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 forwar...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.展开更多
An orthodox sceptical hypothesis claims that one’s belief that“I am not a brain-in-a-vat(BIV)”(or any other ordinary anti-sceptical belief)is insensitive.A form of sensitivity-based scepticism,can thus be construct...An orthodox sceptical hypothesis claims that one’s belief that“I am not a brain-in-a-vat(BIV)”(or any other ordinary anti-sceptical belief)is insensitive.A form of sensitivity-based scepticism,can thus be constructed by combining this orthodox hypothesis with the sensitivity principle and the closure principle.Unlike traditional solutions to the sensitivity-based sceptical problem,this paper will propose a new solution—one which does not reject either closure or sensitivity.Instead,I argue that sceptics’assumption that one's ordinary anti-sceptical beliefs are insensitive will give rise to self-contradiction.The orthodox sceptical hypothesis is thus revealed to be incoherent and arbitrary.Given that there is no coherent reason to presuppose our ordinary anti-sceptical beliefs to be insensitive,the argument for sensitivity-based scepticism can thus be blocked at a lower epistemological cost.展开更多
基金supported by the National Natural Science Foundation of China(61703114,61673126,61703217,U1701261)the Science and Technology Plan Project of Guangdong(2014B090907010,2015B010131014)
文摘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.
文摘An orthodox sceptical hypothesis claims that one’s belief that“I am not a brain-in-a-vat(BIV)”(or any other ordinary anti-sceptical belief)is insensitive.A form of sensitivity-based scepticism,can thus be constructed by combining this orthodox hypothesis with the sensitivity principle and the closure principle.Unlike traditional solutions to the sensitivity-based sceptical problem,this paper will propose a new solution—one which does not reject either closure or sensitivity.Instead,I argue that sceptics’assumption that one's ordinary anti-sceptical beliefs are insensitive will give rise to self-contradiction.The orthodox sceptical hypothesis is thus revealed to be incoherent and arbitrary.Given that there is no coherent reason to presuppose our ordinary anti-sceptical beliefs to be insensitive,the argument for sensitivity-based scepticism can thus be blocked at a lower epistemological cost.
