Control of Beam Halo-Chaos for an Intense Charged-Particle Beam Propagating Through Double Periodic Focusing Field by Soliton

Abstract

We study an intense beam propagating through the double periodic focusing channel by the particle-core model, and obtain the beam envelope equation. According to the Poincare-Lyapunov theorem, we analyze the stability of beam envelope equation and find the beam halo. The soliton control method for controlling the beam halo-chaos is put forward based on mechanism of halo formation and strategy of controlling beam halo-chaos, and we also prove the validity of the control method, and furthermore, the feasible experimental project is given. We perform multiparticle simulation to control the halo by using the soliton controller. It is shown that our control method is effective. We also find the radial ion density changes when the ion beam is in the channel, not only the halo-chaos and its regeneration can be eliminated by using the nonlinear control method, but also the density uniformity can be found at beam's centre as long as an appropriate control method is chosen.

An optimal expression of a Kraus operator as a linear combination of unitary matrices

“…A quantum circuit proposed in ( [4], see also footnote 3, and [6]) can satisfy our need, and the operator E 0 is called a duality gate or generalized quantum gate in this circuit ( [4], see also footnote 3, and [6,[16][17][18][19][20]). It has a clear interference interpretation.…”

“…This process is known as post-selection and is widely used in optical quantum computation [3]. This process can also be used to design damped quantum algorithms ( [4] 3 and [5][6][7][8][9]) and to simulate the evolution of the parity-timesymmetric Hamiltonian system [10][11][12].…”