Abstract
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.
Highlights
Emittance transfer between the transverse planes in circular accelerators has been widely studied in the framework of betatron linear coupling [1,2,3]
Equations governing the emittance transfer have been already derived from single-particle differential equations, in the smooth approximation and assuming a uniformly distributed skew quadrupolar field [1,2]
A more general treatment has been derived in the C matrix formalism
Summary
Emittance transfer between the transverse planes in circular accelerators has been widely studied in the framework of betatron linear coupling [1,2,3]. In machines with unsplit tunes (l 0), when the space-charge forces are no longer negligible, even in the absence of linear betatron coupling similar effects of emittance sharing and exchange have been observed, both in numerical simulations [8] and in measurements [9]. Formalism as illustrated in [10] to derive analogous equations describing the emittance transfer as a function of the RDT, in the static as well as in the dynamic case These new relations describe the emittance transfer to higher accuracy than the existing formulas. The transverse RMS emittances, averaged over a number of turns N 1=jCj, are coupled according to x x0 These equations were derived in the 1970s [1,2] with the aim of increasing the injection efficiency of both the CERN.
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