Single-shot measurement of transverse second moments using the projection method

Abstract

We introduce a diagnostic for measuring the transverse phase space (TPS) and transverse second moments of a particle beam in a single shot. The diagnostic consists of a slit followed by a simple projection beam line to project the TPS onto an imaging screen. The beam line is composed of a skew quadrupole magnet followed by a normal quadrupole magnet with an imaging screen at the end. The skew quadrupole generates a coupling between the initial $x$ and the final $y$, while the normal quadrupole removes the correlation between the initial $x$ and the initial ${x}^{\ensuremath{'}}$. Thus, the initial $(x,{x}^{\ensuremath{'}})$ is mapped onto the final $(x,y)$. The slit is needed before the projection beam line to remove the initial $(y,{y}^{\ensuremath{'}})$ contribution from the final $(x,y)$ image on the screen. We present simulation studies and a demonstration of the diagnostic with an experiment performed at Argonne Wakefield Accelerator facility. We also discuss the method's limitations.