Comparison of beam-position-transfer functions using circular beam-position monitors

A cylindrical beam-position monitor (BPM) used in many accelerator facilities has four electrodes on which beam-image currents induce bunched-beam signals. These probe-electrode signals are geometrically configured to provide beam-position information about two orthogonal axes. An electronic processor performs a mathematical transfer function (TF) on these BPM-electrode signals to produce output signals whose time-varying amplitude is proportional to the beam´s vertical and horizontal position. This paper compares various beam-position TFs using both pencil beams and further discuss how diffuse beams interact with some of these TFs