Emittance sharing and exchange driven by linear betatron coupling in circular accelerators

The influence of linear betatron coupling due to constant-in-time skew quadrupolar fields on the transverse emittances is discussed using both a simplified model of a smooth circular accelerator and a more realistic strong-focusing lattice with localized sources of coupling (thin lens). New formulas for the coupled transverse emittances are derived that include the initial emittances, the coupling strengths, and the tune distance from the resonance. By using the more powerful Lie algebra and the resonance driving terms formalism, equivalent formulas are derived that provide a better understanding of some counterintuitive effects, otherwise not understandable in the smooth approximation. The new formulas have been tested both numerically and experimentally by using data of the CERN Proton Synchrotron showing a remarkable agreement.