Accuracy and feasibility of the $\beta^*$ measurement for LHC and High Luminosity LHC using $k$ modulation

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.