Synchronization and Control of Halo-Chaos in Beam Transport Network with Small World Topology

The synchronous conditions of two kinds of the small-world （SW） network are studied. The small world topology can affect on dynamical behaviors of the beam transport network （BTN） largely, if the BTN is constructed with the SW topology, the global linear coupling and special linear feedback can realize the synchronization control of beam halo-chaos as well as periodic state in the BTN with the SW topology, respectively. This important result can provide an effective way for the experimental study and the engineering design of the BTN in the high-current accelerator driven radioactive clean nuclear power systems, and may have potential use in prospective applications for halo-chaos secure communication.

Control of Halo-Chaos in Beam Transport Network via Neural Network Adaptation with Time-Delayed Feedback

Subject of the halo-chaos control in beam transport networks （channels） has become a key concerned issue for many important applications of high-current proton beam since 1990＇. In this paper, the magnetic field adaptive control based on the neural network with time-delayed feedback is proposed for suppressing beam halo-chaos in the beam transport network with periodic focusing channels. The envelope radius of high-current proton beam is controlled to reach the matched beam radius by suitably selecting the control structure and parameter of the neural network, adjusting the delayed-time and control coefficient of the neural network.

Nonlinear Control of Beam Halo-Chaos in Accelerator-Driven Clean Nuclear Power System

Beam halo-chaos in high-current accelerators has become a key concerned issue because it can cause excessive radioactivity from the accelerators therefore significantly limits their applications in industry,medicine,and national defense.Some general engineering methods for chaos control have been developed in recent years,but they generally are unsuccessful for beam halo-chaos suppression due to many technical constraints.Beam halo-chaos is essentially a spatiotemporal chaotic motion within a high power proton accelerator.In this paper,some efficient nonlinear control methods,including wavelet function feedback control as a special nonlinear control method,are proposed for controlling beam halo-chaos under five kinds of the initial proton beam distributions (i.e.,Kapchinsky-Vladimirsky,full Gauss,3-sigma Gauss,water-bag,and parabola distributions) respectively.Particles-in-cell simulations show that after control of beam halo-chaos,the beam halo strength factor is reduced to zero,and other statistical physical quantities of beam halo-chaos are doubly reduced.The methods we developed is very effective for suppression of proton beam halo-chaos in a periodic focusing channel of accelerator.Some potential application of the beam halo-chaos control in experiments is finally pointed out.

Controlling Beam Halo-Chaos via Time-Delayed Feedback

The study of controlling high-current proton beam halo-chaos has become a key concerned issue for manyimportant applications. In this paper, time-delayed feedback control method is proposed for beam halo-chaos. Particle incell simulation results show that the method is very effective and has some advantages for high-current beam experimentsand engineering.

Control of beam halo-chaos by sample function

The K-V beam through an axisymmetric uniform-focusing channel is studied using the particle-core model. The beam halo-chaos is found, and a sample function controller is proposed based on mechanism of halo formation and strategy of controlling halo-chaos. We perform multiparticle simulation to control the halo by using the sample function controller. The numerical results show that our control method is effective. We also find that the radial ion density changes when the ion beam is in the channel： not only can the halo-chaos and its regeneration be eliminated by using the sample function control method, but also the density uniformity can be found at the beam＇s centre as long as an appropriate control method is chosen.

Controlling beam halo-chaos via backstepping design

A backstepping control method is proposed for controlling beam halo-chaos in the periodic focusing channels （PFCs） of high-current ion accelerator. The analysis and numerical results show that the method, via adjusting an exterior magnetic field, is effective to control beam halo chaos with five types of initial distribution ion beams, all statistical quantities of the beam halo-chaos are largely reduced, and the uniformity of ion beam is improved. This control method has an important value of application, for the exterior magnetic field can be easily adjusted in the periodical magnetic focusing channels in experiment.

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

This paper studies the Kapchinsky-Vladimirsky （K-V） beam through a triangle periodic-focusing magnetic field by using the particle-core model. The beam halo-chaos is found, and an idea of Gauss function controller is proposed based on the strategy of controlling the halo-chaos. It performs multiparticle simulation to control the halo by using the Gauss function control method. The numerical results show that the halo-chaos and its regeneration can be eliminated effectively, and that the radial particle density is uniform at the centre of the beam as long as the control method and appropriate parameter are chosen.

Control of Beam Halo-Chaos by Fraction Power-Law Function in Hackle Periodic-Focusing Channel

The Kapchinsky Vladimirsky(K-V)beam through a hackle periodic-focusing magnetic field is studiedusing the particle-core model.The beam halo-chaos is found,and an idea of fraction power-law function controller isproposed based on the mechanism of halo formation and the strategy of controlling halo-chaos.The method is appliedto the multi-particle simulation to control the halo.The numerical results show that the halo-chaos and its regenerationcan be eliminated effectively by using the fraction power-law function control method.At the same time,the radialparticle density is uniform at the beam's center as long as the control method and appropriate parameter are chosen.

Multi-goal Control of Chaotic Connected Complex Networks

Beam transport network(BTN)with small world(SW)(so-called BTN-SW)and Lorenz chaotic connectednetwork with scale-free(SF)are taken as two typical examples,we proposed a global linear coupling and combined withlocal error feedback methods in sub-networks to realize multi-goal control method of halo and chaos in two networksabove.The simulation results show that the methods above is effective for any chaotic connected networks and has apotential of applications in based-halo-chaos secure communication.