Determination of Proton Beam Waist Positions Using Beam Position Monitors

Abstract: In this work, we examine a novel method for the determination of proton beam waist locations using beam position monitors. Based on the lattice of the final transport line section of the European Spallation Source linac, a simplified version of the beam line composed of quadrupole magnets and correctors is constructed in Python using a matrix formalism. With a known set of Courant-Snyder parameters at the final position of the beam line and a known beam emittance, a set of final beam centroid positions are calculated lying over the 1σ phase space ellipse at that point. Applying the initial condition that all beam centroids are initially placed at the origin, the necessary corrector strength values required to transport the centroids to their final positions along the ellipse are then calculated by solving a coupled system of equations. Beam centroid trajectories are then plotted along with the beam envelope. Space charge effects are shown to be negligible for this work, meaning that beam centroid waist positions will coincide with envelope waist positions. Two BPMs position readings are then used to calculate the waist location. The method presented in this work reliably determines waist locations with the most significant deviations from benchmark values being 0.03 m for the design lattice and 0.14 m for a lattice featuring significant quadrupole errors.