Abstract
The effect of the coherent synchrotron radiation (CSR) becomes evident, and leads to increased beam energy spread and transverse emittance dilution, as both the emittance and bunch length of the electron beams are continuously pushed down in present and forthcoming high-brightness light sources and linear colliders. Suppressing this effect is important to preserve the expected machine performance. Methods of the R-matrix analysis and the Courant-Snyder formalism analysis have been proposed to evaluate and to suppress the emittance growth due to CSR in achromatic cells. In this paper a few important modifications are made on these two methods, which enable us to prove that these two methods are equivalent to each other. With the modified analysis, we obtain explicit and generic conditions of cancelling the CSR-driven emittance excitation in a single achromat consisting of two dipoles of arbitrary bending angles. In spite of the fact that the analysis constrains itself in a linear regime, based on the assumption that CSR-induced particle energy deviation is proportional to both theta and rho(1/3), with theta being the bending angle and rho the bending radius, it is demonstrated through ELEGANT simulations that the conditions derived from this analysis are still effective in suppressing the emittance growth when a more detailed one-dimensional CSR model is considered. In addition, it illustrates that the emittance growth can be reduced to a lower level with the proposed conditions than with the other two approaches, such as matching the beam envelope to the CSR kick and setting the cell-to-cell betatron phase advance to an appropriate value.
Highlights
Electron beams with low transverse normalized emittance, short bunch length, and high peak current are generated or expected in high-brightness light sources and linear colliders. In these machines as beams pass through bending magnets, the emission of the coherent synchrotron radiation (CSR) leads to beam quality degradation, by inducing increased beam energy spread and causing transverse emittance dilution
This method was recently expanded [25] with the Courant-Snyder (C-S) formalism, where the emittance growth is related to the beam C-S parameters and a single-kick approximation of the CSR effect is adopted
By adopting a few important modifications on the R-matrix analysis and the C-S formalism analysis, we have derived the generic conditions for eliminating the CSR kick in a linear regime applicable to a two-dipole achromat with dipoles of arbitrary bending radii and bending angles
Summary
Electron beams with low transverse normalized emittance (at the μm · rad or sub − μm · rad scale), short bunch length (at the subpicosecond scale), and high peak current (up to thousands of amperes) are generated or expected in high-brightness light sources (see, e.g., [1,2,3,4,5]) and linear colliders (see, e.g., [6]). One approach [13] is to cancel the CSR kick through finely tuning the betatron phase advance between identical cells to an appropriate value and imposing certain symmetric conditions on the transport system (hereafter this approach will be denoted by the optical balance method) This method was recently expanded [25] with the Courant-Snyder (C-S) formalism, where the emittance growth is related to the beam C-S parameters and a single-kick approximation of the CSR effect is adopted. It turns out that with the proposed conditions the emittance growth can be reduced to a lower level than with the other two approaches
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