Single-particle dynamics in theoretical minimum emittance cell

Abstract

We have developed a parametrization of the linear optics in a theoretical minimum emittance cell with three quadrupoles. It consists of five independent parameters: two phase advances, a dimensionless horizontal beta function at the center of the dipole, and a bending angle ϕ and a length L of the dipole. For the zero chromaticity cell, we again find that the dynamic aperture in the normalized phase space is scaled according to,Ā ∝ ϕ ffiffiffi ffi L p. Moreover, we study nonlinear dynamics near the third-order coupled resonances in the framework of the resonance normal form. In particular, we derive the effective Hamiltonians using the Lie algebra method and show that the periodic orbits in tracking can be interpreted as solutions of the Hamilton's equations. Surprisingly, we discover that the scheme is not only applicable to the single resonance but also to the double resonances.

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

“…(1) in Ref. [22], where w is the focus length of the quadrupole at the entry and H and L are the distances between the doublet to s 1 and s 2 , respectively.…”

“…(2) in Ref. [22] for the doublet and the matrices of a drift and thin quadrupole, we compute the transfer matrix from s 1 to s 2 and find…”

“…For FODO and TME cells, some analytical expressions can be found in Refs. [21,22], respectively. In the fourth order, the Hamiltonian can be separated into two parts:…”

“…In this paper, we will extend our work of the parametrized alternating focusing and defocusing (FODO) [21] and theoretical minimum emittance (TME) [22] cells to a more practical and realistic DBA cell. Again, for simplicity, we will set the chromaticity to zero with two families of sextupoles in the dispersive region.…”

Magnet Lattice Optimization for Novosibirsk Fourth Generation Light Source SKIF

“…This configuration received the name TME (Theoretical Minimum Emittance) [2][3][4][5][6] and factor F is…”