Simulation Calculations and Analytical Predictions of Eigenmode Projection Parameters

Abstract

In the article, we carry out the element-by-element tracking simulations with the Relativistic Heavy Ion Collider (RHIC) Blue ring lattice to numerically calculate the eigenmode projection parameters. Eigenmode projection parameters are being measured and tested in RHIC for the possible future continuous global coupling measurement and correction. The simulation calculations and analytical predictions prove that the local eigenmode projection measurement does hint the global coupling coefficient, including its amplitude and phase. Therefore, to determine the global coupling, one observation point in the ring is sufficient. And comparisons between the simulation calculations and the analytical predications from different linear weak coupling approaches are also presented.