# Analysis of the non-linear beam dynamics at top energy for the CERN Large Hadron Collider by means of a diffusion model

## TL;DR

This paper models the non-linear beam dynamics at CERN's LHC using a diffusion model derived from Nekhoroshev theorem, accurately reproducing experimental dynamic aperture results at top energy.

## Contribution

It introduces a novel three-parameter diffusion model based on Nekhoroshev theorem to analyze LHC beam dynamics, providing a new theoretical approach.

## Key findings

- High accuracy reproduction of experimental dynamic aperture data
- Derivation of diffusion coefficient from Nekhoroshev theorem
- Enhanced understanding of non-linear beam behavior at top energy

## Abstract

In this paper the experimental results of the recent dynamic aperture at top energy for the CERN Large Hadron Collider are analysed by means of a diffusion model whose novelty consists of deriving the functional form of the diffusion coefficient from Nekhoroshev theorem. This theorem provides an optimal estimate of the remainder of perturbative series for Hamiltonian systems. As a consequence, a three-parameter diffusion model is built that reproduces the experimental results with a high level of accuracy. A detailed discussion of the physical interpretation of the proposed model is also presented.