Abstract
Betatron coupling is usually analyzed using either matrix formalism or Hamiltonian perturbation theory. The latter is less exact but provides a better physical insight. In this paper direct relations are derived between the two formalisms. This makes it possible to interpret the matrix approach in terms of resonances, as well as use results of both formalisms indistinctly. An approach to measure the complete coupling matrix and its determinant from turn-by-turn data is presented. Simulations using methodical accelerator design MAD-X, an accelerator design and tracking program, were performed to validate the relations and understand the scope of their application to real accelerators such as the Relativistic Heavy Ion Collider.
Highlights
Betatron coupling in circular accelerators has been widely studied using both matrix formalism and Hamiltonian perturbation theory
We propose a method to calculate C21 given C12, C11, and C22 at two locations with an arbitrary phase advance in both normal modes
In a coupler free region C matrix is propagated by an arbitrary phase advance in both modes, which is given by [9]
Summary
GSI, Planckstrasse 1, 64291 Darmstadt, Germany (Received 7 December 2004; published 9 March 2005). Betatron coupling is usually analyzed using either matrix formalism or Hamiltonian perturbation theory. The latter is less exact but provides a better physical insight. In this paper direct relations are derived between the two formalisms. This makes it possible to interpret the matrix approach in terms of resonances, as well as use results of both formalisms indistinctly. An approach to measure the complete coupling matrix and its determinant from turn-by-turn data is presented. Simulations using methodical accelerator design MAD-X, an accelerator design and tracking program, were performed to validate the relations and understand the scope of their application to real accelerators such as the Relativistic Heavy
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