Accuracy and feasibility of the β^{*} measurement for LHC and High Luminosity LHC using k modulation

Abstract

The future regimes of operation of the LHC will require improved control of β^{*} measurements to successfully level the luminosities in the interaction points. The method of k modulation has been widely used in other machines to measure lattice beta functions. In the LHC, k modulation of the closest quadrupoles to the interaction point (IP) is the most accurate method to measure β^{*} at the IP. This paper highlights the challenge of high precision tune measurements (down to 10^{-5}) for the correct determination of β^{*} in the high luminosity LHC. Furthermore it presents a new analytical method for the calculation of β^{*} using k modulation.