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It has been realized in recent years that coupled focusing lattices inaccelerators and storage rings have significant advantages over conventionaluncoupled focusing lattices, especially for high-intensity charged particlebeams. A theoretical framework and associated tools for analyzing the spectraland structural stability properties of coupled lattices are formulated in thispaper, based on the recently developed generalized Courant-Snyder theory forcoupled lattices. It is shown that for periodic coupled lattices that arespectrally and structurally stable, the matrix envelope equation must admitmatched solutions. Using the technique of normal form and pre-Iwasawadecomposition, a new method is developed to replace the (inefficient) shootingmethod for finding matched solutions for the matrix envelope equation.Stability properties of a continuously rotating quadrupole lattice areinvestigated. The Krein collision process for destabilization of the lattice isdemonstrated.

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