In this paper, we focus our investigation on providing long-term estimates of the Hamiltonian
deviation computed along numerical approximations to the solutions of stochastic …

In hadron colliders, such as the Large Hadron Collider (LHC) to be built at CERN, the long-
term stability of the single-particle motion is mostly determined by the field-shape quality of …

Backward error analysis is a powerful tool in order to detect the long-term conservative
behavior of numerical methods. In this work, we present a long-term analysis of symplectic …

Noise can have severe impacts on particle beams in high-energy synchrotrons. In particular,
it has recently been discovered that noise combined with wakefields can cause a diffusion …

This book is focused on the numerical discretization of ordinary differential equations
(ODEs), under several perspectives. The attention is first conveyed to providing accurate …

Landau dam** of coherent modes is strongly dependent on the exact shape of the particle
bunches. One often assumes that the transverse distributions in high-energy hadron …

We consider the diffusion processes defined by stochastic differential equations when the
noise is correlated. A functional method based on the Dyson expansion for the evolution …

Controlling nonlinear effects in the transverse dynamics of charged particle beams in
circular accelerators opens new possibilities for controlling some of the beam properties …

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 …

In this paper, we consider stochastic Hamiltonian systems of Itô type driven by a
multiplicative small noise. It is well-known, indeed, that stochastic Hamiltonian problems are …