Optimal matching control of a low energy charged particle beam in particle accelerators

Particle accelerators are devices used for research in scientific problems such as high energy and nuclear physics. In a particle accelerator, the shape of particle beam envelope is changed dynamically along the forward direction. Thus, this reference direction can be considered as an auxiliary “ time ” beam axis. In this paper, the optimal beam matching control problem for a low energy transport system in a charged particle accelerator is considered. The beam matching procedure is formulated as a finite “ time ” dynamic optimization problem, in which the Kapchinsky-Vladimirsky ( K-V ) coupled envelope equations model beam dynamics. The aim is to drive any arbitrary initial beam state to a prescribed target state, as well as to track reference trajectory as closely as possible, through the control of the lens focusing strengths in the beam matching channel. We first apply the control parameterization method to optimize lens focusing strengths, and then combine this with the time-scaling transformation technique to further optimize the drift and lens length in the beam matching channel. The exact gradients of the cost function with respect to the decision parameters are computed explicitly through the state sensitivity-based analysis method. Finally, numerical simulations are illustrated to verify the effectiveness of the proposed approach.