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.alarecre.com/Looney-Tunes-Marvin-the-Martian-Big-Head-Galaxy-S23-Waterproof-Case-p116784/