On the adiabaticity of emittance exchange due to crossing of the coupling resonance

TL;DR

This paper develops a theoretical framework based on adiabatic invariance to analyze how crossing the linear coupling resonance in circular accelerators causes emittance exchange, providing detailed explanations of the process.

Contribution

It introduces a Hamiltonian-based theoretical approach to understand emittance exchange during resonance crossing, advancing previous numerical and conceptual studies.

Findings

The framework explains the adiabatic nature of emittance exchange.

It clarifies the conditions under which emittance exchange occurs.

The theory aligns with and explains previous numerical results.

Abstract

In circular accelerators, crossing the linear coupling resonance induces the exchange of the transverse emittances, provided the process is adiabatic. This has been considered in some previous works, where the description of the phenomenon has been laid down, and, more recently, where a possible explanation of the numerical results has been proposed. In this paper, we introduce a theoretical framework to analyze the crossing process, based on the theory of adiabatic invariance for Hamiltonian mechanics, which explains in detail various features of the emittance exchange process.