[en] Eddy currents are developed in the tuner of the Superconducting Super Collider Low Energy Booster (LEB) cavity during the LEB frequency sweep. The two main difficulties created by the eddy currents are excessive tuner-surface heating, and more important, a reduction in the time response of the tuner. We present a detailed analysis of the eddy currents for various tuner designs. The analysis has been done using 2D and 3D time-domain finite element codes (PE2D by Vector-Field and EMAS by MSC). Non-linear analysis was performed utilizing B-H curves. The codes have been benchmarked analytically and by using measured data for different slotted pillbox structures