Measuring the full transverse beam matrix using a single octupole

We propose a method to fully determine the transverse beam matrix using a simple setup consisting of two steering magnets, an octupole field and a screen. This works in principle for any multipole field, i.e., sextupole, octupole magnet or a radio frequency structure with a multipole field. We have experimentally verified the method at the Compact Linear Collider Test Facility 3 at CERN using a Compact Linear Collider accelerating structure, which has an octupole component of the radio frequency fields. By observing the position shifts of the beam centroid together with changes in transverse beam size on a screen, we determined the full transverse beam matrix, with all correlations.