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 studied using the particle-core model. The beam halo-chaos is found, and an idea of fraction power-law function controller is proposed based on the mechanism of halo formation and the strategy of controlling halo-chaos. The method is applied to the multi-particle simulation to control the halo. The numerical results show that the halo-chaos and its regeneration can be eliminated effectively by using the fraction power-law function control method. At the same time, the radial particle density is uniform at the beam's center as long as the control method and appropriate parameter are chosen