Spectral and structural stability properties of charged particle dynamics in coupled lattices

TL;DR

This paper develops a theoretical framework based on generalized Courant-Snyder theory to analyze the spectral and structural stability of coupled lattices in accelerators, introducing new methods for stability analysis and demonstrating the destabilization process.

Contribution

It introduces a new analytical framework and computational methods for stability analysis of coupled lattices, advancing understanding of their stability properties in accelerator physics.

Findings

Matched solutions are necessary for stable periodic coupled lattices.

A new method replaces the shooting method for finding matched solutions.

The Krein collision process can destabilize the lattice.

Abstract

It has been realized in recent years that coupled focusing lattices in accelerators and storage rings have significant advantages over conventional uncoupled focusing lattices, especially for high-intensity charged particle beams. A theoretical framework and associated tools for analyzing the spectral and structural stability properties of coupled lattices are formulated in this paper, based on the recently developed generalized Courant-Snyder theory for coupled lattices. It is shown that for periodic coupled lattices that are spectrally and structurally stable, the matrix envelope equation must admit matched solutions. Using the technique of normal form and pre-Iwasawa decomposition, a new method is developed to replace the (inefficient) shooting method for finding matched solutions for the matrix envelope equation. Stability properties of a continuously rotating quadrupole lattice are investigated. The Krein collision process for destabilization of the lattice is demonstrated.