Effect of impedance and higher order chromaticity on the measurement of linear chromaticity

Abstract

The combined effect of impedance and higher order chromaticity can act on the beam in a nontrivial manner which can cause a tune shift which depends on the relative momenta with respect to the “on momentum” particle (Δp/p). Experimentally, this tune shift affects the measurement of the linear chromaticity which is traditionally measured with a change of Δp/p. The theory behind this effect will be derived in this paper. Computer simulations and experimental data from the Tevatron will be used to support the theory.