Beam Finder Wire (BFW) devices will be installed at each break in the Undulator magnet line. These devices will scan small wires across the beam causing some electrons to lose energy through bremsstrahlung. The degraded electrons are subsequently detected downstream of a set of vertical dipole magnets after they pass through the vacuum chamber. This signal can then be used to accurately determine the beam position with respect to the BFW wire. The choice of the wire diameter, scan speed, and operating parameters, depends on the trade-off between the signal size and the radiation damage to the undulator magnets. In this note I estimate the rate of undulator magnet damage that results from scanning as a function of, wire size, scan speed, and average beam current. A separate analysis of the signal size was carried out by Wu [1]. Show Partial Abstract