Self-consistent treatment of Intra Beam Scattering, betatron coupling, and vertical dispersion in fourth generation light sources

Abstract

The X-ray brightness delivered by fourth-generation light sources strongly depends on the electron beam current and transverse emittance. Reaching higher brilliance and lower emittances are increasingly limited by intra beam scattering, particularly at low and medium beam energies, where low emittances combined with high beam currents result in large phase-space densities. Increasing the vertical emittance through betatron coupling is commonly employed to mitigate intra beam scattering by relaxing the phase-space density. However, the redistribution of damping partition numbers due to coupling, the presence of vertical dispersion, and consequently their impact on the balance between synchrotron radiation and intra beam scattering are often neglected. In this work, we develop a self-consistent Ordinary Differential Equations-based framework to describe both the steady-state and time evolution of three-dimensional beam emittances in the simultaneous presence of synchrotron radiation, quantum excitation, betatron coupling, vertical dispersion, and intra beam scattering; allowing for realistic damping partition numbers. The model consistently accounts for the modification of synchrotron radiation damping rates and intra beam scattering growth rates arising from betatron coupling. Application to the BESSY III lattice demonstrates that damping partition redistribution and optics modifications significantly influence the equilibrium emittances. A systematic comparison of vertical emittance generation via a transverse feedback-generated excitation, betatron coupling, and vertical dispersion highlights the trade-offs between horizontal emittance reduction and operational constraints.

Figures (8)

• Figure 1: Simulated and calculated (using Eq. \ref{['eq:eps_ss']}) projected emittances against the coupling coefficient for different tune separations.
• Figure 2: Simulated and calculated projected emittance ratios against the coupling coefficient for $\Delta = 10^{-3}$.
• Figure 3: Beta functions and transverse dispersion along a superperiod in the uncoupled and fully coupled cases (using the betatron coupling knob), for $(Q_x, Q_y) = (44.224 - \Delta/2,\; 12.224 + \Delta/2)$ and $\Delta = 10^{-3}$.
• Figure 4: Beta functions and transverse dispersion along a superperiod in the uncoupled and lightly coupled cases (using the vertical dispersion knob), for $\varepsilon_y / \varepsilon_x = 0.1$.
• Figure 5: Time evolution of the transverse projected emittances obtained with the reference and proposed methods.