Determine whether observed low-amplitude oscillations indicate transverse instabilities or betatron oscillations

Determine whether the low-amplitude oscillations observed in the trailing bunch at the end of the underloaded wakefield simulation represent transverse beam-breakup instabilities or are instead energy-dependent betatron oscillations of longitudinal slices within the trailing bunch.

Background

In the underloaded-case simulations, the trailing bunch exhibits low-amplitude oscillations. Distinguishing whether these oscillations are caused by transverse instabilities (e.g., beam-breakup driven by short-range transverse wakefields) or simply reflect energy-dependent betatron motion is crucial for interpreting spectrometer data and quantifying instability growth.

The authors propose an imaging-spectrometer-based method to map the x'–E charge distribution to quantify oscillation amplitudes, but explicitly note that further analysis is required to ascertain the nature of the observed oscillations in this scenario.