Error Minimization in Transverse Phase-Space Measurements Using Quadrupole Scan Based on Projection-Angle Uniformization

Abstract: In beam diagnostics, accurate determination of phase-space distributions plays a crucial role in beam prediction, control, and the understanding of beam dynamics. Among various techniques, quadrupole scan is the most widely used method for transverse phase-space reconstruction. However, in practical applications, this method is susceptible to various perturbations, including measurement noise, magnetic field errors, element nonlinearities, and installation uncertainties. When the scan parameters are improperly chosen, the impact of these perturbations on the reconstructed results can be significantly amplified, thereby affecting subsequent beam control and physical interpretation. To address this issue, this study systematically analyzes the influence of errors on the measurement process from the perspectives of linear algebra and geometric projection, and proposes a parameter optimization method capable of effectively quantifying error sensitivity. By comparing the error amplification characteristics under different focusing conditions, a criterion for parameter selection that minimizes reconstruction errors is established, leading to a more precise and accurate reconstruction of the initial phase-space distribution.