Identify the source of the remaining multiparticle code discrepancy

Identify the cause of the remaining few-percent discrepancy between HELIX and TraceWin multiparticle rms observables after accounting for input-distribution sampling, finite-particle shot noise, and output-grid effects.

Background

The HELIX and TraceWin multiparticle benchmarks agree at the few-percent level, but a stable residual remains in transverse moments and emittances. The paper investigates several possible explanations, including independently sampled input bunches, finite-macroparticle statistical noise, differing diagnostic grids, and differences between the two space-charge implementations.

The authors narrow the leading candidates to the space-charge treatments, mesh choices, and statistical effects, but do not determine which mechanism is responsible for the residual. The unresolved attribution limits interpretation of the remaining cross-code disagreement.

References

The exit reference energies, by contrast, agree to better than $10{-4}$ relative in both modes (10.2614 and \SI{10.2625}{\mega\electronvolt} for envelope and multiparticle against TraceWin's 10.2622 and \SI{10.2624}{\mega\electronvolt}), confirming that the rf energy-gain model is essentially exact; the space-charge treatments, together with the codes' different meshes and the $\sim$1\% shot-noise floor of $104$ macroparticles, remain the leading candidates for the transverse residuals above, though the cause has not been isolated.

— HELIX: a hybrid envelope-multiparticle linac code with differentiable space-charge optimization  (2609.04421 - Pathak, 3 Sep 2026) in Section 7.5, “Comparison with TraceWin on PIP-II lattices”