Analytical method for the calculation of beam to button electrode coupling Available to Purchase

For ultrarelativistic beams, standard 2D electrostatic techniques provide an accurate analytical method for calculating the size and placement of beam position monitor (BPM) electrodes that have constant transverse cross section, such as striplines. For circular electrodes the effect of the longitudinal variation of the cross section of the button must be included. This paper, using only the basic field equations along with charge and energy conservation, presents an exact analytical method to calculate this effect. The field due to the beam is idealized as a TEM wave and its coupling to the button on the vacuum chamber wall is calculated. The coupled fields are then decomposed into the wave modes supported by the button and its associated cylindrically symmetric structures between it and the output coaxial transmission line. This method yields a simple and intuitive result for the transmitted signal while also providing the exact result for the signal reflected back into the vacuum chamber. The technique can be used in conjunction with the 2D techniques to optimize the geometrical design of the BPM. Extension of this method to other electrode geometries is straightforward.