Head-tail modes in bunches with space charge are studied using particle tracking simulations. The eigenfrequencies and eigenfunctions of transverse coherent oscillations in a Gaussian bunch are determined and compared with theories. A model for an airbag distribution in a barrier potential gives good predictions for the head-tail spectrum and for eigenfunctions in bunches with space c... https://www.roneverhart.com/Modern-Rectangular-Keyed-Entry-Pocket-Door-Emtek-2113/