Parametrization, characterization, and optimization of double-bend achromat cell

Abstract

We continue the study of single-particle dynamics in a more realistic cell, namely the double-bend achromat with three families of quadrupoles. The cell is parameterized with the optical parameters including the phase advances and the horizontal beta functions at its entry and center. At zero chromaticity, we find that the landscape of the dynamic aperture in the tune plane can be captured by a simple formula constructed from the effective Hamiltonian of 4th order. Furthermore, the optimal dynamic aperture can be found by simply minimizing the third-order driving terms with equal weight in the effective Hamiltonian.