Analytical and numerical calculation of the second-order moment of the beam using a capacitive pickup

Abstract

Beam emittance has particular importance in particle physics, because it provides information about the quality of the particle beam. There are many techniques for measuring the beam emittance, such as that proposed by Miller et al. [Report No. SLAC-PUB-3186, (A) (1983)]. This technique is based on determining the emittance by measuring the second-order moment of the beam using quadrupole pickups consisting of four symmetrical electrodes placed around the beam pipe at 90° intervals, respectively. Based on Miller’s approach, two signal processing methods are generally used to get the quadrupole moment of the beam, namely the difference over sum and the log ratio [P. Li et al., IEEE Nuclear Science Symposium Conference Record, N24-404, 2007, pp. 1675–1678] methods. However, these traditional methods provide results with a good accuracy only for a well centered beam. The method presented in this paper, which starts with Miller’s approach, considerably reduces the impact of the dipole signal on the quadrupole moment measurement for both small and large values of the beam position. Furthermore, a methodology for the numerical determination of the sensitivity of quadrupole pickups will be presented.