the triangle periodic-focusing channel

“…At present, study of controlling the beam halochaos through a rectangle periodic-focusing channel or a uniform-focusing channel has been carried out in Refs. [7][8][9][10][11][12][13][14][15][16][17][18][19], but the high intensity beam through a triangle periodic-focusing channel has not been studied. In this paper, we investigate the beam halo-chaos in the triangle periodic-focusing magnetic field, and propose the idea of Gauss function controller of strong nonlinearity and stability for controlling the halo.…”