Quasi-static thermoelastic analysis for a semi-infinite plane subjected to a Gaussian heat source: Beam missteering of the storage ring in the APS

A two-dimensional, semi-infinite analytical solution of the transient temperature and the thermal stress due to heating from the bending magnet beam missteering in the APS has been developed. In order to solve the thermal stress analytically, an effective absorption function is introduced, and the transient temperature can be written as a function of the exponential integrals. At the origin where the peak power is applied, the effective stress is found to be the maximum and is undergoing simple compression along the longitudinal direction. The result utilizing finite element method (FEM) applied to the chamber cross section is also presented and agrees fairly well with the current analytical solution during the early small time scale