Manipulation of transverse emittances in circular accelerators by crossing non-linear 2D resonances

TL;DR

This paper introduces a novel method for controlling and manipulating transverse emittances in circular accelerators by crossing non-linear 2D resonances, extending existing techniques that previously affected only one transverse plane.

Contribution

It generalizes the resonance crossing technique to influence both transverse planes simultaneously, supported by theoretical Hamiltonian analysis and realistic simulations.

Findings

Effective manipulation of both transverse emittances demonstrated

Theoretical and simulation results confirm feasibility

Potential for improved beam control in accelerators

Abstract

Controlling non-linear effects in the transverse dynamics of charged particle beams in circular accelerators opens new possibilities for controlling some of the beam properties. Beam splitting by crossing a stable 1D non-linear resonance is part of the routine operation of the CERN Proton Synchrotron. The beam undergoes trapping and transport inside stable islands created in the horizontal plane to allow multi-turn extraction towards the Super Proton Synchrotron, where the beam is used for fixed-target experiments. This process acts only on the horizontal beam emittance, inducing a reduction of its initial value. In this paper, we present a generalisation of this approach, in which both transverse planes are affected by the proposed technique. We will discuss in detail how to manipulate the transverse emittances by means of a controlled crossing of a 2D non-linear resonance. The novel technique will be presented by discussing the theoretical analysis of a Hamiltonian model, as well as simulating the performance of the proposed manipulation using a more realistic non-linear symplectic map.