Emittance dilution due to the betatron mismatch in high-intensity hadron accelerators

The importance of the betatron mismatch between two sections of an accelerator complex was recognized a long time ago. The mismatch together with the filamentation effect will result in a larger diluted beam emittance. However, the influence of the mismatch was underestimated largely in high-intensity hadron synchrotrons in the literature, as the rms emittance is used to represent the dilution. The dilution on the total emittance is significantly larger, which is of more importance in representing the beam loss in proton synchrotrons. This article points out the necessity of using the dilution factor of the total emittance together with the rms emittance in high-intensity hadron accelerators. A proof is given to show that the dilution factor of the rms emittance is the same for any initial beam distribution. The detailed beam distribution after the dilution is discussed for the initial uniform, Gaussian and parabolic distributions, and the numerical simulation results are presented. Examples and discussions about the betatron mismatch in the cases of injection, FODO channel transporting mixed H− and proton beams, fast-changing periodic focusing systems and proton linacs of a large tune depression are also presented.