الاهتزازات المترافقة للجسيمات في المسرّع سريع

الملخص الأصلي

كما كتبه المؤلفون، بالإنجليزية arXiv:2603.04195

Coupled beam optics can be geometrically described in terms of invariant eigenmode planes of a stable symplectic ``one-turn'' map $$\mathcal M\in Sp(4)$$. We show that the non-uniqueness of symplectically normalized bases within each eigenmode plane constitutes an in-plane gauge freedom $$Sp(2)\times Sp(2)$$, and that many coupled-optics parametrizations differ primarily by gauge choice. Building on this fact, we identify basis-independent descriptors of lattice and beam optics and introduce bounded, gauge-invariant coupling parameters or fractions $$u_{k,\mathrm{inv}}$$ computed from orthogonal projectors onto the eigenmode planes. To obtain smooth $$s$$-dependent optics functions and consistent mode labeling, we present a unifying and practical approach based on an $$SO(2)$$ continuity gauge (Procrustes alignment), together with diagnostics for stability and invariance. We further relate Edwards--Teng, Mais--Ripken, Lebedev--Bogacz, Wolski, and Sagan--Rubin parametrizations as gauge-equivalent representations within the respective $$Sp(2)\times Sp(2)$$ gauge freedom. Numerical examples of coupled lattices and beam optics illustrate the proposed invariants and show how representation-dependent scalar coupling parameters (e.g.\ in the Lebedev--Bogacz gauge) can leave their nominal bounds while $$u_{k,\mathrm{inv}}$$, defined here, remain bounded and physically interpretable.