Applicability of the small-κ expansion to large-time regimes in BLTP radiation reaction

Determine how far in time one can extend the small-κ power-series expansion (in κ^n) of the Bopp–Landé–Thomas–Podolsky self-force to obtain mathematically accurate approximations to BLTP solutions for a point charge undergoing straight-line acceleration by a constant applied electric field.

Background

The paper computes radiation-reaction effects in BLTP electrodynamics up to order κ^4 for the straight-line acceleration problem and finds that lower-order truncations can be accurate for short times but may fail for longer times even in parameter regimes where κ e^2/(|m| c^2) ≪ 1. This raises the question of the practical and mathematical range of validity of the perturbative series when more terms are included.

Clarifying the time horizon over which higher-order κ-expansions remain accurate would inform whether perturbative BLTP analyses suffice for long-time dynamics or whether non-perturbative approaches are required.