Determine the sources of the residual longitudinal-energy error

Determine the separate contributions of charge interpolation, neglected finite-field feedback, and numerical discretization to the residual difference in the longitudinal energy distribution between the composed and resolved structured-bunch calculations.

Background

For the resolved Gaussian-hole array, the matched structured–flat periodic composition reproduces the resolved phase space and most global and slice observables accurately. The largest remaining discrepancy occurs in the longitudinal energy distribution.

The paper identifies three possible sources—charge interpolation, neglected feedback from finite-bunch fields, and numerical discretization—but does not quantify their individual effects. Establishing these contributions would clarify the method’s error budget and guide improvements to the composition procedure.