Matching small $beta$ functions using centroid jitter and two beam position monitors

Matching to small beta functions is required to preserve emittance in plasma accelerators. The plasma wake provides strong focusing fields, which typically require beta functions on the mm-scale, comparable to those found in the final focusing of a linear collider. Such beams can be time consuming to experimentally produce and diagnose. We present a simple, fast, and noninvasive method to measure Twiss parameters in a linac using two beam position monitors only, relying on the similarity of the beam phase space and the jitter phase space. By benchmarking against conventional quadrupole scans, the viability of this technique was experimentally demonstrated at the FLASHForward plasma-accelerator facility.