An N-BPM Momentum Reconstruction for Linear Transverse Coupling Measurements in LHC and HL-LHC

The measurement and control of linear transverse coupling is important for the operation of an accelerator. The calculation of the linear transverse coupling resonance driving terms (RDTs) 𝑓1001 and 𝑓1010 relies on the complex spectrum of the turn-by-turn motion. To obtain the complex signal, a reconstruction of the particle motion is needed. For this purpose, the signal of a second BPM with a suitable phase shift is usually used. In this work, we explore the possibility of including more BPMs in the reconstruction of the transverse momentum, which could reduce the effects of statistical errors and systematic uncertainties. This, in turn, could improve the precision and accuracy of the RDTs, which could be of great benefit for locations where an exact knowledge of the transverse coupling or other RDTs is important. We present the development of a new method to reconstruct the particle’s momentum that uses a statistical analysis of several nearby BPMs. The improved precision is demonstrated via simulations of LHC and HL-LHC lattices.