Analysis of the dynamic Faraday cup

The dynamic Faraday cup is an electrostatic device used to measure the charge and velocity of a moving charged particle. In this paper, the interaction between a charged particle and a dynamic Faraday cup is described analytically, including the difficult case where the particle is close to but not in the cup. A summation method is used to extract information from the slowly converging series that results from the approximation that we use, and we are able to determine the charge distribution and mutual capacitance of the system. An example of the calculated and measured responses of a typical Faraday cup is provided. The agreement between the calculated and measured response of the cup, given in terms of the standard deviation, is from 4.5 x 10-3 to 9.4 x 10-3 for the inside of the cup and from 3.3 x 10-2 to 3.6 x 10-2 for the outside of the cup