The E302 instability-versus-efficiency experiment at FACET-II

We discuss plans for the E302 instability-efficiency experiment, starting in 2024 at the recently upgraded FACET-II facility at SLAC National Accelerator Laboratory. The beam-breakup instability will be the main area of study for the E302 experiment. With the imaging spectrometer at FACET-II, we introduce a novel technique for observing and quantifying the amplitude growth of the trailing bunch due to the transverse instability. Using the transverse position on the spectrometer screen and the transfer matrix of the magnetic lattice used for the spectrometer, we aim to extract a $x'$-$E$ charge distribution that can be used to quantify the amplitude of the beam. By varying the trailing bunch's charge and, hence, the beam loading of the accelerating field, we aim to adjust the wake-to-beam power transfer efficiency in the E302 experiment. We plan to quantify the amplitude for different configurations of the beam charge and, hence, investigate the relationship between the beam-breakup instability and efficiency. We use a combination of particle-in-cell (PIC) codes to simulate a beam-driven plasma wakefield accelerator from start-to-end with a FACET-II-like spectrometer and demonstrate the methodology that will be used for the instability studies at the E302 experiment.